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Logist. Res. (2011) 3:101–120 DOI 10.1007/s12159-011-0046-9 OR IGINAL PAPER A multi-agent and auction-based framework and approach for carrier collaboration Bo Dai Haoxun Chen Received: 3 September 2010 / Accepted: 17 January 2011 / Published online: 11 February 2011 Springer-Verlag 2011 Abstract Carrier collaboration in transportation means conflict resolution procedure is used to determine which multiple carriers form an alliance to optimize their trans- carrier wins it. The approach is decentralized, asynchro- portation operations through sharing transportation nous, and dynamic, where multiple auctions may occur requests and vehicle capacities. In this paper, we propose a simultaneously and interact with each other. The perfor- multi-agent and auction-based framework and approach for mance of the approach is evaluated by randomly generated carrier collaboration in less than truckload transportation. instances and compared with an individual planning In this framework, the carriers outsource/acquire requests approach and a centralized planning approach. through multiple auctions, one for outsourcing each request; a carrier acts as an auctioneer when it wants to Keywords Collaborative transportation planning outsource a request to other carriers, whereas the carrier Carrier collaboration Multi-agent systems Auction acts as a bidder when it wants to acquire a request from Outsourcing Pricing other carriers; for each carrier, which requests it should outsource and acquire are determined by solving its out- sourcing requests selection problem and requests bidding 1 Introduction problem, respectively. These two decision problems are formulated as mixed integer programming problems. The In collaborative logistics, multiple carriers or shippers may auction of each request is multiround; in each round, the form an alliance to optimize their transportation operations auctioneer determines the outsourcing price of the request by sharing vehicle capacities and delivery requests. The and each bidder determines whether it acquires the request objective of the collaboration is to reduce empty backhauls, at the given price; the auctioneer lowers the outsourcing to raise vehicle utilizations, and thus to increase the profit price if multiple carriers bid for the request or raises the of each carrier involved. In practice, two types of trans- price if no carrier bids for it. The auction process continues portation services are often provided: truckload (TL) until only one carrier bids for the request or a given number transportation and less than truckload (LTL) transportation. of rounds are achieved. In the second case, if no agent bids The two types have respective application domains and for the request, then it is returned to the outsourcing agent; advantages. TL is often used in the transportation of a if multiple bidding agents compete for the request, a single product of large quantity from a shipper to a cus- tomer, whereas LTL is usually used to transport one or multiple products in small volumes from multiple shippers B. Dai H. Chen (&) to multiple customers such as in parcel delivery. The main Laboratoire d’optimisation des Systemes Industriels (LOSI), advantage of LTL is that a shipment may be performed Institut Charles Delaunay (ICD) and UMR CNRS STMR 6279, with a fraction of the cost of hiring an entire vehicle or Universite de Technologie de Troyes, 12 rue Marie Curie, trailer for an exclusive shipment. A number of accessorial BP 2060, 10010 Troyes Cedex, France services are available for LTL, which are not typically e-mail: haoxun.chen@utt.fr offered by TL [25]. In case that customers demand frequent B. Dai deliveries in small quantities in order to reduce their e-mail: bo.dai@utt.fr 123 102 Logist. Res. (2011) 3:101–120 inventory costs, LTL shipment must be used by carriers to decentralized combinatorial auction model for the collab- increase their vehicle utilization rates. That is why LTL oration among independent freight forwarding entities. became more popular in recent years. Two types of col- Their collaboration model includes three phases: prepro- laboration are used. One is shipper collaboration, which cessing, profit optimization, and profit sharing. In the pre- focuses on the collaboration among multiple shippers processing phase, each carrier specifies its lowest cost for whose transportation requests are served by a single carrier. fulfillment of each request outsourced to its collaboration Through collaboration, the shippers may be able to identify partners. In the profit optimization phase, the outsourcing and submit routes with less asset reposition to the carrier requests are reallocated to the collaborating partners. In the for obtaining more favorable rates. The other is carrier profit sharing phase, the profit gained from the fulfillment collaboration that considers the reassignment of transpor- of each outsourcing request is allocated among the coali- tation requests among carriers in order to reduce their total tion members according to a collaboration advantage transportation costs for serving the requests. The cost index. Krajewska et al. [14] considered profit sharing in a savings as a result of the collaboration will be shared horizontal cooperation (collaboration) among freight car- among the carriers. Two key issues for carrier collaboration riers, with customer requests for each carrier as those of a are optimal reassignment of transportation requests among pickup and delivery problem with time windows. The profit carriers to maximize their total profit and fair allocation of margins resulting from the cooperation were analyzed, and the profit among the carriers. In this paper, we study carrier the possibilities of sharing these profit margins fairly collaboration in less than truckload transportation with among the carriers were discussed. The Shapley value in pickup and delivery requests and propose a multi-agent and cooperative game theory was used to determine a fair profit auction-based framework and approach for the problem. allocation. Berger and Bierwirth [3] utilized decentralized The literature relevant to our work is first reviewed in the control and auction-based exchange mechanisms for the following. request reassignment problem in collaborative carrier net- works. A five-step procedure was proposed for the request 1.1 Collaboration in transportation reassignment: forming a request candidate set, composition of bundles from the candidate set, determination of mar- Previous studies on collaborative transportation can be ginal profits, assignment of bundles to carriers, and profit classified into two categories according to whether the sharing. They compared their decentralized method with a considered transportation service is TL or LTL. For TL centralized method by numerical experiments. Their transportation, most papers adopt a centralized planning approach belongs to the category of single-round auctions. approach in which profit/cost allocation among collabora- Moreover, they ignored the vehicle capacity constraint by assuming that all shipments take only a very small fraction tive partners is a key issue. Ergun et al. [9, 10] studied shipper collaboration and formulated its centralized plan- of the capacity of a vehicle. ning problem as a lane covering problem; Houghtalen et al. [11] studied carrier collaboration and proposed a mecha- 1.2 Multi-agent systems in transportation nism for allocating both resources and profits among car- riers by appropriately setting prices for the resources. A system with multiple autonomous agents interacting with Kwon et al. [15] and Lee et al. [18] proposed a combina- each other is called a multi-agent system (MAS). It is a new torial auction mechanism for transportation procurement of paradigm for modeling and studying distributed systems. In a shipper from carriers. Agarwal and Ergun [1] considered an MAS, all agents are autonomous computational compo- carrier collaboration in a multicommodity service network nents that are able to control their own behaviors in the and designed a mechanism for allocating benefits among furtherance of their own goals [31]. They can cooperate, carriers based on a decentralized multicommodity flow coordinate, and negotiate with each other as human beings. game, capacity exchange costs, and inverse optimization. Davidsson et al. [8] provided a survey of existing research on For LTL transportation, Dai and Chen [6, 7] proposed a agent-based approaches for transportation and traffic man- centralized framework for the problem without time win- agement with the focus on freight transportation. They dows for pickup and delivery operations of requests, and concluded that agent-based approaches seem very suitable the global optimal transportation planning problem for the for this domain but need to be verified by more deployed carrier alliance was formulated as a mixed integer pro- systems. Lang et al. [16] gave a literature review on the gramming model. To solve the model, a Lagrangian application of MAS in logistics with the emphasis on the role relaxation approach and a revised benders decomposition of MAS coordination architectures. They concluded that approach were developed. The performances of the solu- planning problems in transportation have characteristics tion approaches were evaluated by randomly generated complying with the specific capabilities of agent systems instances. Krajewska and Kopfer [13] presented a and their capability of dealing with inter-organizational and 123 Logist. Res. (2011) 3:101–120 103 event-driven planning settings meets requirements in supply bundle of items it wants to get at the given prices. The chain planning and execution. auctioneer adapts the prices to balance the supply and For the application of MAS in collaborative logistics, demand [26]. Price-setting auctions and quantity-setting Mes and Van der Heijden [20] and Mes [21] used a multi- auctions are dual to each other. Price-setting auctions agent system to model a transportation marketplace, where correspond to the primal–dual algorithms of CAP. shippers offer time-sensitive full truckload pickup and Auctions were used in transportation planning early in delivery jobs through sequential auctions and carriers Wellman [29]. The author proposed a general ‘‘market- compete with each other to service these jobs. To cope with oriented programming’’ environment (approach) to the the interdependencies among jobs, they used reserve prices construction and analysis of distributed transportation and decommitment penalties and proposed two strategies planning systems, based on general equilibrium theory and for shippers to maximize their revenue in sequential auc- competitive mechanisms. The environment provides basic tions, namely delaying and breaking commitments. The constructs for defining computational market structures and idea of delaying commitments is that a shipper will not a procedure for deriving their corresponding competitive agree with the best bid whenever it is above a certain equilibria. Sandholm [22] presented a formalization of the reserve price. The idea of breaking commitments is that the bidding and awarding decision process for the contract net- shipper allows the carriers to break commitments against based task allocation. This formalization is based on mar- certain penalties. In this way, the pricing and scheduling ginal cost calculations based on local agent criteria. In the decisions of carriers can take into account both the direct proposed model, agents having very different local criteria costs of jobs and their impact on future opportunities [21]. (based on their self-interests) can interact with distribute tasks so that the network of the agents as a whole operates 1.3 Auctions in transportation more effectively. The contract net protocol was verified by transportation cooperation net, where dispatch centers of An auction is a protocol that allows agents to indicate their different companies cooperated automatically in vehicle interests in one or more resources and that uses these routing. Bu ¨ rckert et al. [5] described a multi-agent dis- indications of interest to determine both an allocation of patching system developed in cooperation with a for- resources and an allocation of payments among the agents. warding company. The system can deal with dynamical In the literature, different types of auctions were proposed, arrival of transportation requests. The novelty of the system which include single-good auctions, multiunit auctions, is that it uses holonic agents, which are composed of combinatorial auctions, and exchanges [24]. As an impor- subagents that interact in a cooperative way. tant category of auction, exchanges signify that agents are Combinatorial auction has been applied to truckload transportation service procurement. Kwon et al. [15] pro- able to act both as buyers and sellers. One important type of auction in exchanges is called two-sided auction or posed an integrated multiround combinatorial auction double auction. A double auction is associated with a mechanism, where shippers allow bids on packages of single-dimensional double market, where multiple poten- lanes (requests). In each round, each carrier must solve a tial buyers and sellers of multiple units of the same good bid generation problem (BDP, [18] to discover the most exist. The double auctions are further classified into two profitable bundle of lanes that maximizes its profit, and the types, continuous double auction (CDA) and periodic auctioneer must solve a winner determination problem double auction (call market). In combinatorial auctions, (WDP) to assign bundles of lanes to carriers. The price each bidder may bid not only for a (single) combination of information derived from the solution of WDP in each items but also for any subset of all combinations of items. round is used by bidders to identify the most profitable The combinatorial auction problem (CAP) that determines requests in next round. The mechanism integrates the the winners of the bids is usually formulated as a NP-hard shipper and bidder optimizations. The numerical results set packing problem (SPP). Two kinds of combinatorial indicate that better allocations are obtained for both ship- auctions are studied in this literature: single-round auction pers and carriers, i.e., shippers reduce costs of procurement and multirounds auction (iterative auction). The multi- of services and carriers are able to identify alternative rounds auction has several advantages over the single- valuable packages of lanes. However, BDP is a non-linear round auction [15, 27]. Iterative auctions have two types of integer programming problem and WDP is a 0–1 integer modes: quantity-setting auctions and price-setting auctions. programming problem, both of them are very hard to solve In each round of a quantity-setting auction, bidders send for large instances. their valuations over the items they want to buy. The For combinatorial auctions applied to carrier collabo- auctioneer makes a provisional allocation that depends on ration in LTL transportation, Schwind et al. [23] designed a the submitted prices, and bidders adjust the prices. In each combinatorial exchange mechanism ComEx for the inter- round of a price-setting auction, each bidder submits a division exchange of delivery orders in a logistics company 123 104 Logist. Res. (2011) 3:101–120 organized in a profit center structure. The exchange winner determination problem by the auctioneer. The mechanism is subdivided into four phases: initialization price-setting-based auction can avoid the two difficulties, phase, outsourcing phase, insourcing phase, and final which is adopted in our framework. evaluation phase. The outsourcing phase and the insourcing In our framework, each carrier is regarded as an phase determine, respectively, the delivery orders to be autonomous agent, and the collaboration among carriers is outsourced to other profit centers and the delivery orders to realized by auction. As a self-governed agent, it determines be acquired from other profit centers. In the final evaluation its requests to be outsourced to other carriers and set the phase, a combinatorial auction is performed by finding the price for each outsourcing request in each iteration of the cost-minimal allocation of order clusters to the profit cen- auction. The auction of each outsourcing request organized ters. To further reduce the delivery costs of the entire by an agent belongs to the category of exchange or double logistics company, an iterative auction mechanism is also auction, in which each agent acts both as an auctioneer and proposed. Their numerical experiments demonstrate that as a bidder. For an outsourcing request, its auction process using ComEx, the total transportation cost of the logistics starts when the offering agent acts as an auctioneer who company can be reduced by up to 14%. announces the outsourcing of the request with its initial In addition, Wellman et al. [30] studied auction proto- outsourcing price. Each of the other agents then acts as a cols for a decentralized scheduling problem. They inves- bidder and expresses its attitude to this request (bid or not tigated the existence of equilibrium prices for some general for the request). If the auctioneer does not receive any bid classes of scheduling problems, the quality of equilibrium after a given time period corresponding to a round of solutions, and the behavior of an ascending auction auction, that is, no bidder is willing to acquire the request, mechanism and bidding protocol. Each task in the sched- the auctioneer will increase the outsourcing price. Other- uling problem corresponds to an ascending auction. All wise, if more than one agents bid for the request, the auctions involved are performed asynchronously. Walsh auctioneer may lower the price. The price update is similar and Wellman [28] studied the supply chain formation to what in some well-known single-good auctions. There problem. A market price system about the resources pro- are two stopping conditions for terminating the auction duced along the chain is introduced to decentralize the process: only one agent bids for the request or a given formation process. In a competitive equilibrium of this number of rounds are achieved. In the former case, the system, agents select local optimal allocations based on request will be allocated to the unique bidder. The latter prices, leading to a globally optimal allocation. A market case indicates that no agent is interested in the request or protocol based on distributed, progressive auctions, and multiple agents compete for the same request. In the sec- myopic, non-strategic agent bidding policies is used to ond situation, a conflict resolution procedure will be used to assign the request to one of the bidding agents. The determine prices. The price of each resource is determined by an ascending auction similar to what used in Wellman framework is decentralized, asynchronous, and dynamic, et al. [30]. The protocol produced better solutions than the where multiple auctions may occur simultaneously and greedy protocols common under resource contention. interact with each other. In the framework, two decision In this study, we choose MAS and auction as two major problems for each carrier are the outsourcing requests components of our approach because: (1) Each carrier in selection problem that determines non-profitable requests carrier collaboration is an autonomous unit with its own to be outsourced and the requests bidding problem that private information and decision-making authority; (2) As determines requests to be acquired from other carriers. pointed out by Lang et al. [16], transportation firms engage Mixed integer programming models are provided for the in a high level of negotiation and cooperation in perform- two problems. ing their daily transport tasks, and MAS can model such The previous studies relevant to ours are Mes and Van cooperative capabilities; and (3) It is in the nature of der Heijden [20], Mes [21], Wellman et al. [30], and Walsh auctions to address the reassignment of transportation and Wellman [28]. Compared with sequential auctions for requests and the allocation of the profit gained by carrier truckload pickup and delivery jobs proposed in Mes and collaboration simultaneously. Instead of designing a post- Van der Heijden [20] and Mes [21], our proposed auction is collaboration profit allocation mechanism, we propose a not sequential but asynchronous. In our auction, each agent multi-agent and auction-based collaboration framework (carrier) may engage in multiple auctions at the same time. whose profit allocation among carriers is determined by the Moreover, in their auctions, the interdependencies among auction process of each request. So far, most studies using jobs (objects) are coped by using reserve prices and de- combinatorial auction for carrier collaboration adopted a commitment penalties, whereas our auction takes into single-round auction, which requires preselection of pref- account such interdependencies by considering all open erable bundles of requests from an exponential number of auctions in outsourcing requests selection problem and bundles by each carrier and the resolution of a NP-hard requests bidding problem of each carrier (bidder as well as 123 Logist. Res. (2011) 3:101–120 105 auctioneer). Finally, our auction is applied to carrier col- preferable bundle from an exponential number of bundles laboration in less than truck load transportation rather than nor needs to determine a price for each bundle. The per- shippers–carriers collaboration in full truck load transpor- formance of the proposed framework and approach is tation dealt with their auctions. Both our proposed auction evaluated by simulation and is compared with the case of and the auctions proposed in Wellman et al. [30] and no collaboration among agents and with a centralized Walsh and Wellman [28] run asynchronously without framework and approach. The simulation results show that direct coordination. However, our auction distinguishes by reducing transportation costs, our proposed decentral- from theirs with the following three aspects: (1) Our auc- ized collaboration mechanism can increase the total profit tion permits the ascending and descending of the price of of all carriers as well as each agent’s individual profit. each object (request), whereas theirs only allow the The rest of this paper is organized as follows. Section 2 ascending of the price of each object; (2) In our auction, describes the carrier collaboration problem studied and each bidder only determines whether to acquire a request Sect. 3 outlines our multi-agent and auction-based frame- (object) at its price currently announced by the corre- work. Section 4 formulates the outsourcing requests sponding auctioneer, whereas each bidder in their auctions selection problem, which includes a method for setting an has to determine the bidding price for each bid in each initial outsourcing price for each outsourcing request. round; (3) Our auction is applied to carrier collaboration in Section 5 introduces the requests bidding problem. Sec- collaborative logistics, whereas theirs are applied to tion 6 presents the asynchronous multi-agent multi-auction decentralized scheduling and supply chain formation, process. Section 7 evaluates our proposed framework and respectively. In addition, our proposed approach is quite approach by simulation and compares it with a centralized different from that proposed by Berger and Bierwirth [3]. framework and approach, where random instances are The former is an asynchronous multiround (iteration) generated for the evaluation and comparison. Section 8 auction approach in which multiple auctions may occur concludes this paper by some remarks on future research. simultaneously and each carrier may act both as an auc- tioneer and as a bidder, whereas the latter is a (synchro- nous) single-round combinatorial auction approach in 2 Problem description which only one auction is performed (with a single auc- tioneer). The advantages of our price-based iterative auc- In this paper, we study a carrier collaboration problem in tion approach beyond their approach are that our approach less than truckload transportation with pickup and delivery neither needs to select a set of preferable bundles of requests (CCPLTL). One application of such problem is requests from an exponential number of bundles of requests parcel delivery. To be general, we do not specify particular product types to transport in this problem. for each bidder (carrier) nor needs to solve a NP-hard combinatorial auction problem (CAP) to determine the In the problem, multiple carriers with a depot and a assignment of bundles to carriers. Besides, our problem and limited number of capacitated vehicles operate in a com- their problem have different settings; for instance, the mon transportation network. Initially, each carrier has capacity of each vehicle is ignored in their problem by collected certain transportation requests from its customers assuming that the shipments take only a very small fraction (shippers) with a price for serving each request paid by a of its capacity, whereas we do consider the vehicle customer to the carrier (a request collected by a carrier capacity. from its shipper is also called a request of the carrier The novelty and contribution of our work are mainly in hereafter). Each request is specified by a pickup location four aspects: (1) In our multi-agent and auction-based and time window, a quantity, and a delivery location and framework, each carrier keeps its decision autonomy, no time window. To increase vehicle utilization rates and central coordinator (auctioneer) is required, and all the reduce empty backhauls, all carriers form a collaborative auctions operate asynchronously and are driven by indi- alliance that shares vehicle capacities among them. For vidual agents; (2) No private information is shared among each carrier, its collected requests are not always profitable, agents, and the framework is entirely decentralized; (3) it may outsource non-profitable requests to other carriers in The decentralized decision making in the framework can the alliance, and all outsourcing requests are available to all reduce computational complexity and is thus well suitable carriers. If a request is not served by its offering carrier, for dynamic collaboration environments where transporta- then the offering carrier gains the difference between the tion requests of each carrier arrive dynamically, the exe- price paid by its customer for serving the request and the cutions of the requests finish dynamically, and the outsourcing price of the request determined by the carrier. availability of resources of each carrier changes dynami- It is assumed that each carrier wants to assure a ‘‘min- cally. (4) Through employing price-setting-based auctions imum profit margin’’ [12]. The minimum profit margin of a in our framework, each carrier neither needs to select its carrier represents its profitability expectation. The higher 123 106 Logist. Res. (2011) 3:101–120 the expectation, the larger the minimum profit margin. length of each arc in the transportation network; the Different carriers may have different minimum profit number of vehicles of each carrier; the capacity of every margins. In our problem, the profit of the carrier is defined vehicle of each carrier; the depot node of each carrier; the as its transportation revenue minus its transportation cost. transportation cost between any two nodes for every The minimum profit margin plays an important role in vehicle of each carrier; the set of requests collected by each determining whether the carrier will serve a request carrier from its shippers; the price paid by shippers to demanded by a shipper, whether it will outsource a request carriers to serve each request, pickup node, delivery node, to other carriers, and what should be the outsourcing price quantity, pickup time window, and delivery time window of the request. One important decision problem for a carrier of each request; the minimum profit margin of each carrier. is to set its minimum profit margin. If the carrier accepts all The decision variables of the problem for each carrier requests that are profitable, its minimum profit margin is include: the set of requests served by itself, the set of set to zero. Otherwise, if the carrier accepts only high requests to be acquired from other carriers and served by profitable requests, its minimum profit margin should be set itself, a set of vehicle tours to serve the two sets of requests, to a large percentage. According to an investigation of the outsourcing price and the winner of each request out- Holguı ´n-Veras et al. [12], the profit of a carrier is deter- sourced by the carrier. mined by its direct costs and the profit margin it selects. A To better understand CCPLTL described above, we minimum value of the profit margin of 5% was assumed as design an illustrative example that has a transportation the opportunity cost of the capital. For this reason, most network with 21 nodes, three carriers a, b, c with nodes 5, carriers chose 5% as their minimum profit margin in order 17, 11 as their depots, respectively. Each carrier has 10 to win a bid, which is what economic theory would predict vehicles with the same capacity C = 10. The transportation in a competitive market, i.e., rates set at marginal costs. Of network is given in Fig. 1. The total number of transpor- course, in reality, each carrier can freely set its minimum tation requests of the carriers is nine; the requests are profit margin according to its own profitability expectation. represented by r1to r9, respectively. For each request, its In our study, we assume that the minimum profit margin of quantity is indicated by a number associated with the arc each carrier is given. representing the request. For example, request r1 is to pick In the studied carrier collaboration problem, the objec- up five quantity of freight at node 21 and deliver this tive of each carrier is to maximize its own profit, while the quantity to node 13. Carrier a has requests r1, r2, r3, carrier collaboration among carriers is achieved by exchanging b has requests r4, r5, r6, and carrier c has requests r7, r8, transportation requests among them. The profit is obtained r9. The coordinates of each node in the transportation by subtracting the total transportation cost from the total network is given in Table 1, and the time windows and the revenue for serving the requests. A solution of the problem price paid by a shipper for serving each request are given in is given by a set of requests to be served by each carrier, a Table 2. The time window of each depot node is [0, 240]. set of optimal vehicle tours for the carrier to serve the set of requests, and the outsourcing price of each request out- sourced by each carrier to other carriers. Note that the set 3 Multi-agent and auction-based framework of requests to be served by a carrier includes the requests it collects from its shippers and serves by itself and the Motivated by multi-agent system models applied to requests it acquires from other carriers. Multiple requests scheduling problems [2] and the combinatorial auction may be served by the same vehicle tour. For each carrier, mechanism proposed for truckload transportation service its feasible transportation plan is defined by a set of vehicle procurement [15, 18], we propose a multi-agent and auc- tours; each vehicle tour leaves from and returns to its tion-based framework for CCPLTL. In the framework, depot; the load of each vehicle does not exceed its each carrier is an autonomous agent with decision author- capacity; for each request served, its pickup operation is ity, and the interactions between carriers are realized performed before its delivery operation; and each pickup through multiple auction processes of outsourcing requests. or delivery operation is performed within the time window. Since each carrier both outsources (sells) and acquires In the problem, the transportation network considered is (buys) requests, it acts both as an auctioneer and as a bidder represented by a directed graph D = (N, A) with node set in auction terms. N and arc set A. Each arc is associated with a traveling time For each request that is outsourced by an agent (carrier), which is the length of the arc, which may be different for its auction process starts when the agent announces the different carriers. So different carriers may have different outsourcing of the request together with its initial out- transportation costs associated with each arc. Other sourcing price, where the agent is an auctioneer. After the parameters of the problem include the following: the auction is started, if the auctioneer does not receive any number of carriers; the coordinates of each node and the reply for the request from a bidder (carrier) for a given time 123 Logist. Res. (2011) 3:101–120 107 Fig. 1 Transportation network of the illustrative example Table 1 Coordinates of the nodes in the transportation network Node 1 2 3 4 5 6 7 8 9 10 11 X 35 41 35 55 55 15 25 20 10 55 30 Y 35 49 17 45 20 30 30 50 43 60 60 Node 12 13 14 15 16 17 18 19 20 21 X 20 50 30 15 30 10 5 20 15 45 Y 65 35 25 10 5 20 30 40 60 65 Table 2 Time windows, quantity, and service price of the requests Request 1 2 3 4 5 6 7 8 9 Pickup node 21 20 15 18 4 8 16 7 12 Delivery node 13 9 14 19 10 3 1 6 2 Pickup time window [97,122] [109,147] [112,144] [123,161] [91,144] [127,172] [129,173] [159,188] [68,127] Delivery time window [139,193] [115,130] [120,141] [166,221] [106,130] [168,195] [127,182] [162,193] [99,140] Quantity 5 2 8 10 2 5 10 3 5 Service price 129 70 197 127 63 115 259 52 62 period determined by the auctioneer, the bidder is consid- request at the end of the auction. In the latter case, a ered not willing to acquire the request. After the given time conflict resolution procedure, which will be introduced in Sect. 6, is used to determine who wins the request. The is elapsed for the request, the auctioneer can lower the outsourcing price if more than one agents bid for the interactions among multiple agents are illustrated in Fig. 2. request or raise the price if no agent bids for the request. The proposed framework (multi-agent system) is The price update is similar to what in some well-known decentralized, asynchronous, iterative, and dynamic. Here, single-good auctions, which will be introduced in Sect. 6. ‘‘decentralized’’ means that each agent makes its own The process continues until one of two stopping conditions decision; ‘‘asynchronous’’ means all auction processes is satisfied: only one agent bids for the request or a given happened are asynchronous, there is no order among out- number of iterations are achieved. If the process is termi- sourcing requests selection, bid generation, and price nated by the second condition, either no agent wants to adjustment of different carriers, and the only relationship acquire the request or multiple agents compete for the same among the carriers is the exchange of information on 123 108 Logist. Res. (2011) 3:101–120 Fig. 2 The interactions among multiple agents requests outsourcing and acquisition among them; ‘‘itera- (updated) by the agent during the auction process of the tive’’ means that the auction process of each outsourcing request. When an agent selects a set of requests to be request is a multirounds iterative process; and ‘‘dynamic’’ outsourced, it must consider its uncompleted requests that means that the multi-agent system is a dynamic system, are collected from its shippers (self-executed requests with new requests arrive dynamically, the execution of requests state before execution or in execution), already acquired finishes dynamically, and the availability of resources other agents’ outsourcing requests that have not been (vehicles) of each carrier may change dynamically, etc. completed (outsourcing requests with state before execu- The dynamic behavior of the multi-agent system can be tion or in execution), and probably, the requests in the described by the evolution of its state over time. The state current outsourcing request pool if the agent determines its of the system consists of the states of all carriers. The state requests outsourcing and acquisition jointly. A request can of a carrier is represented by the states of all requests be outsourced only if it is at the state of before execution. concerning the carrier and the states of the resources Each agent also determines the requests acquired from (vehicles) of the carrier. For a self-executed request, it has other agents. A request can be acquired by an agent only if it is an outsourcing request at the state of in auction. When three possible states: before execution, in execution, and executed. On the other hand, for an outsourcing request, it an agent acts as an auctioneer and announces the auction of has five possible states: before auction, in auction, auc- an outsourcing request, each of the other agents, which is a tioned (auction is completed), in execution, and executed. bidder, can reply to this outsourcing announcement by For each outsourcing request, which agent (carrier) will choosing whether it acquires (bids for) the request or not. execute, it is determined as soon as its auction process is When an agent chooses to acquire a set of outsourcing finished. Such request is executable only when its auction requests, it must consider its uncompleted requests that are process is completed. An outsourcing request pool is collected from its shippers (self-executed requests with introduced in our framework to gather all outsourcing state before execution or in execution), already acquired requests that are announced by all agents and are currently other agents’ outsourcing requests that have not been in auction. All requests in the pool are available to each completed (outsourcing requests with state before execu- agent. In the framework, except for the price adjustment tion or in execution) and the requests in the outsourcing (update) of outsourcing requests by agents, two decision request pool. Once an agent is awarded an outsourcing problems for each carrier are involved: one is to determine request, this allocation is irreversible in later rounds. non-profitable requests to be outsourced and the other is to Compared with other auction-based frameworks previ- determine requests to be acquired from other carriers. ously proposed for the carrier collaboration, our proposed These two decision problems are referred to as outsourcing framework has several new features and advantages: (1) requests selection problem (ORSP) and requests bidding Each carrier is totally autonomous, which makes its own problem (RBP), respectively, hereafter. decisions, there is no central auctioneer (coordinator) that When an agent has chosen to outsource a request, the makes decisions on behalf of the carriers; each carrier can agent must determine at the same time an initial out- play both the role of an auctioneer and the role of a bidder; sourcing price for the request. The price will be adjusted (2) The price paid by a shipper to a carrier for serving a 123 Logist. Res. (2011) 3:101–120 109 request is private information reserved only by the carrier R the set of requests acquired by the carrier from and not disclosed to other carriers; (3) In our price-setting other carriers and at the state of before execution framework, each carrier does not need to select its pref- P the set of requests whose pickup location is erable bundle from an exponential number of bundles (2 node i, P R [ R i a b for n requests). What each carrier should do is to determine D the set of requests whose delivery location is a set of requests to be outsourced by solving an outsourcing node i, D R [ R i a b requests selection problem and a set of requests to bid by d pickup and delivery quantity of request l, solving a requests bidding problem based on the current l 2 R [ R a b price of each request. They do not need to determine a a the minimum profit margin that the carrier price for executing a bundle of requests; (4) In our wants to earn for serving a request framework, carriers act as both buyer and seller and the p price paid by a shipper to serve request l, price of each resource (request) is determined (adjusted) by l 2 R its demand and supply as in a market economy, and the p the willingness-to-pay of the carrier for prices may be increased and decreased according to the request l, l 2 R , p ¼ p a p a l l l bidders’ attitudes. p the outsourcing price of request l set by other carriers, which is the revenue obtained by the carrier to serve request l, l 2 R 4 Outsourcing requests selection problem p the willingness-to-pay of the carrier for o o o request l, l 2 R , p ¼ p a p l l l To initiate an auction-based collaboration process among W the number of vehicles of the carrier carriers, each carrier must select a set of requests to be C vehicle capacity of the carrier outsourced from its own requests. Our requests outsourcing o the depot node of the carrier model for each carrier is based on the idea of minimum c transportation cost from node i to j for each ij profit margin as explained in Sect. 2. For a carrier con- vehicle of the carrier, where c = c and the ij ji sidered, suppose that its minimum profit margin is a triangle inequality c ? c C c , holds for im mj ij (0 \ a \ 1). For a request l of the carrier, let p denotes the any i, j, m with m = i, m = j price paid by a shipper to the carrier for serving request l, s the traveling time from node i to node j for ij that is, p is the revenue obtained by the carrier if it serves each vehicle of the carrier the request. Since the carrier wants to achieve a minimum a the earliest pickup/delivery time at node i profit margin a, its least profit to gain by serving the b the latest pickup/delivery time at node i request is ap . Let p = p - ap , then p can be interpreted l l l l l T a large number, T = b - a ij ij j i as the maximum amount that the carrier is willing to pay Note that each time window is usually associated with for serving the request or willingness-to-pay for short. the pickup or delivery operation of a request; in this paper, Based on this observation, we can formulate the out- we consider the situation where each node involves at most sourcing requests selection problem for each agent as a one request, that is, the node is either the pickup location or mixed integer programming, in which the total revenue the delivery location of a single request. For the situation term in its objective function is replaced by the total where some nodes involve multiple requests, we can maximal expenditure term. The notations used in the model replace each of the nodes by a number of duplicate nodes are given as follows. where each duplicate node involves a single request, and the transportation costs among these duplicate nodes are set Indices to zero. In this way, we can assume that each node in the transportation network involves only one request. i, j, m: node index, where i, j, m = 1,…,N and N represents the number of nodes in the Variables transportation network. The nodes include all q quantity of freight transported through arc (i, j) ij pickup and delivery locations and all vehicle x the number of times that arc (i, j) is visited by ij depots of the carriers vehicles of the carrier l: request index y binary variable, y = 1 if request l 2 R is served l l a by the carrier itself, y = 0 otherwise; y = 1if l l Parameters request l 2 R the set of requests collected by the carrier from t the time at which a vehicle of the carrier leaves a i its shippers and at the state of before execution node i. Since only one request involves the node, 123 110 Logist. Res. (2011) 3:101–120 conservation equations, assuring the flow balance at each which implies that only one vehicle visits the node (except for the depot node). Constraints (5)and (6)are node, t is well defined the flow conservation equations at the depot node, which With the notations, the mixed integer programming model insure that only empty vehicle is returned to the depot. of the outsourcing requests selection problem (ORSP) for Constraints (7) guarantee that the number of vehicles used by the carrier is given as (1–13). Model ORSP: the carrier is at most equal to W. Constraints (8) ensures that N N X X X X each customer node is visited at most once by vehicles of the Z ¼ Max p y þ p c x ð1Þ l l ij ij l carrier. Constraints (9) indicate the relationship between l2R l2R i¼1 j¼1;j6¼i a b the departure times of a vehicle from any two nodes. The constraints also assure that each vehicle of the carrier starts Subject to: with and ends at its depot. Constraints (13) are the time N N X X window constraints for pickup/delivery operations at all x ¼ x ; i ¼ 1; ...; N; ð2Þ ij ji nodes. Note that the objective function (1) of model ORSP is j¼1;j6¼i j¼1;j6¼i not the profit of the carrier, it is the part of the profit P P q C x ; i; j ¼ 1; ...; N ; i 6¼ j; ð3Þ ij ij exceeding the expected profit p y a þ p a. l l l2R l2R l a b N N That is, when we calculate the profit of the carrier from the X X X X q q ¼ d y d y ; ij ji l l l l objective function value of the model, we should add the ð4Þ j¼1;j6¼i j¼1;j6¼i l2P l2D i i expected profit to the value. That is why we call the objective i ¼ 1; ...; N; i 6¼ o; function the surplus profit of the carrier. The objective of the N problem is to maximize the surplus profit. X X X q ¼ d y d y ; ð5Þ Note that in the aforementioned model, we assume each oj l l l l j¼1;j6¼o l2P l2D o o carrier cannot outsource the requests acquired from other carriers, but it may outsource any request collected from its q ¼ 0; ð6Þ shippers with the state of before execution, i.e., it may jo j¼1;j6¼o choose to outsource an unexecuted request of its shippers later even if the request is chosen as a self-execution x W ; ð7Þ request currently. Each carrier solves its ORSP when it oj j¼1 receives new requests from its shippers or it acquires requests from other carriers. Furthermore, a solution of the aforementioned model does not directly provide vehicle x 1; i ¼ 1; ...; N; i 6¼ o; ð8Þ ij j¼1;j6¼i tours for fulfilling all selected requests (requests with y = 1), but the vehicle tours can be constructed easily t t þ s x T ð1 x Þ; i; j ¼ 1; ...; N; j i ij ij ij ij ð9Þ from the solution since each node except for the depot node j 6¼ o; i 6¼ j; is visited at most once by a vehicle of the carrier. x 0; x 2 Z; i; j ¼ 1; ...; N; i 6¼ j; ð10Þ ij ij Initial outsourcing price setting for outsourcing y 2f0; 1g; l 2 R and y ¼ 1; l 2 R ; ð11Þ l a l b requests of each carrier q 0; q 2 R; i; j ¼ 1; ...; N; i 6¼ j; ð12Þ ij ij After the outsourcing requests selection process, each 0 a t b ; i ¼ 1; ...; N; ð13Þ i i i carrier must set an initial outsourcing price for each of its The objective function (1) represents the surplus profit of outsourcing requests. Since the objective function (1)of model ORSP can be interpreted as the profit surplus gained the carrier obtained from serving requests, which includes three terms. The first term denotes the maximal expenditure by the carrier for serving requests, the carrier naturally wants to maximize the profit surplus. If in an optimal of the carrier for fulfilling the requests collected from its shippers and selected (accepted) by it; the second term is a solution of the model, y = 1, l 2 R implies that serving constant term representing the maximal expenditure of the request l can increase the profit surplus; otherwise y = 0, carrier for fulfilling its acquired outsourcing requests; the l 2 R implies that serving request l will decrease the profit third term represents the total transportation cost of the surplus. So the request l should be outsourced to other carrier for fulfilling the above-mentioned two sets of carriers. In this case, since serving request l by the carrier requests. Constraints (2) ensure that the number of vehicles itself cannot achieve the expected profit ap , the initial leaving from a node (including the depot node) is equal to the outsourcing price of the request l, denoted by p , should be number of vehicles arriving at the node. Constraints (3)are set to in the interval [0, p ], where p ¼ p ðÞ 1 a . Thus, l l l the vehicle capacity constraints. Constraints (4) are the flow the carrier can gain at least the expected (minimal) profit 123 Logist. Res. (2011) 3:101–120 111 for request l if there is another carrier who accepts the y ¼ 1; l 2 R and y 2f0; 1g; l 2 R ; ð15Þ l a l b outsourcing price for serving the request. According to this The objective function (14) represents the surplus profit outsourcing price-setting method, the higher the minimum of the carrier obtained from serving requests, which profit margin of the carrier, the lower the initial outsourc- includes four terms. The first and second terms are ing price of the request. constant terms representing the maximal expenditure of the carrier for fulfilling the requests collected from its shippers and the requests acquired from other carriers, 5 Requests bidding problem respectively; the third term represents the willingness-to- pay of the carrier for its bidding outsourcing requests; the In our proposed multi-agent and auction-based framework, fourth term represents the total transportation cost of the once the outsourcing requests are selected and priced by carrier for fulfilling the above-mentioned three sets of each agent, they will be added to an outsourcing request requests. The meanings of constraints (2–10), (12), and pool that gathers all outsourcing requests. All the requests (13) are the same as those of model ORSP. Note that for are available to every agent. Each carrier can then deter- each carrier, its requests bidding problem considers its mine whether it bids some requests in the pool as long as resources (vehicles) and its currently acquired requests at it is not empty, this decision problem is referred to as the the same time. Similar to model ORSP, the objective requests bidding problem (RBP) or the requests acquisi- function (14) of model RBP is not the profit of the carrier, tion problem that is formulated as a mixed integer pro- but it is the part of the profit exceeding the expected profit gramming (MIP) model in this section, which is similar P P P o o p a þ p a þ p y a: l l l2R l2R l l2R l to that of ORSP. The only difference between the two as ac b models is that some notations (parameters and variables) have different meanings. The notations with different 6 Multiple asynchronous auction processes meanings and used in the model of RBP are given as follows. In the multi-agent and auction-based framework, multiple Parameters auction processes of multiple outsourcing requests can happen at the same time. These processes progress asyn- R the set of requests accepted by the carrier for its chronously and interact with each other through requests self-execution at the state of before execution outsourcing/acquisition and the adjustment of the out- R the set of requests collected from shippers and as sourcing prices by the carriers. The processes have three accepted by the carrier for its self-execution at important features: (1) Each auction process is request the state of before execution oriented rather than agent oriented, that is, each auction R the set of requests acquired from other carriers ac process corresponds to a request; (2) Each auction process and accepted by the carrier for its self- involves multiple agents (carriers); and (3) The interaction execution at the state of before execution; of multiple auction processes (corresponding to multiple obviously, R ¼ R [ R a as ac requests) and its impact on the behaviors of the agents are R the set of requests outsourced by other carriers realized by the resource (vehicle) requirements (occupa- and at the state of in auction tion) of these requests, because if an agent bids for a request, it may not able to bid for another request as the Variables fulfillment of the former request will occupy some resource y binary variable, y = 1 if request l 2 R ; y = 1if l l a l (vehicle) of the agent. In our framework, each auction is a l 2 R is selected to be acquired by the carrier, double auction [24]; each agent plays two roles, one is y = 0 otherwise auctioneer and the other is bidder. When an agent has chosen to outsource a request by solving an outsourcing With the above-mentioned notations and other notations requests selection problem described by model ORSP, it introduced in Sect. 4, the mixed integer programming will act as an auctioneer and initiate the auction of the model of RBP is given as (14)–(15). request; each of the other agents, which acts as a bidder, Model RBP: determines whether to bid for the request by solving a N N X X X X X I o o requests bidding problem described by model RBP. During Z ¼ Max p þ p þ p y c x l l ij ij l l the auction of a request, when the situation of a bidder is l2R l2R l2R i¼1 as ac b j¼1;j6¼i changed because it receives new requests from its shippers ð14Þ or its environment is changed because other agents Subject to constraints (2–10), (12), (13), and announce the auction of new requests or the outsourcing 123 112 Logist. Res. (2011) 3:101–120 prices of the requests in auction are updated, the bidder can parameter d for the price update halved, i.e., set d to d/2. change its bidding decision on the request made in a pre- Note that since an agent may engage in multiple auctions at vious round and determine whether it stays in, drops from, the same time, any request acquired by the agent from an or resubmits a bid in the current round of the auction. For auction may influence acquisition choices of the agent in this reason, each agent solves its ORSP and RBP every other auctions. So even for the same outsourcing request, a time when its situation is changed. In the following, we bidding agent may take different acquisition decisions at introduce in detail the auction for an outsourcing request, different moments. including iterative nature of the auction process, out- The auction process is iteratively conducted by the sourcing price adjustment in the process, and conflict res- auctioneer until one of the following two stopping condi- olution in assigning it to an agent. tions is satisfied: (1) Only one agent bids for request l and Given an outsourcing request l from the outsourcing the request is allocated to the agent; (2) A given number of request pool, its initial outsourcing price, its auction start- rounds is achieved or d is small than a given number, if no ing time t , and a fixed time period T are set by the out- agent bids for request l even with the price p , then it is l l l sourcing agent (auctioneer), the auction of request l is returned to the outsourcing agent; if multiple bidding initiated by the auctioneer at time t and advances in an agents compete for request l, a conflict resolution proce- iterative way. At the end of each round when T is elapsed, dure is employed to determine which agent wins the the auctioneer may face three situations for determining request. The procedure allocates the request to the bidding which agent request l should be allocated to. agent who announces its bid earlier than others. Once an Situation 1: no agent bids for request l. In this situation, agent is awarded request l, this allocation is irreversible the auctioneer increases the outsourcing price of the and the auction is terminated. request to attract more agents’ interests in the request and restart another round of the auction. The new price should be adjusted in the interval [0, p ], which has been explained 7 Simulation evaluation and comparison in Sect. 4. The agent can increase the price in a regular fashion, which is similar to what in a well-known single- To evaluate the performance of our multi-agent and auc- good auction named Japanese auction [19], where the price tion-based framework for carrier collaboration, we com- is successively raised. The price update rule increases the pare it with a centralized framework (introduced in the price by a fixed small amount d from the current price, ‘‘Appendix’’) proposed in the literature and the case of which is introduced by Lavi and Nisan [17]. More recently, no collaboration among carriers by simulation. Twenty Biswas and Narahari [4] applied this rule in developing instances are randomly generated and simulated to evaluate efficient iterative auction mechanisms for combinatorial the effectiveness of our proposed framework and approach. exchanges. Their numerical experiments show that the choice of different d leads to different results. In their 7.1 Simulation design study, the value of various bidding and asking prices lies in the intervals [0, 1]. Accordingly, in this paper, we set d ¼ l In the simulation, we consider the following situation: all 0 o q p for request l, where p is the outsourcing price of this requests from different carriers are served on the same day, l l request and q is an adjustable parameter between 0 and 1. and they are not executed in advance until the collaborative Situation 2: only one agent bids for request l. Thus, the transportation planning among all carriers is done. For request is allocated to the bidding agent. simplicity, for each carrier, the time period for each round Situation 3: more than one agent bids for request l. Then of auction is the same for all its outsourcing requests and the auctioneer decreases the outsourcing price of request l. all these requests with state before auction are auctioned The price decrease can employ a regular fashion similar to simultaneously. However, different carriers may start their what in a well-known single-good auction named Dutch auctions at different times. For the first ten instances, each auction [19], where the price is successively lowered in the carrier has three requests and no other requests arrive interval [0, p ] by applying the same rule as proposed in l during its auction processes, which means its outsourcing Situation 1 with the same parameter d. requests selection is performed only at the beginning; During the auction, the outsourcing price increases if whereas for the second ten instances, each carrier only has Situation 1 appears and the outsourcing price decreases if two requests initially and the third request arrives at a Situation 3 appears. If at the end of a round, the situation of random time in the auction processes. During the auction the auction is changed from 1 to 3 or from 3 to 1, the processes, each agent will not consider any of its out- outsourcing price is set back to its value at the last round, sourcing requests once they are auctioned, and when an then the auctioneer starts a new round of auction with auction is over with no other agents acquire a request, it 123 Logist. Res. (2011) 3:101–120 113 will be returned to the auctioneer for reconsideration. An carriers a, b, c from outsourcing their requests, respec- agent can organize multiple auctions and bid for multiple tively. The minimum profit margin of each carrier, a, is set outsourcing requests at the same time. to 5%. p denotes the price paid by a shipper for request l; The simulation is separated from the resolution of two p denotes the outsourcing price of request l, which is set to decision problems (outsourcing requests selection problem p initially and is adjusted in the interval [0, p ], where l l and requests bidding problem) and other decision problems p ¼ p ð1 aÞ. The parameter q of the outsourcing price l l in the multi-agent and auction-based framework. This update rule is set to 0.1 for all carriers, and d in the price means that the resolution of these problems is assumed to update rule is set to p q request l. The time period for take no time or take very short time. A system clock is each round of auction for each outsourcing request of introduced in the simulation. When a decision problem carriers a, b, c is set to 5, 10, 15 s, respectively. Carriers a, needs to be solved, we freeze the clock until the problem is b, c has two requests initially, the arrival time of the third solved. This can be regarded as that each decision problem request is set to 4, 8, 13 s, respectively. Carriers a, b, c is solved off-line. In addition, the simulation is driven by enter the actions at 1, 2, 3 s, respectively. discrete events. The time is advanced in a discrete way. Besides, some abbreviations and symbols are defined as That is, we always advance the time to the moment at follows. ORSPi represents the outsourcing requests selec- which the next event(s) will happen. After an event (or tion process for carrier i. RAPilk denotes round k of the multiple events) happen (simultaneously), we update the auction process of outsourcing request l of carrier i. RBPilk system’s state and determine the next event(s) and its denotes round k of bidding process of request l for carrier i. (their) occurrence time. RLAlik denotes that request l is allocated to carrier i in Multiple events may occur in the simulation: the starting round k of its auction. All involved decision problems and the end of the auction process of a request, the arrival (models) are solved directly by using IBM MIP Solver of a new request; the starting and end of a round of the ILOG Cplex 12. The events happened in all the auction auction of a request, etc. To implement the simulation, we processes for each carrier are listed in Table 3. define the state space of the multi-agent system and all The profit comparison is given in Table 4, where IP events that may happen in the system, where the state of denotes the initial profit of each carrier before collaboration the system is represented by the state of each agent that is calculated by model ORSP; PMAA denotes the profit defined in turn by the states of its requests and the avail- obtained by our multi-agent and auction-based framework; ability profile of its resources (vehicles). In the simulation, PC denotes the profit obtained by the centralized frame- we assume that the auction of each outsourcing request work presented in the appendix, in which all collected starts immediately after the outsourcing carrier solves its requests from carriers are allocated in a globally optimal ORSP problem. When a request is not allocated to any way. carrier after the termination of its auction, it is reconsidered From Table 4, we can see that PMAA can generate a by the outsourcing carrier as a new arrival request. All new better requests allocation solution compared with IP. arrival requests of each carrier will be only considered PMAA fulfills all requests as well as PC. Each carrier’s when it solves its ORSP problem. To help us understand profit increases in PMAA. This example demonstrates the the simulation, we first explain it by an illustrative example effectiveness and feasibility of our proposed approach. in the next subsection. 7.3 Simulation results on randomly generated instances 7.2 Demonstration of the simulation by an illustrative example To evaluate the performance of our framework, we ran- domly generate two sets of instances, where each set has We first use the illustrated example in Sect. 2 to carry on ten instances. The parameters of the instances are taken as the simulation process. The parameters of the example are follows. The transportation network for each instance has explained as follows. R , R , and R denote the self-exe- 21 nodes (N = 21). The coordinates of each node are a b c cuted requests set for carriers a, b, c, respectively, which randomly and uniformly generated from 42 9 42 square; includes the requests collected from shippers and the as soon as the coordinates of all nodes are generated, the requests acquired from other carriers. R , R , and R Euclidean distance between any two nodes i and j, denoted ab bb cb denote the set of requests bid for by carriers a, b, c, by d , is calculated. For simplicity but without loss of ij respectively. R and R , R , R denote the set of out- generality, we set c = s = d for all carriers. There are o ao bo co ij ij ij sourcing requests for all carriers and carriers a, b, c, three carriers (K = 3) operated in the transportation net- respectively. P , P , and P denote the profit gained from work. Every carrier randomly selects a node as its depot a b c fulfilling self-executed set and bided set for carriers a, b, c, node, but different carriers have different depot nodes; each respectively. P , P , and P denote the profit gained by carrier owns a random number of vehicles chosen between ao bo co 123 114 Logist. Res. (2011) 3:101–120 Table 3 Discrete event lists for the illustrative example Time Events of carrier a Events of carrier b Events of carrier c 1 ORSPa; R ¼fr1g –– RAP121; R ¼fr2g ao R ¼fg r2 ; p ¼ 66:5 R ¼fg; P ¼ 0; P ¼ 36:8 ab ao a 2– – ORSPb; R ¼fr4g RAP251; R ¼fr2; r5g R ¼fr5g; p ¼ 59:85 bo RBP221; R ¼fr2g bb P ¼ 0; P ¼ 81:3 bo b 3 – – ORSPc, R = {r7,r8} RBP321, RBP351 R = {r2}, P = 178.6 cb c 4 ORSPa, R = {r1,r3} –– RBP151, R = {r5}, P = 200.75 ab a 6 RAP122; p ¼ 59:85 – – 7 – RBP222 RBP322, RBP351 R = {}, P = 75.6 R = {}, P = 171 bb b cb c 8 – ORSPb, R = {r4,r6} – RBP222, R = {r2}, P = 118.95 bb b 11 ORSPb, R = {r4,r6,r2} – RLA222; R ¼fr5g o b P = 118.95 P ¼ p p ¼ 70 59:85 b ao 2 12 ORSPa, R = {r1,r3,r5} – RLA511; R ¼fg a o P = 200.75 a P ¼ p p ¼ 63 59:85 bo 5 13 – – ORSPc; R ¼fr7; r9g RAP381; R ¼fr8g co R ¼fr8g; P ¼ 0 o co p ¼ 49:4; P ¼ 182:4 14 RBP181 RBP281 – R = {r8}, P = 217.35 R = {r8}, P = 158.45 ab a bb b 28 – – RAP382; p ¼ 44:46 29 RBP182 RBP282 – R = {r8}, P = 212.41 R = {r8}, P = 153.51 ab a bb b 43 – – RAP383, p ¼ 39:52 44 RBP183 RBP283 – R = {r8}, P = 207.47 R = {r8}, P = 148.57 ab a bb b 58 – – RAP384; p ¼ 34:58 59 RBP184 RBP284 – R = {r8}, P = 202.53 R = {r8}, P = 143.63 ab a bb b 73 – – RAP385; p ¼ 29:64 74 RBP185 RBP285 – R = {}, P = 200.75 R = {r8}, P = 138.69 ab a bb b 88 – ORSPb, P = 138.69 RLA825; R ¼fg R = {r4, r6, r2, r8} P ¼ p p ¼ 52 29:64 bb co 8 Total profit is P ? P = 210.9 Total profit is P ? P = 141.84 Total profit is P ? P = 204.76 a ao b bo c co 1 and 10, and each vehicle has the same capacity C = 10. request 4, 5, 6, and carrier c owns request 7, 8, 9. The The number of transportation requests L is set to (N - K)/2 requests are generated by randomly choosing a pickup (L = 9). Carrier a owns request 1, 2, 3, and carrier b owns node i (not depot node) and a delivery node j (j = i, not 123 Logist. Res. (2011) 3:101–120 115 Table 4 Profit comparison Profit without collaboration Profit with collaboration between three cases for the illustrative example IP PMAA PC Carrier a Carrier b Carrier c Carrier a Carrier b Carrier c 684.4 146 97.7 182.4 210.9 141.84 204.76 426.1 in total 557.5 in total Fulfilled requests Carrier a Carrier b Carrier c Carrier a Carrier b Carrier c Carrier a Carrier b Carrier c r1, r2, r3, r2, r4, r1, r3 r4, r6 r7, r9 r1, r3, r5 r7, r9 - r4, r8 r5, r6, r6, r8 r7, r9 Table 5 The time parameters Instance 1 2 3456 78910 of the twenty instances Time period (s) – 15 10 15 – – 15 10 5 5 10 5 – 5 5 10 10 – 10 – 5 – 1510 105 55 15 10 Instance 11 12 13 14 15 16 17 18 19 20 Time period (s) 5 – 10 10 5 15 – 10 15 5 15 – 5 15 10 5 15 – 10 15 10 5155 ––10 – 5 10 New request arrival time (s) 6 10 15 10 15 13 16 11 4 4 9 5 20 5 18 15 3 5 19 9 10 16 10 15 13 7 10 18 6 13 depot node), each node is just chosen once; each request is sufficiently larger than its service cost in order to avoid the assigned with a random quantity of freight d that is not situation that no carriers choose to serve the request. The larger than a predefined number. For the first set of time windows are generated in the following way: the time instances, this number is set to five for instances 1–5 and interval for serving all requests is set to [0, 240] set to 10 for instances 6–10. For the second set of instances, (480 min = 8 h, time unit is taken as 2 min); the earliest this number is set to five for instances 11–15 and set to 10 service time a at pickup node i is randomly chosen in for instances 16–20. The ask price paid by a shipper to a [s , 240-s - s ], where s is calculated by considering oi oj ij oi carrier for serving a request is defined by c*(1 ? a)* b* the farthest depot o (three depots in total) from node i; the (c ? c ? c ), where o denotes the depot of the carrier latest service time b is randomly chosen from (a ? 15) to oi ij oj i i and c ? c ? c is the direct shipping cost of the request, (a ? 45); the earliest service time a at delivery node j is oi ij oj i j b is the average utilization of vehicle in ideal situations for randomly chosen in [s ? s , 240-s ]; and latest service oi ij oj serving the request, a denotes the minimum profit margin time b is randomly chosen from (a ? 15) to (a ? 45). j j j of the carrier, c is an adjustable parameter no less than one. And the conditions (b - a ) [ c , b B 240 and b B 240 j i ij i j The calculation of b is explained through a simple example are verified during the time windows generation process. as follows: assume that the capacity of each vehicle of the The time windows for each carrier’s depot are set to [0, carrier is 10 and it has three requests to serve, whose 240]. The parameter q in the outsourcing price update rule pickup/delivery quantities are 3, 5, and 8, respectively, and is set to 0.1 for all carriers. the considered request is the request with quantity five, so The other parameters are given in Table 5. For each the total quantity of the requests is (3 ? 5 ? 8) = 16 and column (instance), the three (sub)rows in row ‘‘Time per- the carrier requires at least two vehicles to serve all the iod’’ denote the time period for each round of auction for requests, b is then calculated as 2*5/16 for the second three carriers, respectively, which is randomly chosen from request. Parameter a is set to 5% for all carriers according three numbers (5, 10, 15), and it is vacant if a carrier does to Holguı ´n-Veras et al. [12]. Parameter c is set to two, not outsource requests. For the second set of instances, which ensures that the ask price of the request is each carrier has two requests initially, the three (sub)rows 123 116 Logist. Res. (2011) 3:101–120 Table 6 Results comparison of the first set of instances Instance 1 2 3 4 5 IP Carrier a 75.3 15.4 41.3 10.2 36.5 Carrier b 36 12.7 155 133.9 105.6 Carrier c 2 167.8 19 96.9 19.8 Total 113.3 195.9 215.3 241 161.9 Fulfilled requests r1, r2, r3, r5, r6, r7 r3, r6, r7, r8, r9 r1, r3, r4, r5, r6, r8 r1, r3, r5, r6, r7, r8 All except r5, r7 PMAA Carrier a 75.3 15.4 46.955 28.96 45.34 Carrier b 59.35 36.82 155 200.59 126.96 Carrier c 3.35 200.48 26.145 99.2 19.8 Total 138 252.7 228.1 328.75 192.1 Fulfilled requests All except All except All except All except All except r4, r8 r1, r2 r7, r9 r2 r7 PC Total 184.3 346.8 366.6 458.4 340.6 Fulfilled requests All except All r1, r3, r4, r5, r6, r8 All except All r4, r8 r2 Instance 6 7 8 9 10 IP Carrier a 184.2 150.1 148.4 92.9 73.1 Carrier b 60.4 94.6 93.7 173.5 160.4 Carrier c 135.6 183.1 120.6 139.8 153.9 Total 380.2 427.8 362.7 406.2 387.4 Fulfilled requests r1, r2, r3, r4, r7 r1, r2, r4, r5, r8, r9 r2, r3, r4, r5, r6, r7 r1, r3, r4, r6, r7, r8 r1, r4, r5, r6, r8, r9 PMAA Carrier a 287.575 154.4 189.945 92.9 77.45 Carrier b 85.725 118.8 116.7 175.1 227.15 Carrier c 140 183.1 151.855 143.6 157.7 Total 513.3 456.3 458.8 411.6 462.3 Fulfilled requests All All except All All except All except r7 r2, r9 r2 PC Total 615 591.3 607.8 450.7 519.3 Fulfilled requests All All except All All except All except r6 r2, r9 r2 in row ‘‘New request arrival time’’ denote the arrival time (sub)rows, the first four (sub)rows indicate the profit of of a new request for each carrier; in each instance, it is carriers a, b, c, and the total profit of the three carriers, generated randomly in the intervals [1, 20]. respectively, the last (sub)row indicates the fulfilled All decision problems (models) involved in these requests. The row PC has only two (sub) rows, which instances are solved by using ILOG Cplex 12 directly. All indicate the total profit and the fulfilled requests, simulation results are given in Tables 6 and 7, where IP, respectively. PMAA, and PC have the same meaning as in Table 4 in last From the results, we can observe that our multi-agent subsection. Both of the rows IP and PMAA have five and auction-based framework (row PMAA) can obtain a 123 Logist. Res. (2011) 3:101–120 117 Table 7 Results comparison of the second set of instances Instance 11 12 13 14 15 IP Carrier a 123.7 231.4 10.6 144.7 21.4 Carrier b 145.3 119.6 0 192.7 170.7 Carrier c 10.9 88.4 116.9 2 102.6 Total 279.9 439.4 127.5 339.4 294.7 Fulfilled requests All except All except r2, r7, r9 r1, r3, r4, r6, r9 All except r6, r9 r7 r3, r6 PMAA Carrier a 131.75 231.4 14.4425 147.6 22.95 Carrier b 148.35 136.375 13.6075 194.95 172.8 Carrier c 26.2 100.125 158.95 60.55 116.05 Total 306.3 467.9 186.98 403.1 311.8 Fulfilled requests All except All r2, r5, r6, r7, r9 All except All r9 r7, r8 PC Total 393.5 551.4 243.9 534.3 496.4 Fulfilled requests All except All All except All All r9 r1, r4 Instance 16 17 18 19 20 IP Carrier a 192.5 124.8 139.9 111 92 Carrier b 99.1 180.4 134.8 176.3 32.5 Carrier c 146.4 119.8 116.6 142.7 55.5 Total 438 425 391.3 430 180 Fulfilled requests All except All except All except r1, r2, r4, r5, r7, r8 All except r3, r6 r6, r7 r1, r8 r1, r5 PMAA Carrier a 192.5 124.8 149.005 132.4 100.45 Carrier b 102.55 200.63 134.8 179.6 55.65 Carrier c 169.45 141.87 139.595 142.7 55.5 Total 464.5 467.3 423.4 454.7 211.6 Fulfilled requests All except All All except All except All r3 r1, r8 r3, r9 PC Total 587.6 622.2 561.7 511.4 212 Fulfilled requests All All All All except All r9 larger profit in total than the profit gained in the case alliance by sharing all information of the carriers, and it is without collaboration among carriers (row IP) in all based on global optimization; the other is that some high instances. PMAA can fulfill more requests than IP. The profitable requests for a carrier may be already acquired by profit of each carrier is not decreased in PMAA compared other carriers in PMAA. However, PC needs a fair and with its profit in IP. Most of them can increase their profits. feasible post-coordination profit allocation mechanism, The centralized framework (row PC) leads to better results although it is not easy to measure the contribution of each than PMAA, which is probably because of two reasons. carrier in the alliance. Furthermore, PMAA is more One is that PC maximizes the total profit of the whole acceptable by carriers since no private information of each 123 118 Logist. Res. (2011) 3:101–120 carrier is revealed to others and no profit reallocation Indices mechanism is needed. PMAA is more flexible to deal with k: carrier index, k = 1, …,K, where K represents the dynamic market situations, where the time for the auction number of carriers and acquisition of each request is uncertain in advance. l: request index, l = 1, …,L, where L represents the Therefore, PMAA is more realistic, promising, and easier to total number of requests of all carriers be applied in practice. Parameters 8 Conclusion C vehicle capacity of carrier k W the number of vehicles owned by carrier k A carrier collaboration problem in less than truckload o the depot of carrier k transportation with pickup and delivery requests a the minimum profit margin of carrier k (CCPLTL) has been studied in this study. A multi-agent c transportation cost from node ito j for each ij and auction-based framework is proposed for the problem vehicle of carrier k together with relative decision models. The decentraliza- the traveling time from node i to node j for each ij tion is the major feature of the framework, where each vehicle of the carrier k carrier acts both as an auctioneer and as a bidder, no private information is shared among carriers, and no post-coordi- Variables nation profit reallocation among the carriers is required. Two key decision issues for each carrier in the framework quantity of freight transported through arc (i, j) ij are addressed: one is outsourcing requests selection prob- by vehicles of carrier k lem and the other is outsourcing requests bidding problem. the number of times that arc (i, j) is visited by ij These two problems are formulated mathematically. vehicles of carrier k Twenty instances are randomly generated and simulated to y 1 if request l is reallocated to carrier k,0 lk evaluate the performance of our framework compared with otherwise the case without collaboration among carriers and with a the time at which a vehicle of carrier k leaves node i centralized framework. The results show that our approach With the notations, the mixed integer programming model can increase the profit of each carrier and the total profit of is given as (16–29). all carriers in most instances through reducing transporta- Model CRRP: tion costs. In our future work, we will try to extend our K L K N N XX XX X proposed framework to deal with the outsourcing and II k k Z ¼ Max p y ð1 a Þ c x l lk k ij ij acquisition of bundles of transportation requests. k¼1 l¼1 k¼1 i¼1 j¼1;j6¼i ð16Þ Appendix: centralized framework for carrier Subject to: collaboration N N X X k k x ¼ x ; i ¼ 1; ...; N; k ¼ 1; .. .; K; ð17Þ Under the centralized framework, multiple carriers come to ij ji j¼1;j6¼i j¼1;j6¼i an agreement for cooperating each other and constitute a k k collaborative alliance with a coordinator in charge of q C x ; i; j ¼ 1; ...; N; i 6¼ j; k ¼ 1; ...; K; ð18Þ ij ij making collaborative transportation plans for the alliance. N N X X X X The coordinator may be a virtual one. The objective of the k k q q ¼ d y d y ; l lk l lk ij ji coordinator is to maximize the total profit of the alliance, j¼1;j6¼i j¼1;j6¼i l2P l2D i i which will then be allocated among the carriers. Regarding i ¼ 1; ...; N; i 6¼fo g; k ¼ 1; ...; K; ð19Þ the problem investigated in this paper, the coordinator in the centralized framework determines the reallocation of X X X q ¼ d y d y ; k ¼ 1; ...; K; l lk l lk all transportation requests to the carriers so as to maximize o j j¼1;j6¼o l2P l2D k o o k k the total profit. This centralized requests reallocation problem (CRRP) for CCPLTL can be formulated as a ð20Þ mixed integer programming (MIP). The notations used in the MIP model include the notations introduced in Sect. 4 q ¼ 0; k ¼ 1; ...; K; ð21Þ jo and the following notations. j¼1;j6¼o 123 Logist. Res. (2011) 3:101–120 119 N 2. Agnetis A, Pacciarelli P, Pacifici A (2007) Combinatorial models for multi-agent scheduling problems. Chapter 2 of book multi- x W ; k ¼ 1; ...; K ; ð22Þ o j processor of scheduling: theory and applications. Itech Education j¼1;j6¼o and Publishing, Austria 3. 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Published: Feb 11, 2011
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