Centralized Auctions for the Procurement of Truckload Transportation Services:
Impacts on Carriers
Intissar Ben Othmane Sehl Mellouli
Monia Rekik
December 2019
Document de travail également publié par la Faculté des sciences de l’administration de l’Université Laval, sous le numéro FSA-2019-019.
2 Department of Operations and Decision Systems, Université Laval, 2325 de la Terrasse, Québec, Canada G1V 0A6
3 Department of Information Systems, Université Laval, 2325 rue de la Terrasse, Québec, Canada G1V 0A6
Abstract. Our paper proposes a novel auction-based procurement mechanism in which carriers are offered the opportunity to bid on the contracts required by different shippers simultaneously in a single combinatorial auctions where shippers requests are centralized.
Our paper investigates the benefits/drawbacks of such a centralized mechanism for carriers by comparing it to the traditional decentralized mechanism under different carrier's risk behaviours. Our results prove that a centralized procurement mechanism offers generally the best alternative for the carrier to increase its profit, reduce its empty moves and diversify its business network.
Keywords. Bidding, truckload transportation services, centralized and decentralized procurement, combinatorial auctions, carrier's risk behaviour.
Acknowledgements. This research was supported by the Natural Sciences and Engineering Research Council of Canada (NSERC) under grants 2016-04482. This support is greatly acknowledged.
Results and views expressed in this publication are the sole responsibility of the authors and do not necessarily reflect those of CIRRELT.
Les résultats et opinions contenus dans cette publication ne reflètent pas nécessairement la position du CIRRELT et n'engagent pas sa responsabilité.
_____________________________
* Corresponding author: [email protected]
Dépôt légal – Bibliothèque et Archives nationales du Québec
1. Introduction
The use of combinatorial auctions for the procurement of Full Truckload (FTL) transportation services has achieved great success in the last decades (Caplice and Sheffi, 2006). In these auctions, shippers act as auctioneers that seek for outsourcing all or a part of their FTL operations and carriers act as bidders on shippers’ requests. To alleviate the presentation, we will use the term contract to refer to a shipper request. In its simple form, a contract is defined by an origin-destination pair (also called a lane). When participat- ing to a combinatorial auction, a carrier must decide on the bids to submit to maximize its profit while taking into account its existing transportation network and other operational constraints (Ben Othmane et al., 2019; Ham- mami et al., 2019). This is known as the Bid Construction Problem (BCP) or the bid generation problem.
In combinatorial auctions, carriers are allowed to bid on packages of con- tracts rather than on each contract separately (Ledyard et al., 2002; El- maghraby and Keskinocak, 2004). A combinatorial bid is generally defined by a package of contracts, the associated ask price and possibly other in- formation related to the minimum and maximum volumes to transport, etc.
(Caplice and Sheffi, 2006; Ma et al., 2010; Remli and Rekik, 2013). Com- binatorial bids are all-or-nothing bids. That is, if the bid is won, all the contracts it covers must be allocated to the bidder or nothing at all. This helps circumventing the well-known exposure problem: it avoids the carrier to win only a subset of the contracts submitted in a bid that may become non profitable if the other contracts in the package are not won. This is particu- larly interesting for carriers which aim to acquire adjacent lanes and/or lanes that form a closed loop so that empty move costs are reduced. Indeed, when solving the BCP, lanes covered by the same route are generally submitted in the same package bid (Ben Othmane et al., 2019; Hammami et al., 2019) and are profitable only if they are all allocated to the carrier.
Traditionally, each shipper runs a separate auction to satisfy its proper
transportation needs independently from other shippers. In the following, we refer to such auction as a “decentralized auction”. Basu et al. (2015) report that the negotiation process for establishing contracts between shippers and carriers takes one to two years. In some cases, carriers are led to bid in more than one auction at the same time before knowing which of the bids they sub- mitted are effectively won. Thus, a carrier participating asynchronously into different decentralized auctions may face a problem similar to the exposure problem: when it is invited to participate into an auction run by a shipper s2, it probably had already submitted bids to another auction previously run by another shipper s1 without knowing yet if the bids it submitted tos1 has won or not. Hence, depending on the carrier’s strategy, it may happen that when some bids submitted to the first auction are rejected by s1, the bids submitted tos2 are no more profitable. This is exactly the exposure problem initially criticized in simple-bid auctions.
As already mentioned, combinatorial auctions came to face the exposure problem (as classically defined) by allowing a carrier to bid on a package of contracts simultaneously. Our paper extends the same idea by considering what we call a “ centralized auction” in which the carrier has the opportu- nity to bid on the contracts required by the different shippers simultaneously.
That is a single auction where multiple shippers present their transportation requests simultaneously and carriers submit package bids covering a set of contracts belonging to different shippers. Our paper investigates the ben- efits/drawbacks of such a centralized auction for carriers by comparing it to decentralized auctions under different carrier’s risk-behaviour attitudes.
Comparison is done over a large set of generated instances by computing relevant performance measures.
To the best of our knowledge, our paper is the first to investigate the im- pacts of such a centralized procurement mechanism on carriers. Our results show that a centralized procurement offers the best compromise between profit, network efficiency and business diversification. A carrier participat-
ing in a centralized auction generally realizes more or equal profits than in decentralized ones by bidding on less contracts. Its resulting network is more efficient and includes less empty movement distances, reducing thus its ecological footprint. Our results also prove that a centralized procurement mechanism helps a carrier diversify its business network and commit with a variety of shippers.
The remainder of the paper is or organized as follows. Next section is a literature review on FTL transportation procurement auctions from the carrier’s perspective. Section 3 describes in more details centralized and de- centralized procurement mechanisms under study. Section 4, formally defines the different performance measures considered to compare both mechanisms.
In Section 5, we describe the instances considered and discuss the obtained results. Section 6 is a conclusion.
2. Literature review
Our literature review first reports the main papers dealing with the BCP for combinatorial bidding in FTL transportation procurement markets. We then present papers addressing the so-called exchange mechanisms presented in the literature as a form of auction-based collaboration between carriers.
In the last decades, several papers have addressed the BCP in combina- torial auctions for the procurement of FTL services. Song and Regan (2004) propose a greedy search heuristic and compare combinatorial auctions with traditional single-item one. Results show that both shippers’ procurement costs and carriers’ average empty movement costs are lower in combinatorial auctions. Later, Song and Regan (2005) present approximation methods to solve the BCP under two scenarios: with and without pre-existent commit- ments. The objective is to minimize the total empty travel cost. The authors propose a two-phase solution approach: (1) an exhaustive search algorithm enumerates all the routes with respect to a number of routing constraints (2) A set covering model is solved to select optimal routes (packages) that mini-
mize empty movement costs. The proposed model considers a homogeneous vehicle fleet and does not take into consideration vehicles’ time constraints.
A “modified” branch-and-bound algorithm is used to solve the set covering formulation.
Wang and Xia (2005) consider a homogeneous vehicle fleet where a pick- up time window is associated with each transportation contract origin. The objective is to minimize the total expected empty repositioning costs. To solve this problem, the authors developed and compared two heuristic ap- proaches. The first one is based on a fleet assignment model and presented as a generic formulation for the routing and scheduling problem. The second one is based on the nearest insertion method. Results show that the fleet assignment based heuristic generates slightly better bids than the nearest insertion method.
Lee et al. (2007) consider vehicle routing models (VRP) to help carriers identify sets of bids that maximize their profits rather than just minimiz- ing empty traveling costs. The authors consider a homogeneous fleet with limited size and propose a quadratic integer program that simultaneously generates and selects profitable routes while taking into account existing commitments. To solve the problem, column generation and Lagrangian re- laxation techniques are combined. Reported experimental results show that despite the good quality of the output solutions, instances involving more than 355 contracts required very large computing times.
Chang (2009) developed a so-called bidding advisor in a context of one- shot combinatorial auctions for spot markets. It considers a homogeneous fleet and model the BCP as a synergetic minimum-cost flow problem, claim- ing that the BCP is better formulated as a time-space network based fleet management problem instead of a VRP. The BCP is solved by a column gen- eration method using a shortest path algorithm with synergy considerations in order to generate all optimal paths. The proposed approach determines only approximate solutions and was not compared with an exact solution
approach.
Triki et al. (2014) address the BCP in a single-round sealed-bid com- binatorial auction for an FTL spot market. They propose a probabilistic mixed integer programming model with the objective to maximize the profit of the carrier. Their model takes into account uncertainty on the bids clear- ing prices. The BCP is formulated as a fleet management problem based on a time-space network. The authors report that the proposed model is intractable by the exact branch-and-cut procedure of CPLEX. They develop and compare two heuristics approaches.
Recently, Hammami et al. (2019) propose exact and heuristic methods to solve a BCP with a heterogeneous fleet. An hybrid Adaptive Large Neighbor- hood Search (ALNS) heuristic is proposed and compared to the branch-and- cut procedure of CPLEX applied to an arc-based Mixed Integer Programming (MIP) model. ALNS is hybridized with a Set Partitioning model layer that helps improve solution quality for large-sized instances. The reported results show that the ALNS heuristic requires very short computing times for small instances. Solution times increase when the number of auctioned contracts exceeds 75.
Ben Othmane et al. (2019) address a new variant of the BCP in which auctioned contracts must be integrated within the deadhead arcs of the car- rier’s existing routes. This enables generating multiple bids with the guar- antee that the carrier realizes a non negative profit no matter how many and which bids are won. The authors propose a heuristic approach to solve in- stances including up to 300 existing contracts and 300 auctioned ones within very small computing times. When compared to an exact method for small instances, the proposed heuristic identifies either optimal or near-optimal solutions.
All the papers discussed above consider one-sided reverse auctions in which a single shipper acts as the auctioneer and carriers are the only bidders.
There exist other transportation auctions in which each participant can act
both as an auctioneer and a bidder. These auctions are referred to as two- sided auctions or double auctions or multi-lateral auctions or many-to-many auctions or exchanges (Hosseini Motlagh et al., 2010; Dai and Chen, 2011).
We report in the following the main papers addressing such mechanisms from the carrier’s perspective.
In exchange mechanisms, different carriers share their requests to maxi- mize their profits. Each carrier firstly defines the contracts to exchange with its collaborators, then appropriate requests are exchanged through different profit maximizing auction mechanisms (Verdonck et al., 2013). Schwind et al.
(2009) propose a request reallocation mechanism labeled ComEx to exchange delivery contracts among medium-sized logistics companies operating inde- pendent centers. The authors report that the exchange of customer orders reduced the distribution costs.
Berger and Bierwirth (2010) address the exchange of customer requests between carriers through combinatorial auction mechanism. Their frame- work distinguishes between carriers collaborating with confidential exchange of relevant information and carriers collaborating by sharing all necessary in- formation. The authors report that the success of requests sharing increase with the degree of information sharing. Li et al. (2015) integrate requests se- lection and routing problems assuming a limited sharing of carriers requests information. Recently, Xu et al. (2017) propose a double combinatorial auc- tion mechanism for the truckload carrier collaboration problem. The authors report that their mechanism lead to considerable cost savings for the carrier collaboration network.
Our paper proposes a novel mechanism for transportation procurement auctions and studies its impact on the carrier’s profit as well as other relevant performance measures. The proposed mechanism corresponds to a one-sided combinatorial auctions in which each participating carrier is offered the pos- sibility to bid on different contracts submitted by different shippers. No exchange of contracts is performed between carriers and shippers are the
only auctioneers. To the best of our knowledge, the impact of such a cen- tralized auction on carriers has never been studied in the literature. Next section formally describes the proposed procurement mechanism.
3. Problem setting
3.1. Context and assumptions
We consider a set of n shippers S = {s1, s2, . . . , sn} that need to out- source their FTL operations to external carriers through one-sided reverse combinatorial auctions where carriers are the only bidders. Two procurement mechanisms are studied: (1) a decentralized mechanism where each shipper si, i= 1, . . . , nruns its own combinatorial auctionA(si) by presenting its set of contractsKi to the participating carriers Ti; and (2) a centralized mecha- nism where all shippers in S run a unique auction A(S) and submit all their contracts in Kn=∪i=1,...,nKi to all carriers in T =∪i=1,...,nTi.
Our paper studies the impacts of auctions centralization with regard to different criteria to be detailed in Section 4. To this end, we consider two sce- narios for a carrier t∈ ∩i=1,...,nTi. For the first scenario, carriertparticipates in the multiple decentralized auctionsA(si), i= 1, . . . , norganized separately by shippers si, i = 1, . . . , n. It is assumed that auctions A(si), i = 1, . . . , n start either at the same time or at different times but when the carrier t submit bids in one of these auctions, none of the results of any of the other auctions is yet known. In the second scenario, carrier t participates in the centralized auction A(S).
In all cases, the carrier’s objective is to generate bids on auctioned con- tracts to maximize its profit while satisfying its operational constraints. Ob- serve that in a decentralized procurement mechanism, a bid submitted in an auctionA(si), i= 1, . . . , ncan only cover contracts inKi. For the centralized auctionA(S), the carrier is offered the possibility to bid on a package includ- ing contracts submitted by different shippers. All auctions are assumed to use a “pay-as-bid” pricing strategy. That is, if a carrier wins a bid, then it
must be allocated a price equal to the price asked in its winning bid. For all auctions, the bids are generated using the heuristic proposed in Ben Othmane et al. (2019).
Ben Othmane et al. (2019) consider a BCP in which the carrier has ex- isting contracts it already committed with other shippers and aims to bid on new contracts to maximize its profit. Operational constraints related to the fleet size and maximum durations for each vehicle tour are considered. In the proposed heuristic, a new auctioned contract is added if, when inserted in a deadhead arc of the existing routes, it generates a non-negative profit.
When no more contracts can be inserted in the existent routes and there are still unused vehicles, routes composed of only new contracts are defined so that unused vehicles could be operated when profitable.
Ben Othmane et al. (2019)’s heuristic gets as input the carrier existing network, its operational constraints and the set of new auctioned contracts.
It outputs multiple OR combinatorial bids. OR bids imply that the carrier is able to serve all the contracts covered by the bids if they are all won.
Each bid covers the set of new contracts belonging to the same vehicle route.
An interval of ask prices is associated for each bid: the lowest ask price corresponds to the cost incurred to serve the new contracts covered by the bids; the highest ask price is the sum of the new contracts’ maximum prices.
The final bid price is determined by the carrier depending on the profit margin, α ∈ [0,1] it decided to apply. We refer the reader to the paper of Ben Othmane et al. (2019) for more details.
Our paper aims to study the benefits/drawbacks of a centralized mech- anism from the carrier’s perspective when compared to decentralized ones under two risk-behaviour attitudes. Section 3.2 formally describes the dif- ferent procurement strategies addressed. Section 4 defines the performance indicators used to compare them.
3.2. Procurement mechanisms
Let t be a carrier in ∩i=1,...,nTi. It is assumed that ∩i=1,...,nTi 6=∅ which is a realistic assumption since carriers generally participate into different auctions to increase their profits. Let Ke denote the set of contracts already contracted by the carrier t before its participation to these auctions (the so- called existing contracts).
Recall that for the decentralized procurement mechanism, when the carrier t is invited to participate into an auction run by a shipper sj, it has probably already submitted bids to another auction previously run by another shipper si without knowing yet if the bids it submitted to A(si) are won or not. In such cases it may adopt different strategies depending on its risk behaviour.
To alleviate the presentation, we assume in the rest of the paper that shippers in S are indexed so that shipper si initiates its auction before shipper si+1 in the decentralized mechanisms. Hence, shipper s1, respectively, sn, is the first, respectively, the last, shipper to initiate an auction.
A too risky carrier would construct the bids to submit to A(si+1) taking into account its full capacity as if no bids submitted toA(si) would win. This is risky because if bids submitted to A(si) and A(si+1) are won afterwards, the carrier must find the lacking capacity to ensure its commitments with both shippers, possibly at relatively large costs. In our case, this is modeled by solving a series of BCP using the heuristic proposed in Ben Othmane et al. (2019), one BCP for each auction A(si), i = 1, . . . , n. In the BCP solved for A(si), the set of existing contracts correspond to Ke and the set of new contracts corresponds to those requested by si (Ki).
An averse-to-risk carrier would do the opposite. It would generate the bids to submit to A(si+1) by considering only its residual capacity assuming that all the bids submitted to A(si) would be won. This is an averse-to- risk behaviour given that the carrier prefers to ensure the internal capac- ity required to meet uncertain commitments at the expense of additional potential incomes. This is modeled by solving a series of BCP, one for
each auction A(si), i = 1, . . . , n. In the BCP considered for A(si+1), i ∈ [1, . . . , n−1], the set of new contracts is Ki+1 and the set of existing con- tracts is Ke = ∪ij=1 ∪b∈Bj Kb, where Bj denotes the set of bids submitted to auction A(sj), j = 1, . . . , i and Kb is the set of contracts covered by bid b. Hence, when solving the BCP, the profitability of the bids submitted to A(si+1) relies on the assumption that all of the bids submitted to A(si) would be won. But, if all or a part of these bids are rejected by si, there is no guarantee that the bids submitted to A(si+1) are still profitable if won.
In the following we consider the decentralized procurement under two contexts related to the carrier risk behaviour: (1) a context where the carrier adopts an averse-to-risk strategy, referred to as “Decentralized Procurement with a risk-Averse bidding” (DPA) and (2) a context where the carrier adopts a risky behaviour, referred to as a “Decentralized Procurement with a Risky bidding” (DPR). The centralized procurement mechanism is referred to as
“Centralized Procurement” and is denoted by CP. Observe that the carrier may show an intermediate behaviour and constructs bids by considering only a part of its residual capacity. In other words, it would assume that not all of the bids submitted to A(si) would win (by at least some bids would). Our paper studies the two extreme scenarios to evaluate worst-case outputs.
4. Comparison between centralized and decentralized procurement mechanisms
Comparison is done based on four main criteria: (1) the carrier’s potential profit, (2) the percentage of contracts bid on, (3) empty movement distance, and (4) market diversification.
4.1. Potential profit
Our objective here is to measure the gain/loss in potential profits that could be obtained by the carrier in a centralized versus a decentralized mech- anism. To this end, let Pid denote the profit that could be obtained by the
carrier when participating to the decentralized auctions A(si);i = 1, . . . , n.
Similarly, letPcdenote the profit that could be obtained by the carrier when a unique centralized auction is run. These profits are determined through solving the BCP with the heuristic proposed by Ben Othmane et al. (2019).
They represent the maximum -and not the real- profit that could be obtained by the carrier if all the bids submitted in the auction are won. Hence, the total potential profit that could obtained by a carrier in a decentralized pro- curement mechanism could be computed as the sum of the profits output by solving the n BCPs (Pn
i=1Pid).
However, under the DPR context, a carrier is likely to end up with a set of contracts it can’t serve by it self with its internal capacity. In this case, the carrier may subcontract certain contracts to other carriers at larger costs and the effective total potential profit that could be obtained by a carrier is much lower than Pn
i=1Pid.
Let Kw denote the set of contracts covered by the bids submitted to all the decentralized auctions A(si), i = 1, . . . , n and that could be served by the carrier with its internal capacity. LetKw denote the subset of contracts that must be subcontracted to other carriers. To determine the contracts in Kw and Kw, we solve a BCP in which the set of existing contracts is Ke and the set of new contracts is ∪i=1,...,n∪b∈Bi Kb (i.e., all the contracts bid on in the decentralized auctions). The set of new contracts retained by the BCP algorithm defines Kw and those not retained define Kw.
Based on the algorithm output, one can also determine the cost, denoted C(Kw), incurred for serving the contracts inKw. Hence, the effective poten- tial profit, denoted Pd, that could be obtained by a carrier under the DPR context is :
Pd=
n
X
i=1
X
b∈Bi
pab −C(Kw)− X
k∈Kw
csk,
where pab is the price asked by the carrier in bid b and csk is the cost incurred by the carrier for subcontracting contract k.
Based on this, different profit-based performance measures are proposed to compare decentralized and centralized mechanisms taking into account the carrier’s risk behaviour.
For the DPA context, the gain/loss in total profit is denoted by ∆Pda and computed as:
∆Pda = Pc−Pi=n i=1Pid Pi=n
i=1Pid . (1)
For DPR, the gain/loss in total profit is denoted by ∆Pdr and computed as:
∆Pdr = Pc−Pd
|Pd| . (2)
Observe that Pd could take negative values if Kw and/or subcontracting costs csk, k∈Kw are relatively large.
An additional profit-based criteria is considered for the DPR context which takes into account only the contracts that can be served by the carrier’s network (contracts in Kw ). It is denoted by ∆Pdr, and is computed as:
∆Pdr = Pc−(Pn i=1
P
b∈Bipab −C(Kw)) Pn
i=1
P
b∈Bipab −C(Kw) . (3)
4.2. Contracts covered by submitted bids
This performance measure aims to compare the level of coverage of auc- tioned contracts between the two mechanisms. In other words, does a cen- tralized mechanism enable submitting bids on more contracts than a decen- tralized one? To make the measure independent of the number of auctioned contracts, we determine for each mechanism the percentage of covered con- tracts with respect to all auctioned contracts and compute the relative dif- ference in these percentages.
Recall that in a decentralized context, each shipper si, i = 1, . . . , n runs its proper auction A(si) to request transportation services for a set of contracts Ki. The carrier submits a set of bids toA(si), i= 1, . . . , n, we denoted by Bi
and each bidb inBi covers a set of contractsKb ⊂Ki. Then, the percentage of covered contracts in a decentralized mechanism is given by:
Qd = Pn
i=1
P
b∈Bi|Kb| Pn
i=1|Ki| .
In the centralized mechanism, a unique auction is run including all the con- tracts in ∪i=1,...,nKi. If we denote by Bc the set of bids submitted by the carrier to the centralized auction, then the percentage of contracts covered in a centralized mechanism is:
Qc= P
b∈Bc|Kb| Pn
i=1|Ki| .
The deviation in the percentage of covered contracts between the centralized and decentralized mechanisms, denoted by ∆Q, is thus given by:
∆Q= Qc−Qd
Qd . (4)
As mentioned before, under the DPR context, it is more likely that the carrier would subcontract certain contracts won to external entities due to a lack in its internal capacity. Hence, as for the profit-based performance measure, we consider an additional performance measure for the covered contracts -proper to the DPR context- in which we take into account only the contracts that could effectively be served by the carrier. This performance measure, denoted by ∆Q, is computed as:
∆Q= Qc−Qd
Qd where Qd= |Kw| Pn
i=1|Ki|. (5)
4.3. Empty movement distance
The total empty movement distance related to the carrier’s network re- flects its efficiency in vehicles utilization and consequently its ecological foot-
print. In our context, we aim to measure the relative difference (in percent- age) between the total empty move distances for both mechanisms.
Let Ec denote the total empty move distance associated with the carrier’s network to serve the contracts covered by the bids submitted in the central- ized auction A(S). Ec is computed based on the set of routes output by the BCP algorithm applied for A(S).
For the decentralized mechanism, the total empty move distance is computed differently depending on the risk-behaviour of the carrier. This is due to the fact that not all the contracts bid on in a DPR context would effectively be integrated in the carrier’s network. In this case, the total empty move distance is computed based on the network output by the BCP algorithm for which the set of new contracts is restricted to Kw. For the DPA context, the total empty movement distance is computed based on the carrier’s network output by the BCP algorithm run on the last auction A(sn).
In the following, we denote by Ed the total empty move distance associ- ated with the carrier’s final network in a decentralized context (obtained as explained before depending on the carrier’s risk attitude). Then, the empty- movement-based performance measure, denoted by ∆E, is given by:
∆E = Ec−Ed
Ed . (6)
4.4. Market diversification
This performance indicator aims to evaluate the opportunities offered to the carrier to make business with a variety of shippers. From the carrier’s perspective, diversifying its business partners helps to avoid losing large prof- its in case submitted bids are not won, or the shipper does not respect its commitments after the auction clearance. Based on this, we determine for each mechanism the percentage of contracts of shipper si, i = 1, . . . , n cov- ered by the carrier’s bids. Observe that for the DPR context, we consider only the contracts that can effectively be served by the carrier and not those subcontracted to external entities. The percentage of covered contracts of
shipper si is denoted by Vic, respectively, Vida and Vdri , for the centralized, respectively, the DPA and DPR mechanisms. Formally,
Vic = P
b∈Bc|Kb ∩Ki|
|Ki| , (7)
Vida = P
b∈Bi|Kb|
|Ki| , (8)
Vdri = |Kw ∩Ki|
|Ki| . (9)
5. Experimental Study
5.1. Problem tests
Our experimental study considers one carrier and three shippers s1, s2
and s3. Following our notation of Section 3, in a decentralized procurement mechanism, shipper s1 is the first to initiate an auction, followed by s2 then by s3. Table 1 describes the problem tests considered in our experimental study. Four main classes are generated depending on the geographical cov- erage (column “region”) of the existing and auctioned contracts: Quebec, Quebec-Ontario, Canada, and Canada-USA. Each class includes three in- stances sets that consider the same number of existing contracts |Ke| and the same restriction on the maximum tour duration Tmax (given in hours in Table 1). Recall that Ke represents the set of contracts the carrier already engage on before participating to the shippers’ auctions. Tmax is associated with the carrier operational constraints and represents the maximum route duration. The three instances sets of a given region differ by the total num- ber of new contracts|Kn|that takes three values: 100, 200 and 300. For each value of |Kn|, the number of contracts requested by shippers s1, s2 and s3 are generated as displayed under columns |K1|, |K2|, and |K3|, respectively.
For each instances set defined by the tuple (region, |Ke|, TM ax, |Kn|), five instances are generated by randomly selecting contracts’ origin and destina-
tion locations (for both existing and new contracts) in a list of 50 cities in North America taking into account the region attribute.
For all the problem tests (60 in total), the distances and the traveling times between all pairs of origin-destinations are generated using the software Optiroutesprovided by our research center. The maximum price that could be obtained by the carrier for serving a contract is generated based on the
spot prices information provided by the web sitehttp://www.uship.com/shipping- calculator.aspx in which we consider vehicles with a capacity of 40000 £.
The costs associated with charged (contracts), respectively, empty, move- ments are generated by multiplying the corresponding maximum price with a coefficient 0.5, respectively, 0.2.
Instances set Region |Ke| TM ax |Kn| |K1| |K2| |K3| 1
Quebec 50 40
100 32 28 40
2 200 65 50 85
3 300 100 107 93
4
Quebec-Ontario 100 80
100 32 28 40
5 200 65 50 85
6 300 100 107 93
7
Canada 200 120
100 32 28 40
8 200 65 50 85
9 300 100 107 93
10
Canada-USA 300 160
100 32 28 40
11 200 65 50 85
12 300 100 107 93
Table 1: Description of the instances sets
To compare centralized and decentralized mechanisms, we consider dif- ferent cases in which either two or three shippers centralize their auctions.
Table 2 describes the different alternatives. The column “Shippers” give the identity of the shippers to consider. The column “Order” gives the order in which the shippers initiate their respective auctions in a decentralized mech- anism. For example, for case 1, the 60 instances correspond to the data associated with shippers s1 and s2 (only the contracts in K1 and K2). The centralized mechanism includes only shippers s1 and s2. The decentralized
mechanism considers two decentralized auctions A(s1) followed by A(s2).
Case Shippers Order 1 s1,s2 s1→s2 2 s1,s3 s1→s3 3 s2,s3 s2→s3 4 s1,s2,s3 s1→s2→s3
Table 2: Cases for centralized and decentralized mechanisms’ comparison
The BCP algorithm of Ben Othmane et al. (2019) is coded inC+ + and embedded within a simulator. All the instances are solved on an IBM server with 2 processors Xeon E5450 and 32 GO RAM.
We report in the following sections the results obtained with regard to the performance measures described in Section 4. Section 5.2, respectively, Sec- tion 5.3, compares the results obtained for a CP mechanism to a DPA, re- spectively, a DPR mechanism.
5.2. Comparative results for CP and DPA
Table 3 summarizes the results obtained for ∆Pda, ∆Q and ∆E when comparing CP do DPA mechanisms. It reports the averages values for these measures obtained for each instance set and for the cases including the same number of shippers. For example, the relative gain in profit obtained for instances set 1 with a centralized versus a DPA mechanism is on average equal to 10% when considering all the instances (15 in total) corresponding to the cases where only two shippers are considered (cases 1,2 and 3 in Table 2) and to 12% when three shippers centralize their auctions (case 4).
Observe that a positive value of ∆Pdaimplies that the centralized mechanism generates more profit than the decentralized one. A negative value for ∆Q means that in a CP mechanism the carrier bids on less contracts than in a DPA one. Finally, a negative value for ∆E shows that the carrier’s network resulting from serving all the contracts bid on in the centralized auction includes less empty movements than that obtained by serving the contracts bid on in a DPA mechanism.
∆Pda(%) ∆Q(%) ∆E(%) Instances Nb. shippers Nb. shippers Nb. shippers
Set 2 3 2 3 2 3
1 10 12 -8 -17 -4 -4
2 5 3 -14 -21 1 3
3 2 4 -6 -6 0 -1
4 1 8 1 -5 -2 -5
5 10 9 -10 -20 -5 -1
6 -1 2 -13 -17 5 7
7 -3 0 1 -1 2 -1
8 1 18 -1 -2 0 -8
9 19 41 -1 1 -8 -14
10 -5 1 0 0 2 1
11 3 12 0 4 -2 0
12 7 12 0 -1 -2 -5
Average 4 10 -4 -7 -1 -2
Table 3: CP versus DPA: Average results for ∆Pda, ∆Qand ∆E
The results of Table 3 show that, when compared to a DPA mechanism, a CP mechanism generally enables a carrier to bid on less contracts while being offered the possibility to realize more profits and generate less empty moves when serving the contracts bid on. These gains are more important in case three shippers centralize their auctions.
Given that an analysis based only on averages values may not accurately reflect the actual performance of a mechanism, especially when there are too many variations between the instances, we present in the following more detailed results for each performance measure. More specifically, we report in Figure 1, respectively, Figures 2 and 3, the number of instances (y axis) for which the values of ∆Pda, respectively, ∆Q and ∆E, lie within specified intervals (x axis). In each Figure, we display the results obtained for the two-shippers and the three-shippers cases separately.
Figure 1: Gain/loss in profits for CP versus DPA
As depicted in Figure 1, participating in a centralized auction instead of
Figure 2: Variation in the percentage of contracts bid on in CP versus DPA
Figure 3: Gain/loss in empty movement distance for CP versus DPA
two decentralized ones (the case of two shippers) enables a carrier with an averse to risk behaviour to increase its potential profit by more than 2% for 102 instances over the 180 considered. For two instances the profit was the same and for 20 instances the increase in profit was less than 2%. Although for 56 instances the carrier would obtain less profit with a CP mechanism compared to a DPA one, this loss in profit does not exceed 2% for 25 in- stances. In case three shippers centralize their requests, the increase in the carrier’s profit is obtained for 54 instances over the 60 considered. For 26 instances, the profit was larger than 10% and for 34 instances it was larger than 5%. The increase in profit exceeds 30% for four instances.
Loss in potential profits obtained for some instances with a CP mechanism could be explained by the fact that the bid generation algorithm used in our experimental study is not exact: it outputs approximate solutions with no guarantee of their optimality. As explained in Section 3, the BCP heuristic selects the contracts to bid on based on the profit they generate when inte-
grated within a carrier’s existing route. Under the DPA context, the carrier’s existing network is updated from a decentralized auction to the next taking into account the contracts bid on in each auction. So, it may happen that in some situations, the alternatives offered to place an auctioned contract in an existing route under the DPA context are more profitable than those offered under a CP mechanism. To the best of our knowledge, there is no exact method reported in the literature that could solve to optimality BCP problems including up to 600 contracts. Moreover, the heuristic of Ben Oth- mane et al. (2019) has the great advantage to ensuring a non negative profit for the carrier independently of the bids won once the auction is cleared.
The results displayed in Figure 2 show that in a DPA mechanism, a carrier generally bids on either the same number or on a larger number of contracts than in a CP mechanism. When two shippers are considered, the number of contracts covered by submitted bids was larger for 99 instances and equal for 41 instances over the 180 considered. When three shippers centralize their auctions, the bids submitted by the carrier in a DPA mechanism cover more contracts for 40 instances over the 60 considered. They cover the same number of contracts for five instances.
Regarding the empty move measure, the results of Figure 3 prove that for the majority of the instances, there is a gain in empty movement distances when a CP mechanism is used. This gain is even more observable when the number of shippers centralizing their requests increases from two to three.
The gain in empty movement distance obtained under a CP mechanism ex- ceeds 5% for 21.66%, respectively, 35%, of the instances when two, respec- tively, three shippers are considered. For the instances where the carrier’s network incorporates larger empty movement distances for a CP mechanism, this increase exceeds 5% only for 18, respectively, 7, instances when two, respectively, three, shippers centralize their requests.
Figure 4 displays the results obtained for the market diversification per- formance measure for the case including three shippers (60 instances in total).
It reports, for each shipper, the number of instances for which the percentage of contracts covered by the carrier’s bids lies within a specified interval. These values are reported for both mechanisms CP and DPA as defined in equations (7) and (8), respectively. As one can notice, a CP mechanism generally en- ables a carrier to diversify its business so that it is not dependent on a single shipper. This is clearly not the case for a DPA mechanism in which the car- rier’s bids cover almost only the contracts of shipper s1 (V1da ∈[90%,100%]) - the first to run a decentralized auction. The distribution of Vic values, i= 1, . . . ,3 is much more balanced for a CP mechanism.
Figure 4: Market diversification: CP versus DPA
5.3. Comparative results for CP and DPR
Table 4 compares the results obtained for CP and DPR mechanisms.
It reports the averages values obtained for performances measures ∆Pdr,
∆Pdr, ∆Q, ∆Q and ∆E. These averages are computed for each instances set and for the cases including the same number of shippers. As explained in Section 3, in a DPR mechanism the carrier constructs the bids to submit to each decentralized auction taking into account its full capacity as if no bids submitted to previous auctions would win. ∆Pdr measures the relative gain/loss in potential profit that could be obtained by the carrier taking into account its limited capacity and the fact that it could pay large costs to obtain the lacking capacity from external entities. ∆Pdr gives the potential
profit that could be realized by the carrier with its own capacity taking into account only the contracts that can be really served by it and ignoring those subcontracted to other service providers.
∆Pdr(%) ∆Pdr(%) ∆Q(%) ∆Q(%) ∆E(%)
Instances Nb. shippers Nb. shippers Nb. shippers Nb. shippers Nb. shippers
set 2 3 2 3 2 3 2 3 2 3
1 491 176 0 0 -45 -67 0 0 0 0
2 752 244 0 0 -53 -71 0 0 0 0
3 725 176 0 1 -52 -68 0 0 0 0
4 4 582 0 0 -2 -26 0 0 0 0
5 502 174 0 0 -44 -66 0 0 0 0
6 1054 649 1 0 -54 -70 1 0 -1 0
7 6 5 1 1 -1 -4 2 0 1 0
8 25 111 1 0 -10 -31 0 -2 0 0
9 122 513 0 0 -31 -48 0 0 0 0
10 -1 -7 0 0 0 -3 0 0 0 0
11 9 56 0 0 -17 -35 0 0 0 0
12 86 842 0 0 -31 -50 0 0 0 0
Average 315 293 0 0 -28 -45 0 0 0 0
Table 4: CP versus DPR: Average results for ∆Pdr, ∆Pdr, ∆Q, ∆Qand ∆E
The results of Table 4 show that participating in a centralized procure- ment auction enables a carrier to obtain almost the same potential profit than the one it could realize by its available capacity when participating in decentralized auctions with a risky behaviour (∆Pdr = 0 for almost all the instances). Most importantly, the potential profit for a CP mechanism is ob- tained with the guarantee that the contracts bid on could be ensured by the carrier’s own capacity. For a DPR mechanism, a lack in capacity is recurrent and generally results in considerable additional costs making the deviation in profits with regard to the CP context very large. This can be observed under the column ∆Pdr: 842 % for some instances and 304% on average for all the instances.
The same trend is observed for ∆Qand ∆Q. For a CP mechanism, the car- rier bids on almost the same number of contracts than the ones it can serve with its own fleet in a DPR context (∆Q = 0 for almost all the instances).
Contrarily to CP, in a DPR mechanism the number of contracts that could be effectively ensured by the carrier are much less than those bid on: up to
−71% for some instances and −36.5% on average over all the instances.
Finally, when considering the carrier’s network required to serve the contracts bid on, the total empty move distance yielded is almost the same under both
contexts. Observe that for instances set 10, the carrier has all the required capacity to serve all the contracts bid on in all decentralized auctions. This results in better profits due to the approximate BCP algorithm used as ex- plained earlier.
As in Section 5.2, we report in Figures 5, 6 and 7 the number of instances for which ∆Pdr, respectively ∆Q and ∆E, values lie within specified inter- vals. The detailed results displayed in these figures confirm our previous analysis based on the average results of Table 4.
Figure 5: Gain/loss in profits for CP versus DPR
Figure 6: Variation in the percentage of contracts bid on in CP versus DPR
Figure 8 compares the results for the market diversification measures ob- tained for the CP and DPR mechanisms computed with equations (7) and (9). As expected based on the results obtained for the other performance measures, a CP mechanism offers almost the same opportunity for diversify- ing the carrier’s business as a DPR mechanism.
As a conclusion, our experimental study clearly proves that a centralized
Figure 7: Gain/loss in empty movement distance for CP versus DPR
Figure 8: Market diversification: CP versus DPR
procurement mechanism offers generally the best alternative for the carrier to increase its profit as if it participated in multiple decentralized auctions with a risky attitude. This is ensured without incurring the risk that the contracts bid on cannot be served by its own network. Furthermore, a CP mechanism is generally the alternative that allows the carrier not only to design a network where empty movements are reduced but also to diversify its business partners.
6. Conclusion
In this paper, we proposed a novel FTL transportation procurement mechanism where different shippers centralize their requests and run together a single combinatorial auction offering thus to the bidding carriers the pos- sibility to submit in the same package bid contracts belonging to different
shippers. To highlight the benefits of such a mechanism on the carrier, we compared it to a decentralized mechanism where each shipper runs separately its own combinatorial auction. These decentralized auctions are assumed to be run in a context where the carrier doesn’t know if the bids submitted to an auction has won when participating into the next one. Based on this, we considered two extreme scenarios that take into account the risk behaviour attitude of the carrier when generating its bids for the decentralized auctions:
an averse-to-risk and a risky attitudes. Our results prove that a centralized procurement mechanism generally offers the best alternative with regard to the potential profit that could be obtained by the carrier, its network effi- ciency and the diversity of the shippers it would commit with.
Although a centralized procurement auction has proven to be beneficial for carriers on different levels, it requires willingness from a number of shippers to centralize their requests. Hence, the next step would be to study the advantages/drawbacks of centralized mechanisms on shippers.
Acknowledgments
This research was supported by the Natural Sciences and Engineering Research Council of Canada (NSERC) under grant 2016-04482. This support is gratefully acknowledged.
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