Combinatorial clock-proxy exchange for carrier collaboration in less than truck load transportation

Highlights

• A carrier collaboration problem in LTL transportation is studied.

• Combinatorial clock-proxy exchange is applied to the problem for the first time.

• This mechanism is better adapted to the problem than combinatorial auctions.

• Experimental results are quite promising.

• They show the indispensability of the proxy phase of the mechanism.

Abstract

A carrier collaboration problem in less-than-truck load transportation is considered, where multiple carriers exchange their pickup and delivery requests in order to improve their operational efficiency. We extend the clock-proxy auction proposed by Ausubel et al. (2006) to a combinatorial clock-proxy exchange for the problem. This mechanism combines the price discovery of the clock exchange designed based on Lagrangian relaxation with the efficiency of the proxy exchange determined based on the information observed in the clock phase. Numerical experiments on randomly generated instances demonstrate the necessity of the proxy phase and the effectiveness of the clock-proxy exchange.

Introduction

Collaboration among small to medium-sized freight carriers are emerging as an effective strategy for them to improve profitability by reducing empty vehicle repositions and increasing vehicle fill rates. An empirical study conducted by Cruijssen et al. (2007) indicates the potential benefits of horizontal cooperation in logistics. Some pilot projects implemented in USA show that Collaborative Transportation Management (CTM) can reduce the mileage traveled by empty vehicles by 15%, reduce the waiting and pause time of vehicles by 15%, increase the fill rate of vehicles by 33%, and reduce the turnover/change of drivers by 15% (Sutherland, 2009).

In carrier collaboration, multiple carriers form an alliance and exchange their transportation requests so that each carrier can find its complementary requests from other carriers while outsourcing unprofitable requests. Such exchange can increase the vehicle fill rates of the carriers and consequently reduce their transportation costs. One problem for carrier collaboration is to optimally exchange (reallocate) requests among carriers so that their total profit is maximized. Another problem is to fairly allocate the total profit gained by the collaboration among all carriers in the alliance so that they are willing to collaborate with each other to achieve their maximum total profit. In this paper, we address the first problem which is also referred to as collaborative transportation planning problem.

Collaborative transportation planning among carriers may be realized by using a centralized approach based on a centralized mathematical programming model or by using a decentralized approach such as combinatorial auctions or exchanges. Because carriers are generally autonomous units or even competitors, they do not want to reveal their confidential business data to other carriers. Such data include transportation costs and prices paid by customers to serve transportation requests. For this reason, the dominating approach for collaborative transportation planning is combinatorial auctions. In almost all combinatorial auctions for carrier collaboration, there are a virtual or real auctioneer and multiple bidders which are carriers. Before an auction, each carrier identifies a set of unprofitable requests to be outsourced to other carriers. This set is submitted to the auctioneer, who announces the outsourcing requests of all carriers late. The auction may be a single round sealed-bid auction or an iterative multi-round auction. In the first case, all carriers first submit their bids (desired bundles of requests and associated prices) to the auctioneer, who then determines the winning carriers and their winning bids by solving a winner determination problem. In the second case, the auctioneer determines/updates the price for servicing each outsourcing request, and each carrier determines which requests to acquire from the other carriers based on the prices announced by the auctioneer in each round. The main problem for implementing a single-round combinatorial auction is that each carrier, who is a bidder, has to identify one or few desired bundles of requests from an exponential number of possible bundles (Triki et al., 2014, Kuyzu et al., 2015). This problem may be intractable in terms of computational complexity. On the other hand, an iterative multi-round combinatorial auction may suffer from the difficulty of reaching market-clearing prices, which may lead to an inefficient request allocation. Here, the market-clearing prices are the prices at which supply equals demand for each outsourcing request. In fact, such market-clearing prices may not exist. Moreover, most combinatorial auctions proposed in the literature are not well adapted to carrier collaboration since all carriers are both sellers and buyers. For those combinatorial auctions, the offering phase in which each carrier determines its requests to outsource (sell) and the bidding phase in which each carrier determines the requests to acquire (buy) are separated and carried out sequentially. Although such separation can reduce computational complexity, a carrier may face a suboptimal or even an infeasible transportation plan if it wins a bid whose feasibility relies on the assumption that all its outsourcing requests are sold to other carriers but some of the requests may be not sold out finally. To avoid the risk of generating such infeasibility, in some auctions (Ackermann et al., 2011), each offering bundle of requests of a carrier is also considered as a bidding bundle of the same carrier, but the determination of the price for such bundle is a challenging problem, and it may be more favorable if some requests of the bundle are sold out to other carriers. Since each carrier plays double roles (seller and buyer) in carrier collaboration, it is natural to apply combinatorial exchanges rather than combinatorial auctions for the exchange of requests among them. However, to the best of our knowledge, no previous study applied combinatorial exchanges to carrier collaboration, let alone combinatorial clock-proxy exchange. Note that the word “exchange” has appeared in the titles of some published papers, but they really deal with combinatorial auctions rather than combinatorial exchanges.

In this paper, we consider carrier collaboration in less-than-truck load transportation, where multiple carriers exchange their pickup and delivery requests with time windows in order to improve their profitability. Motivated by the clock-proxy auction proposed by Ausubel et al. (2006), we develop a Combinatorial Clock-Proxy Exchange (CCPE) for the carrier collaboration. This exchange has two phases. The first clock phase is an iterative exchange designed based on Lagrangian relaxation, whereas in the second proxy phase, the bids that each carrier submits to its proxy agent are determined based on the information observed in the clock phase. The proposed approach combines the simple and transparent price discovery of the clock exchange with the efficiency of the proxy exchange. Numerical experiments on randomly generated instances demonstrate the necessity of the proxy phase and the effectiveness of the clock-proxy exchange.

The main contributions of this paper include: (1) it extends the combinatorial clock-proxy auction proposed by Ausubel et al. (2006) to a combinatorial clock-proxy exchange (CCPE) and applies the latter to carrier collaboration for the first time. (2) In the work of Ausubel et al. (2006), they proposed the combinatorial clock-proxy auction mechanism but did not provide any concrete method for the generation of proxy bids. We have provided such method in the context of carrier collaboration and proved by numerical experiments that the method of generating proxy bids is effective and the proxy phase is indispensable for the CCPE to be effective. (3) Our numerical experiments show that the Walrasian mechanism outperforms the ascending mechanism for price discovery, and no significant variation exists in the allocation of requests among carriers found by CCPE when the auctioneer maximizes its revenue or the profit of all carriers.

The rest of this paper is organized as follows: Section 2 reviews previous studies on collaborative transportation planning and combinatorial auctions/exchanges that are related to our work. Section 3 describes the problem studied in this paper and its centralized mathematical programming model. Section 4 presents the CCPE for carrier collaboration proposed in this paper. Section 5 presents and analyzes the results of numerical experiments on the combinatorial exchange. Section 6 concludes this paper with perspectives for future research.