Coordination of a two-level supply chain with contracts
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Coordination of a two-level supply chain with contracts Siao-Leu Phouratsamay1 · Safia Kedad-Sidhoum3 · Fanny Pascual2 Received: 28 April 2019 / Revised: 15 February 2020 © Springer-Verlag GmbH Germany, part of Springer Nature 2020
Abstract We consider the coordination of planning decisions of a single product in a supply chain composed of one supplier and one retailer, by using contracts. We assume that the retailer has the market power: he can impose his optimal replenishment plan to the supplier. Our aim is to minimize the supplier’s cost without increasing the retailer’s cost. To this end, the supplier (or a trusted third party) proposes to the retailer a contract, which is made of a replenishment plan and a side payment. This side payment compensates the increase of cost of the retailer due to the fact that the proposed replenishment plan may have a cost larger than the retailer’s optimal replenishment plan. We evaluate how much the supplier can gain by using contracts under several scenarios which depend on the side payment coverage. From a theoretical point of view, in all the scenarios, contracts may decrease the cost of the supplier by an arbitrarily large factor. We perfom experiments which measures the gain that can be obtained in practice on various instances types. If side payments are allowed, experiments show that the use of contracts decreases significantly the cost of the supplier, and that side payments on the holding costs are sufficient. We show that if there is no side payment, or if there is no constraint on the side payment, then the problem can be solved in polynomial time. On the contrary, if the side payment is limited to the holding costs of the retailer, then the problem is NP-hard. We extend this study to the case where the information is asymmetric (the supplier—or the trusted third entity—does not know all the costs of the retailer): in this case, the situation is modelled by a screening game. Keywords Supply chain management · Dynamic lot-sizing · Contracts · Complexity analysis · Screening game Mathematics Subject Classification 90B05 Inventory, storage, reservoirs · 90B06 Transportation, logistics and supply chain management · 91-08 Computational
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Siao-Leu Phouratsamay [email protected]
1
Inria Bordeaux Sud-Ouest RealOpt, IMB UMR CNRS 5251, Talence, France
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Laboratoire d’Informatique de Paris 6, LIP6, Sorbonne Université, CNRS, 75005 Paris, France
3
CNAM-CEDRIC, 75141 Paris Cedex 03, France
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S.-L. Phouratsamay et al.
methods for problems pertaining to game theory, economics, and finance · 68Q25 Analysis of algorithms and problem complexity · 91A68 Algorithmic game theory and complexity
1 Introduction We address the problem of coordinating planning decisions in a supply chain for a single item. We consider a supply chain with two actors: one supplier and one retailer. In general, the supplier and the retailer are individual entities with conflicting objectives. Each of them wants to optimize his decisions in his best interest. However, there are some supp
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