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.
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Notes
We recall that a cost parameter is stationary if it is constant over the planning horizon.
Different cost structures have been considered for \(p^S\) in a preliminary work. The results show that: for \(p^S \in [1,10]\) or \(p^S \in [1,50]\), the supplier’s gain when \(p^S\) is stationary is significantly smaller than the one obtained when \(p^S\) is not stationary. For \(p^S \in [40,50]\), the supplier’s gain does not depend on the stationarity assumption of \(p^S\). Moreover, when \(p^S \in [1,10]\) or \(p^S \in [40,50]\), the supplier’s gain is smaller than the one observed when \(p^S \in [1,50]\). The previous behavior can be explained by the fact that when \(p^S\) is not stationary, the number of plans allowing the supplier’s to decrease his cost are larger compared to the case where it is stationary. Preliminary results also show that other values of \(\delta \) do not change the qualitative results of the analysis. Both costs \(f^S\) and \(f^R\) are computed using \(\delta \) implying that there is a correlation between the results.
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Acknowledgements
This work was supported by FUI project RCSM “Risk, Credit Chain & Supply Chain Management”, financed by Région Ile-de-France. The authors declare that the experiments comply with the current laws of the country in which they were performed.
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Phouratsamay, SL., Kedad-Sidhoum, S. & Pascual, F. Coordination of a two-level supply chain with contracts. 4OR-Q J Oper Res 19, 235–264 (2021). https://doi.org/10.1007/s10288-020-00443-0
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DOI: https://doi.org/10.1007/s10288-020-00443-0