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 to impose his optimal replenishment plan to the supplier. Our concern is on the minimization of the supplier's cost. In order to influence the retailer's planning decisions, the supplier can propose a side payment to the retailer by offering a contract to the retailer composed of a replenishment plan and a side payment. The focus of analysis is on evaluating how much the supplier can gain by designing contracts under complete or asymmetric information assumption. Different scenarios are identified and explored depending on the side payment coverage. We set the boundary between polynomially solvable and NP-complete cases. Under complete information, we show that for some scenarios the problem of designing contracts can be solved in polynomial time. Whereas if the side payment is on the retailer's holding cost, we prove that the problem of designing contracts is weakly NP-hard. Under asymmetric information, the problem without side payment is still polynomial. When side payment is allowed, we show that the supplier's cost can be arbitrarily large compared to the cost obtained under complete information assumption. We provide an experimental analysis that shows that side payment restricted to the retailer's holding cost is sufficient to decrease the cost of the supplier: the supplier's gain (resp. expected gain) can reach 30.8% (resp. 31%) under complete (resp. asymmetric) information assumption. We extend the experimental analysis in order to evaluate the supplier's gain when more than one retailer is considered.
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