Accès Online First (SpringerLink)International audienceIn this paper, we study a structure issued from a real case. Raw materials (RMs) are sent by suppliers to a distribution center (DC) and then transported to a unique plant where they can be stored. The inventory capacity is limited in the plant as well as in the DC. The transportation capacity between the DC and the plant is also limited. The objective is to determine the flows between suppliers and the DC, and from the DC to the plant in order to satisfy the demand during the planning horizon while minimizing the global cost. A mixed-integer programming (MIP) formulation is presented and a Lagrangean relaxation solution procedure is proposed. Computational experiments are carried out

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In this paper we study the coordination of different activities in a supply chain issued from a real case. Multiple suppliers send raw materials (RMs) to a distribution center (DC) that delivers them to a unique plant where the storage of the RMs and the finished goods is not possible. Then, the finished goods are directly shipped to multiple customers having just‐in‐time (JIT) demands. Under these hypotheses, we show that the problem can be reduced to multiple suppliers and one DC. Afterwards, we analyze two cases; in the first, we consider an uncapacitated storage at DC, and in the second, we analyze the capacitated storage case. For the first case, we show that the problem is NP‐hard in the ordinary sense using the Knapsack decision problem. We then propose two exact methods: a mixed integer linear program (MILP) and a pseudopolynomial dynamic program. A classical dynamic program and an improved one using the idea of Shaw and Wagelmans are given. With numerical tests we show that the dynamic program gives the optimal solution in reasonable time for quite large instances compared with the MILP. For the second case, the capacity limitation in DC is assumed, which makes the problem solving more challenging. We propose an MILP and a dynamic programming‐based heuristic that provides solutions close to the optimal solution in very short times.