A multi-stage stochastic integer programming approach for a multi-echelon lot-sizing problem with returns and lost sales - Quezada, Franco; Gicquel, Céline; Kedad-Sidhoum, Safia; Vu, Dong Quan (Computers & operations research, 2020)
•We study a multi-echelon stochastic lot-sizing problem within remanufacturing environment.•It is modelled as a multi-stage stochastic integer program and solved by a Branch & Cut algorithm.•We propose a new family of tree valid inequalities generated by a mixing procedure.•A heuristic algorithm is studied to solve the separation problem.•The time needed to obtain guaranteed optimal solutions is significantly reduced and the value of the stochastic solution is assessed providing significantly improvement. We consider an uncapacitated multi-item multi-echelon lot-sizing problem within a remanufacturing system involving three production echelons: disassembly, refurbishing and reassembly. We seek to plan the production activities on this system over a multi-period horizon. We consider a stochastic environment, in which the input data of the optimization problem are subject to uncertainty. We propose a multi-stage stochastic integer programming approach relying on scenario trees to represent the uncertain information structure and develop a branch-and-cut algorithm in order to solve the resulting mixed-integer linear program to optimality. This algorithm relies on a new set of tree inequalities obtained by combining valid inequalities previously known for each individual scenario of the scenario tree. These inequalities are used within a cutting-plane generation procedure based on a heuristic resolution of the corresponding separation problem. Computational experiments carried out on randomly generated instances show that the proposed branch-and-cut algorithm performs well as compared to the use of a stand-alone mathematical solver. Finally, rolling horizon simulations are carried out to assess the practical performance of the multi-stage stochastic planning model with respect to a deterministic model and a two-stage stochastic planning model.