Assessing the impact on optimal production capacities in a closed-loop logistics system of the assumption that returns are stochastically independent of sales

Purpose: This paper is concerned with a reverse logistic system where returns are stochastically dependents on sales. The aim of the paper is to assess the influence on optimal production capacities when is assumed that returns are stochastically independent of sales. Design/methodology/approach: This paper presents a model of the system. An approximated model where is assumed that returns are stochastically independent of sales, is formulated to obtain the optimal capacities. The optimal costs of the original and the approximated models are compared in order to assess the influence of the assumption made on returns. Findings: The assumption that returns are stochastically independent of sales is significant in few cases. Research limitations/implications: The impact of the assumption on returns is assessed indirectly, by comparing the optimal costs of both models: the original and approximated. Practical implications: The problem of calculating the optimal capacities in the original model is hard to solve, however in the approximated model the problem is tractable. When the impact of the assumption that returns are stochastically independent of sales is not significant, the approximated model can be used to calculate the optimal capacities of the original model. Originality/value: Prior to this paper, few papers have addressed with the problem of calculating the optimal capacities of reverse logistics systems. The models found in these papers assumed that returns are stochastically independent of sales.