Simulated Annealing–Golden section algorithm for the multiproduct replenishment problem with stochastic demand.

Abstract

The joint replenishment problem (JRP) has been studied for over 30 years and there are both heuristic and exact algorithms to determine the frequency of orders and fundamental cycle; in recent years it has been considered the model with stochastic demand. If we assume a behavior of normal distribution for the demand, we may obtain a non linear mixed-integer programming for costs, for which only is reported one heuristic solving method. In this paper we propose a simulated annealing algorithm with golden section for one-dimensional search in order to solve the JRP considering a normal distribution demand. Its performance is compared with the reported heuristic method. The results showed that the new algorithm obtains lower costs.