Distribution-free approach for stochastic Joint-Replenishment Problem with backorders-lost sales mixtures, and controllable major ordering cost and lead times

In this paper, we study the periodic-review Joint-Replenishment Problem (JRP) with stochastic demands and backorders-lost sales mixtures. We assume that lead times aare made of two major components: a common part to all items and an item-specific portion. We further suppose that the item-specific component of lead times and the major ordering cost are controllable. To reflect the practical circumstance characterized by the lack of complete information about the demand distribution, we adopt the minimax distribution-free approach. That is, we assume that only the mean and the variance of the demand can be evaluated. The objective is to determine the strict cyclic replenishment policy, the length of (the item-specific component of) lead times, and the major ordering cost that minimize the long-run expected total cost. To approach this minimization problem, we present a first optimization algorithm. However, numerical tests highlighted how computationally expensive this algorithm would be for a practical application. Therefore, we then propose two alternative heuristics. Extensive numerical experiments have been carried out to investigate the performance of the developed algorithms. Results have shown that the proposed alternative heuristics are actually efficient and seem therefore promising for a practical application.