Joint-Replenishment Problem under stochastic demands with backorders-lost sales misture, controllable lead times and investment to reduce the major ordering cost

In this paper, we study the periodic-review stochastic Joint-Replenishment Problem (JRP), with backorders-lost sales mixtures, controllable lead times and investment to reduce the major ordering cost. The purpose is to determine a strict cyclic replenishment policy, the length of lead times, and the major ordering cost that minimize the total system cost. We first present an effective heuristic algorithm to approach the problem. However, results illustrate how computationally expensive the algorithm would be for a practical application. Hence, we then propose an efficient and more practically applicable solution procedure. In particular, approximating part of the cost function with its second-order Taylor series expansion, we obtain an expression that resembles the deterministic cost structure. Therefore, the problem can be approached exploiting a standard algorithm suitable for the deterministic JRP. Numerical tests compare the performances of the algorithms developed and show that the approximated approach is actually promising for a practical application.