An efficient heuristic for joint replenishment problems

We consider joint replenishment problems with stochastic demands. A major setup cost is incurred for every order, and a minor, item specific setup cost is incurred for every item. Proportional holding cost is incurred for every item carried from one period to the next period, and proportional shortage cost is incurred for every item unable to be filled immediately on demand. In this paper, we present a mixed integer linear programming (MILP) formulation, which employs the piecewise linearization technique, for computing the near-optimal policies. In contrast to other approaches in the literature, our heuristic can be easily implemented and solved by using off-the-shelf mathematical programming packages. Computational experiments demonstrate that the optimality gap of the MILP model is tighter and the computational time is reasonable.