A heuristic joint replinishment policy for the case of heterogeneity among items

The Q(s,S) policy is considered among the best for solving the well-known stochastic joint replenishment problem. However, it has some shortcomings if much heterogeneity exists among the items. Consequently, a new heuristic control policy is constructed. The cornerstone is a policy iteration improvement step, assuming a single possibility for making a joint order and thus to deviate from the rule that the items are governed by independent, re-order and order-up-to, (s,S) policies. But this policy iteration improvement step is done repeatedly at each demand epoch. It is only required the development of one-dimensional value functions of state variables in order to accomplish the policy iteration improvement step. Knowledge about good order-up-to values is important. Furthermore, a relaxation parameter α is introduced such that one can, make it easier or more difficult to issue a joint order, when following the policy iteration improvement step. Finally, in case a joint order is made, a vector of can-order points is used to include additional items. The policy is denoted a (c,S,α) policy. Numerical results shows that the new policy performs significantly better than the Q(s,S) policy for cases with heterogeneity among items. Furthermore, from a given optimal can-order policy, one can construct a better (c,S,α) policy.