An effective heuristic for the review period in an inventory model with staggered deliveries and normal demands

Consider a single-item, periodic review, infinite-horizon, undiscounted, inventory model with stochastic demands, proportional holding and shortage costs, and full backlogging. Orders can arrive in every period, and the cost of receiving them is negligible (as in JIT). Every T periods, one audits the stocks and chooses a delivery schedule for each of the next T periods, thus incurring a fixed audit cost and—when one schedules actual deliveries—a fixed order cost. The problem is to find a review period T and an ordering policy minimizing the average cost. An earlier article developed an algorithm for computing an optimal T, and undertook a numerical study to evaluate various approximations. Assuming normal demands, we characterize the asymptotic behavior (for large μ/σ) of the optimal T and establish the asymptotic optimality of a heuristic, calculable on a spreadsheet. A numerical study indicates that patterns established here for large μ/σ hold for σ/μ above 2.