This paper examines the effects on the optimal ordering policy (and its cost) of allowing for interactions among retail outlets. Specifically, transshipments are allowed as recourse actions occurring after demands are realized but before they must be satisfied. The resultant savings in holding and shortage costs are balanced against the costs of transshipment. A base stock ordering policy is optimal for this model. If the final period base stock order-up-to point is nonnegative, then it will be the base stock order-up-to point for all periods; unfortunately, it can be found analytically only for two special cases, where either the cost parameters are equal at every outlet or there are only two outlets. These two special cases are used to validate a heuristic solution technique employing Monte Carlo integration, which is then compared to an easily calculated base policy in order to gauge the contribution of this model. The additional savings from using this heuristic policy are significant, particularly for problems with many retail outlets and low transshipment costs.

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This paper compares two types of appointment-scheduling policies for single providers: traditional and open-access. Under traditional scheduling, each of a specified number of patients per day is booked well in advance, but may not show up for his or her appointment. Under open-access scheduling, a random number of patients call in the morning to make an appointment for that same day. Thus the number of patient arrivals will be random, for different reasons, under both policies. We find that the open-access schedule will significantly outperform the traditional schedule--in terms of a weighted average of patients' waiting time, the doctor's idle time, and the doctor's overtime--except when patient waiting time is held in little regard or when the probability of no-shows is quite small.service operations, health-care management

This paper addresses the question of when to refuse discount bookings from airline passengers to reserve seats for potential future passengers who are willing to pay a higher fare. When passengers arrive in sequential fare classes, the optimal policy will be to accept reservation requests as long as the cumulative seats booked does not exceed a given booking limit. This paper relates the probability of filling the plane, under the optimal policy, with the ratios of the current to the highest remaining fare classes. In addition, it extends the solution from monotonically increasing fares to fares occurring in arbitrary order. Finally, it demonstrates how Monte Carlo integration is easy to use to get arbitrarily close approximations to the optimal policy.

Order crossover occurs whenever replenishment orders do not arrive in the sequence in which they were placed. This paper argues that order crossover is becoming more prevalent and analyzes the dangers of ignoring it. We present an exact iterative algorithm for computing the distribution of the number of orders outstanding, and formulae for the inventory shortfall distribution (the quantity of inventory in replenishment at the start of a period) and the more common lead-time demand distribution, which are different when order crossover is possible. The lead-time demand distribution can have much higher variability than the shortfall distribution. We show that basing inventory policies on the lead-time demand distribution---rather than the shortfall distribution---can lead to significantly higher inventory cost, even if the probability of order crossover is small. We give an alternative proof to that of Zalkind (1976), which shows that the variance of shortfall is less than the variance of the standard lead-time demand.Inventory Policies, Stochastic Lead Time, Order Crossover