Achieving a Long-Term Service Target with Periodic Demand Signals: A Newsvendor Framework

Abstract

We deal with the problem of a profit-maximizing vendor selling a perishable product. At the beginning of a planning cycle, the vendor determines a minimum committed order per period. During the cycle, he may also place a supplemental order in each period based on the observed demand signal in that period. Moreover, the vendor is committed to a specific service target evaluated over the planning cycle. This is a complex problem, and we, as an approximation, offer a single-period, two-stage modeling approach. Under this approach, the vendor determines a first-stage order as the minimum committed order with the possibility of supplementing it based on a demand signal observed at the second stage. The problem is to maximize his expected profit subject to a constraint on his overall service performance across all possible values of the demand signal. We characterize the optimal policy for in-stock rate and fill-rate targets, and make comparisons. Whereas in the classical newsvendor model a service target can be replaced by a single unit shortage cost, it is not so in our model. Instead, a set of unit shortage costs are imputed—one for each demand signal. The imputed shortage costs reflect trade-offs among the profits under different demand signals in meeting the service targets. We also show that under a given ordering policy, the in-stock rate is lower (higher) than the fill rate when the demand has an increasing (decreasing) hazard rate. This result suggests that the vendor can infer a fill-rate measure from the corresponding in-stock rate without the difficult task of tracking lost sales. Furthermore, we analyze how the order quantity varies according to the observed signal, which allows us to formalize the notion of a valuable demand signal.

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