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

Manufacturing & Service Operations Management, Forthcoming

McCombs Research Paper Series No. IROM-10-09

42 Pages Posted: 25 Feb 2009 Last revised: 28 May 2010

See all articles by Alain Bensoussan

Alain Bensoussan

University of Texas at Dallas - Naveen Jindal School of Management; Hong Kong Polytechnic University - Faculty of Business; Ajou University

Qi Feng

Purdue University - Krannert School of Management

Suresh Sethi

University of Texas at Dallas - Naveen Jindal School of Management

Date Written: May 1, 2010

Abstract

We deal with the problem of a profit-maximizing vendor selling a perishable product. At the beginningof 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. While 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.

Keywords: Inventory models, newsvendor problem, service constraint, Kuhn-Tucker conditions, Two-stage newsvendor, forecast updates, aggregate service target, long-term service level, infinite-dimensional problem, Chance constraints

JEL Classification: M11, C61

Suggested Citation

Bensoussan, Alain and Feng, Qi and Sethi, Suresh, Achieving a Long-Term Service Target with Periodic Demand Signals: A Newsvendor Framework (May 1, 2010). Manufacturing & Service Operations Management, Forthcoming, McCombs Research Paper Series No. IROM-10-09, Available at SSRN: https://ssrn.com/abstract=1348648

Alain Bensoussan

University of Texas at Dallas - Naveen Jindal School of Management ( email )

800 West Campbell Rd
SM 30
Richardson, TX 75080-3021
United States
9728836117 (Phone)

HOME PAGE: http://www.utdallas.edu/~axb046100/

Hong Kong Polytechnic University - Faculty of Business

Dept SEEM
Systems Engr * Engr Mgmt
Hong Kong, Hong Kong
China

Ajou University ( email )

Ajou
France

Qi Feng

Purdue University - Krannert School of Management ( email )

1310 Krannert Building
West Lafayette, IN 47907-1310
United States

Suresh Sethi (Contact Author)

University of Texas at Dallas - Naveen Jindal School of Management ( email )

800 W. Campbell Road, SM30
Richardson, TX 75080-3021
United States

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