Optimal Ordering Policy and Value of Information under Delayed Lost Sales Observations

30 Pages Posted: 5 Nov 2008 Last revised: 18 Jan 2009

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

M. Çakanyıldırım

University of Texas at Dallas - Naveen Jindal School of Management

Qi Feng

Purdue University - Krannert School of Management

Suresh Sethi

University of Texas at Dallas - Naveen Jindal School of Management

Date Written: October 2008

Abstract

Under many circumstances, demand observations are often censored due to the lack of tracking lost sales caused by stockouts. To understand the impact of the lost sales information on the ordering decisions, a periodic-review inventory model is formulated in which only the sales information is obtained immediately upon the realization of the demand. This is equivalent to observing the demand when the sales are less than the available stock and to inferring that the demand is higher than the stock when there is a stockout. Subsequently, the lost sales information is obtained after a delay. In the resulting model, an optimal policy, if exists, reveals a very complex structure. By decomposing the derivative of the value function, we demonstrate two different roles of inventory in our model: satisfying the demand and extracting the demand information. We show that the optimal inventory levels under the delayed observation of the lost sales are always higher than those for which the demands are fully observed. Moreover, as illustrated in numerical examples, the optimal policy possesses a counterintuitive behavior with respect to the problem parameters. To understand the key drivers of the optimal decisions, we further compare the costs under different demand observations. Two important observations are made. First, a lower cost is obtained when the realized demand is observed than when the demand is only observed to be higher than the inventory level, and, furthermore, the cost difference represents the value of demand information. Second, while a higher inventory level induces a more accurate demand forecast, the value of exact demand observation is not monotone in the procurement cost. Consequently, the optimal ordering quantity is not always decreasing in the procurement cost.

Keywords: Inventory, newsvendor problem, partial observation, lost sales, incomplete demand information, dynamic programming, delayed observations

JEL Classification: M11, C61

Suggested Citation

Bensoussan, Alain and Cakanyildirim, Metin and Feng, Qi and Sethi, Suresh, Optimal Ordering Policy and Value of Information under Delayed Lost Sales Observations (October 2008). McCombs Research Paper Series No. IROM-05-09, Available at SSRN: https://ssrn.com/abstract=1295609 or http://dx.doi.org/10.2139/ssrn.1295609

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

Metin Cakanyildirim

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

P.O. Box 830688
Richardson, TX 75083-0688
United States

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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