Managing Perishable Inventory Systems with Multiple Demand Classes

42 Pages Posted: 13 Jul 2018

See all articles by Hossein Abouee Mehrizi

Hossein Abouee Mehrizi

University of Waterloo

Opher Baron

University of Toronto - Operations Management

O. Berman

University of Toronto - Rotman School of Management

David Chen

the Chinese University of Hong Kong, Shenzhen

Date Written: May 24, 2018

Abstract

In this paper, we study a multi-period stochastic perishable inventory system with multiple demand classes that require products of different ages. The firm orders the product with a positive leadtime and sells it to multiple demand classes, each only accepting products with remaining lifetime longer than a threshold. In each period, after demand realization, the firm decides how to allocate the on-hand inventory to different demand classes with different backorder or lost-sale cost. At the end of each period, the firm can dispose inventory of any age. We formulate this problem as a Markov decision process and characterize the optimal ordering, allocation, and disposal policies. When unfulfilled demand is backlogged, we show that the optimal order quantity is decreasing in the inventory levels and is more sensitive to the inventory level of fresher products, the optimal allocation policy is a sequential rationing policy, and the optimal disposal policy is characterized by a set of thresholds. For the lost-sale case, we show that the optimal allocation and disposal policies have the same structure but the optimal ordering policy may be different. Based on the structure of the optimal policy, we develop an efficient heuristic that is at most 4% away from the optimal cost in our numerical examples. Using numerical studies, we show that the ordering and allocation policies are close to optimal even if the firm cannot intentionally dispose products. Moreover, ignoring the difference between demand classes and using a simple allocation policy (e.g., FIFO) can significantly increase the total cost. We examine how the firm can improve the control of perishable items and show that the benefit of decreasing the leadtime is more significant than that of increasing the lifetime of the products or that of decreasing the acceptance threshold of the demand. The analysis is extended to systems with age dependent disposal cost and stochastic supply.

Keywords: Perishable inventory systems; multiple demand classes; stochastic optimal control; demand fulfillment and rationing; multimodularity

Suggested Citation

Abouee Mehrizi, Hossein and Baron, Opher and Berman, O. and Chen, David, Managing Perishable Inventory Systems with Multiple Demand Classes (May 24, 2018). Available at SSRN: https://ssrn.com/abstract=3191819 or http://dx.doi.org/10.2139/ssrn.3191819

Hossein Abouee Mehrizi

University of Waterloo ( email )

Waterloo, Ontario N2L 3G1
Canada

Opher Baron

University of Toronto - Operations Management ( email )

105 St. George st
Toronto, ON M5S 3E6
Canada

O. Berman

University of Toronto - Rotman School of Management ( email )

105 St. George Street
Toronto, Ontario M5S 3E6 M5S1S4
Canada

David Chen (Contact Author)

the Chinese University of Hong Kong, Shenzhen

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