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A Replenishment Inventory Model with a Stock-Dependent Demand and Age–Stock-Dependent Cost Functions in a Random Environment

Yonit Barron ()
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Yonit Barron: Department of Industrial Engineering and Management, Ariel University, Ariel 40700, Israel

Asia-Pacific Journal of Operational Research (APJOR), 2022, vol. 39, issue 03, 1-40

Abstract: This paper investigates an (S,s) continuous-review perishable inventory model with a stock-dependent Poisson demand process, full backordering (with an extension for lost sales) and uncertainty in lead time and shelf life. Four types of costs are considered: a fixed cost of an order and each outdated item; age-dependent costs of an item (i.e., holding and salvage costs), given by a function of its remaining shelf life; and a delay cost of a backlogged demand unit, which is a function of its delay duration.Applying the supplementary variable technique, we obtain the joint probability-density function of the number of items in the system and the remaining time and thereby obtain the optimal parameters minimizing the long-run average total cost. Numerical experiments show that supply chain profits are enhanced by integrating the age components into replenishment decisions, and ignoring the shelf age- and delay-dependent costs may result in a substantial loss (up to 25%). It further appeared that estimating the lead-time distribution by an exponential one is significantly more costly, in particular as the c.v. differs from 1. In contrast, an exponential shelf life may provide a good heuristic for other shelf-life distributions.

Keywords: Age-dependent cost; stock-dependent demand; supplementary variables; (S; s) inventory policy; perishability (search for similar items in EconPapers)
Date: 2022
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Citations: View citations in EconPapers (1)

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DOI: 10.1142/S0217595921500354

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