Managing Production-Inventory Systems with Scarce Resources

Saif Benjaafar (), David Chen () and Rowan Wang ()
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Saif Benjaafar: Department of Industrial and Systems Engineering, University of Minnesota, Minneapolis, Minnesota 55455
David Chen: Rotman School of Management, University of Toronto, Toronto, Ontario M5R 2S3, Canada
Rowan Wang: Lee Kong Chian School of Business, Singapore Management University, Singapore 178899

Manufacturing & Service Operations Management, 2017, vol. 19, issue 2, 216-229

Abstract: We consider the problem of managing production in a production-inventory system where a firm is subject to an allowance (a limit) on either the amount of input it can use or the amount of output it can produce over a specified compliance period (in addition to being subject to a constraint on the production capacity). Examples of such settings are numerous and include those where limits are placed on the use of scarce natural resources as input or on the amount of waste or harmful pollution generated by production as output. We study the structure of the optimal production policy for such systems and show that it is determined by dynamic thresholds that depend only on the sum of the on-hand inventory level and the remaining allowance. We provide an effective approximate solution approach that can compute these thresholds efficiently while retaining their essential properties. We examine the differences between how an allowance constraint and a constraint on production capacity affect production decisions and show that they exhibit opposite effects over time. We also examine, in the context of an extended version of the problem where both the allowance amount and the production capacity are endogenous, optimal investments in allowance and production capacity and the impact of both on firm profit. We also consider the optimal demand fulfillment policy in settings where the firm can decide whether to back-order or to reject demand that cannot be satisfied from on-hand inventory.

Keywords: production-inventory systems; natural resources and the environment; allowance constraints; capacity constraints; stochastic optimal control; demand fulfillment and rationing (search for similar items in EconPapers)
Date: 2017
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Citations: View citations in EconPapers (3)

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Persistent link: https://EconPapers.repec.org/RePEc:inm:ormsom:v:19:y:2017:i:2:p:216-229

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