Economic Production Quantity Under Possible Substitution: A Scenario Analysis Approach

Abstract

This paper designs a Scenario analysis approach to determine the joint production policy for two products under possible substitution. The Scenario analysis is designed to improve decision-making by considering possible outcomes and their implications. The traditional multi-product production models assume that there is no possible substitution between products. However, in real-world cases, there are many substitutable products where substitution may occur in the event of a product stock-out. The proposed model optimizes production quantities for two products under substitution with the aim of minimizing the total cost of the inventory system, including setup and holding costs, subject to a resource constraint. To analyze the problem, four special Scenarios are derived and discussed in detail. Furthermore, the total cost functions are derived for each Scenario separately, and then a solution procedure is suggested based on the Scenarios developed. The numerical examples are implemented, and the results are discussed in detail. Finally, sensitivity analysis is performed to get more insights. It is observed that the presented model is highly sensitive to the demand rate of products.