Uncertain random optimal control model for deteriorating inventory with the finite horizon

Abstract

This paper examines a deteriorating inventory model with combined pricing and production during a limited selling time in an uncertain random setting. Demand is influenced by market size and price, which are portrayed in terms of random variables. The uncertainty factors affecting the inventory are represented by multiple Liu processes. Inventories deteriorate by a certain percentage and back-orders for inventories are permitted. This study aims to determine the optimal level of production rate and pricing that maximizes the producer’s total expected profit through the application of uncertain random optimal control theory, which is based on uncertain theory and probability theory. Numerical examples are used to compare joint pricing dynamic production model with dynamic production model under an optimal static price, highlighting the benefits of implementing joint pricing dynamic production model. Furthermore, it is evident that an increase in deterioration rate results in decreased on-hand inventory, yet higher production rate and price. It should also be noted that different levels of probability expectation of demand can have an impact on production inventory problem.