Economic design of an inventory system involving probabilistic deterioration and variable setup cost through mathematical approach

The purpose of this paper is to present the single-supplier single-buyer integrated production-distribution inventory model with three types of probabilistic deterioration and effectively increase investment to reduce the setup cost. An economic model is designed through mathematical approach to investigate the effects of probabilistic deterioration on the optimal solutions when a capital investment strategy in setup reduction is adopted. We used the differential calculus optimisation technique to optimise the strategies of our setup cost reduction inventory system. An efficient iterative algorithm is designed to obtain the optimal solution of the delivery lot-size, setup cost and total number of deliveries from a supplier to a buyer in one production run simultaneously. Numerical examples are given to demonstrate the application and the performance of the proposed methodology. The results of the numerical examples indicate that if the supplier makes his/her decisions with the capital investment in reducing setup cost, it will help to lower the system cost, and we can obtain a significant amount of savings to increase the competitive edge in business. At the end, we have provided several managerial insights of the proposed model based on the computational results.