Supply chain model having stochastic lead time demand with variable production rate and demand dependent on price and advertisement

Abstract

In this present study, a single manufacturer and single retailer supply chain management model are formulated for a single product. We specifically look at a supply chain with variable production rate, stochastic lead time demand, and price- and advertisement-dependent demand. By incorporating these complex aspects into a model, which enables to examine their combined effects on supply chain performance, this study adds to the body of knowledge. The study reveals unique insights into the complex interplay between pricing tactics, advertising efforts, production dynamics, and the variability brought on by stochastic lead times through meticulous study and modelling.  Finally, the total system profit is calculated and optimized with all the decision variables. A classical approach is performed to obtain the optimized solution of the joint profit function along with the decision variables. Two models are discussed in the study: 1)The model with normally distributed lead time demand and 2) the model with distribution-free lead time demand.  {The joint profit function of the supply chain is found to be lesser by 1% for the normally distributed lead time demand than the distribution-free pattern. The comparison of the shipment policies and the safety factors for the different distribution patterns of the lead time demand has also been shown.  Though the huge increment in the safety factor for unknown lead time demand distribution may help in reducing the uncertainty factor and disruptions in the supply chain, but also it may unnecessarily tie up more capital which could be invested in other sectors of the supply chain.