Controlling random lead time demand through a flexible production system under supply chain management

This study proposes a supply chain management model with a flexible production rate and a price discount offer for the backorder situation, where the ordering cost is lead time dependent. This lead time demand may follow a known distribution, or it may not have any specified distribution with the aim of minimization of supply chain cost under the simultaneous optimization of the production rate, lot size in each shipment, number of shipments, lead time, probability of movement of uncontrolled state to controlled state, safety factor, and price discount backorder. Three-types of inspections are considered to maintain the quality of products. Three different algorithms are designed to solve the model numerically. Three numerical experiments have been considered to validate the stability of this study. The average total cost for the triangular distribution reveals the minimum total cost of the supply chain management. The comparison with the existing literature demonstrates the major benefit of flexible production rate. It provides the reduction of movement of uncontrolled state probability during flexibility of the production rate, which indicates the reduction of defective products. The effectiveness of the key parameters has been tested through a sensitivity analysis. The results show that the material cost parameter is most sensitive parameters among all cost parameters. Quality improvement cost is another sensitive parameter which is obtained from the sensitivity analysis. Finally, this model converges over the existing literature through several aspects like movement of uncontrolled probability, the reduction of defective product and total supply chain cost.