Optimizing Setup Time Reduction Rate in an Integrated JIT Lot-Splitting Model by Using PSO and GS Algorithms for Single and Multiple Delivery Policies

This article develops an integrated JIT lot-splitting model for a single supplier and a single buyer for only one product. The relationship between optimal lot size and setup time reduction is an important subject in such problems. In this model we analyze the effect of setup time reduction in the integrated lot splitting strategy. Two cases, Single Delivery (SD) case, and Multiple Delivery (MD) case are investigated before and after setup time reduction. The Gradient Search (GS) and Particle Swarm Optimization (PSO) are used in proposed model to determine the optimal order quantity (Q*), optimal rate of setup reduction (R*), and the optimal number of deliveries (N*) -just for multiple deliveries case. These optimum values are calculated by minimizing the total cost for both buyer and supplier. Finally numerical example and sensitivity analysis are provided to compare the aggregate total cost for two cases and effectiveness of the considered algorithms. The results show that which policy for lot-sizing is leading to lower total cost. Results show that the aggregate total cost in Single delivery policy is obtained 1.3% lower when we used the optimized setup time reduction rate.