A Bi-Objective Simulation-Based Optimization Approach for Optimizing Price, Warranty, and Spare Part Production Decisions Under Imperfect Repair

Abstract

This paper proposes an efficient methodology based on the Monte-Carlo simulation-based bi-objective optimization, to determine base-warranty (BW) and extended warranty (EW) parameters based on the product lifecycle. The first objective, which is from the manufacturer’s perspective, maximizes the profit while the second objective minimizes the expected number of failures that occurred during the out-of-warranty period. The manufacturer can rectify failed products via minimal repair, imperfect repair and perfect repair. The optimization model has decision variables including the product price, BW length, EW length, EW price, product failure rate, imperfect repair level, and spare part production rate in each time interval. The structure of the model admits the design of a hybrid method based on the multi-objective optimization search algorithm, Monte-Carlo simulation and an exact Out-Of-Kilter (OOK) algorithm. The nondominated sorting genetic algorithm (NSGA-II) and the multi-objective particle swarm optimization (MOPSO) algorithm are used as search algorithms. The proposed approach consists of three stages, where in the first stage, product price, BW length, EW length, EW price, product failure rate, imperfect repair level are set by NSGA-II/MOPSO. In the second stage, the number of failed products is calculated by the Monte-Carlo simulation and in the third stage, we show that the spare part inventory control sub problem can be transformed to a minimum cost network flow problem which is optimized by the OOK algorithm to attain a unified solution. A Taguchi approach is used to find the optimum level of parameters. The performance of algorithms is compared based on three different metrics. Results on a real-world problem demonstrate that the NSGA-II-OOK algorithm is more effective than the MOPSO-OOK algorithm. Through a sensitivity analysis, we analyze how various levels of planning horizon can affect Pareto-set which indicates valuable managerial insight.