Optimizing the Joint Replenishment and Delivery Scheduling Problem under Fuzzy Environment Using Inverse Weight Fuzzy Nonlinear Programming Method

In reality, decision-makers are always in front of imprecise and vague operational conditions. We propose a practical multiobjective joint replenishment and delivery scheduling (JRD) model with deterministic demand and fuzzy cost. This model minimizes the total cost defuzzified by the signed distance method and maximizes the credibility that the total cost does not exceed the budget level. Then, an inverse weight fuzzy nonlinear programming (IWFNLP) method is adopted to formulate the proposed model. This method embeds the idea of inverse weights into the Max-Min fuzzy model. Thirdly, the fuzzy simulation approach and differential evolution algorithm (DE) are utilized to solve this problem. Results show that solutions derived from the IWFNLP method satisfy the decision-maker’s desirable achievement level of the cost objective and credibility objective. It is an effective decision tool since it can really reflect the relative importance of each fuzzy component. Our study also shows that the improved DE outperforms DE with a faster convergence speed.