the quadratic approximation for an inflationary biobjective integrated vendorbuyer inventory model with imperfect manufacturing process and fixed and variable lead time crash costs

In this paper, we develop an integrated bi-objective model of a two-stage supply chain composed of a vendor and a buyer under an imperfect production process. in the stochastic inflationary condition the first objective is to minimize the expected costs of the proposed supply chain model and the second objective is to minimize buyer’s shortage variance. we assume lead time and ordering cost are controllable parameters and lead time crashing cost is considered as a function of both order quantity and reduced lead time. an effective solution procedure is developed to determine the optimal policy of the proposed model. finally, a numerical example and sensitivity analysis are proposed to show the performance of the model.