Joint economic lot sizing model with stochastic demand and controllable lead-time by reducing ordering cost and setup cost

This paper derives a mathematical integrated production inventory model of single vendor and buyer to investigate the effects of capital investment in setup cost of the vendor and order processing cost of the buyer on the decision variables of the model. Main purpose of this study is to minimize the integrated total cost of the vendor and buyer by optimizing the delivery lot size, lead-time, setup and order processing cost and number of deliveries per order simultaneously while lead-time demand follows normal distribution and unknown distribution, i.e., distribution free case. This model is analyzed by calculus method and justified with appropriate numerical illustrations. Numerical results show that significant savings can be achieved at optimal investments in reducing lead time, ordering cost and setup cost. Finally, sensitivity analysis of the key parameters is carried out and some managerial implications are also included.