Computational algorithmic procedure for optimal inventory policy involving ordering cost reduction and back-order discounts when lead time demand is controllable

In many practical situations, the ordering cost can be reduced by capital investment and the back-order rate is dependent on the amount of shortages and back-order price discounts. Hence, in this paper, we consider an inventory model with random yield in which the ordering cost can be reduced through capital investment, lead time can be shortened at an extra crashing cost and allow the back-order rate as a control variable to widen applications of Wu and Tsai's [J.W. Wu, H.Y. Tsai, Mixture inventory model with back-orders and lost sales for variable lead time demand with the mixtures of normal distribution, International Journal of Systems Science 32 (2001) 259-268] model. Moreover, we also consider the back-order rate that proposed by combining Ouyang and Chuang [L.Y. Ouyang, B.R. Chuang, Mixture inventory model involving variable lead time and controllable backorder rate, Computers & Industrial Engineering 40 (2001) 339-348] (or Lee [W.C. Lee, Inventory model involving controllable backorder rate and variable lead time demand with the mixtures of distribution, Applied Mathematics and Computation 160 (2005) 701-717]) with Pan and Hsiao [J.C.-H. Pan, Y.C. Hsiao, Inventory models with back-order discounts and variable lead time, International Journal of Systems Science 32 (2001) 925-929; J.C.-H. Pan, Y.C. Hsiao, Integrated inventory models with controllable lead time and backorder discount considerations, International Journal of Production Economics 93-94 (2005) 387-397] (also see Pan et al. [J.C.-H. Pan, M.C. Lo, Y.C. Hsiao, Optimal reorder point inventory models with variable lead time and backorder discount considerations, European Journal of Operational Research 158 (2004) 488-505]) to present a new general form. The objective is to simultaneously optimize the order quantity, ordering cost, back-order discount and lead time. In addition, we also develop an algorithmic procedure and use the computer software Compaq Visual Fortran V6.0 (inclusive of IMSL) to find the optimal inventory policy. Finally, a numerical example is also given to illustrate the results.