Inventory Models Involving Lead Time Crashing Cost as an Exponential Function

Inventory management and control is concerned with the acquisition and storage of materials required for supporting various business operations. Lead time reduction is another important production activity in an integrated inventory control. Lead time plays a vital role and has been a topic of interest for many authors in inventory organization. Lead time is a necessary aspect in any supply chain management and inventory management system. The time gap between placing of an order and its actual arrival in the inventory is known as lead time. In most of the literature dealing with inventory problems, either in deterministic or probabilistic model, lead time is viewed as a prescribed constant or a stochastic variable, which therefore, is not subject to control. But, in numerous sensible circumstances, lead time can he reduced by an additional crashing cost; in other words, it is controllable, so in this article, we have considered the lead time crashing cost is an exponential function of lead time. A solution procedure is developed to find the optimal solution. In this article, both lead time and the order quantity are considered as the decision variables. The behaviour of the model is presented graphically. The result is illustrated with the help of a numerical example. Finally, Graphical representation is presented to illustrate the model. The solution procedure with the help of the software Matlab 2008 is furnished to determine the optimal solution.