دو مشکل ذخیره سازی موجودی با تقاضای پویا و بازه زمانی ارزش زمان پیشبرد در افق زمانی محدود تحت شرایط تورم و ارزش زمانی پول

A finite time horizon inventory problem for a deteriorating item having two separate warehouses, one is a own warehouse (OW) of finite dimension and other a rented warehouse (RW), is developed with interval-valued lead-time under inflation and time value of money. Due to different preserving facilities and storage environment, inventory holding cost is considered to be different in different warehouses. The demand rate of item is increasing with time at a decreasing rate. Shortages are allowed in each cycle and backlogged them partially. Shortages may or may not be allowed in the last cycle and under this circumstance, there may be three different types of model. Here it is assumed that the replenishment cycle lengths are of equal length and the stocks of RW are transported to OW in continuous release pattern. For each model, different scenarios are depicted depending upon the re-order point for the next lot. Representing the lead-time by an interval number and using the interval arithmetic, the single objective function for profit is changed to corresponding multi-objective functions. These functions are maximized and solved by Fast and Elitist Multi-objective Genetic Algorithm (FEMGA). The models are illustrated numerically and the results are presented in tabular form.

Since the development of EOQ model by Harris [1], a lot of development/extension on the inventory control system with constant demand has been reported in the literature [2], [3] and [4]. In reality, there are many situations where the demand rate depends on time. Silver and Meel [5], Doneldson [6], Wee and Wang [7], Change and Dye [8], Goyal et al. [9] and others developed their models with dynamic demand. Dey et al. [10] considered a demand function, which is increasing with time at decreasing rate.

In reality, it is not possible for a manufacturing firm/wholesaler to supply the goods immediately with the placement of an order. Hence lead-time is an integral part of manufacturing/business. Moreover it is very difficult to predict the lead-time precisely. Normally, it is a time interval. Here, with lead-time as an interval number, real-life inventory models have been formulated and a particular model have been numerically illustrated. In this investigation, lead-time is unknown and a set of pareto optimal solution with different lead-time intervals have been presented for DM’s choice. For the first time a multi-objective genetic algorithm is developed and implemented to solve a two storage inventory problem with interval-valued lead-time and this can be used to solve other multi-objective inventory models in different environments. The present analysis can be applied for seasonable/fashionable goods which are marketed for a fixed time period.