Abstract
In this paper, we address an inventory system where the demand rate multiplicatively combines the effects of time and selling price. It is assumed that the demand rate is the product of two power functions, one depending on the selling price and the other on the time elapsed since the last inventory replenishment. Shortages are allowed and fully backlogged. The aim is to obtain the lot sizing, the inventory cycle and the unit selling price that maximize the profit per unit time. To achieve this, two efficient algorithms are proposed to obtain the optimal solution to the inventory problem for all possible parameter values of the system. We solve several numerical examples to illustrate the theoretical results and the solution methodology. We also develop a numerical sensitivity analysis of the optimal inventory policy and the maximum profit with respect to the parameters of the demand function.
Highlights
Inventory Theory collects a set of mathematical models which describe the properties of a wide variety of inventory systems, and studies different methodologies to seek and analyze the best strategies that may be applied in the management of inventories
In this paper, we develop an inventory model to determine the optimal policy for products in which demand depends on time and the selling price of the item
We have studied an inventory model where demand depends on time and the unit selling price
Summary
Inventory Theory collects a set of mathematical models which describe the properties of a wide variety of inventory systems, and studies different methodologies to seek and analyze the best strategies that may be applied in the management of inventories. For some types of products, the demand rate often depends on time or/and other characteristics For this reason, in this paper, we develop an inventory model to determine the optimal policy for products in which demand depends on time and the selling price of the item. We know of no papers on inventory systems that simultaneously assume the following characteristics: demand rate is the product of a time-dependent power demand and a price-dependent power demand, shortages are completely backordered and the length of the inventory cycle is a decision variable. We give a numerical sensitivity analysis for the best selling price, the optimal inventory policy and maximum profit with respect to the parameters of the demand rate function.
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