Profit optimisation for deterministic inventory systems with linear cost

A well-designed inventory system is critical to the success of any business organisation. One of the major challenges of inventory managers is to determine an inventory optimisation strategy that ensures the right balance between keeping enough inventory on hand to meet customer demand and optimising costs related to holding inventory. This paper focuses on providing a general inventory optimisation strategy to support business organisations. We examine a general deterministic model of inventory in which the rate of demand is determined by price and the rate of decay can change over the cycle time. For this general model we examine the profit function arising when the costs are linear with respect to the number of items purchased in the inventory cycle and the total item-time of holding. This framework encompasses a wide range of deterministic models that have appeared in the literature and are useful in practice. Within this framework we derive optimisation results for the cycle time and price. We show how these results apply for particular deterioration functions and demand functions. This allows us to extend present inventory literature to give the solution to a more generalised problem. Our results are analytically and numerically compared with existing specific results in the inventory literature.