Profitability Index Maximization in an Inventory Model with a Price- and Stock-Dependent Demand Rate in a Power-Form

Valentín Pando,Luis A San-José,David Alcaide-López-De-Pablo,Joaquín Sicilia

doi:10.3390/math9101157

Valentín Pando, Luis A San-José + Show 2 more

Open Access

https://doi.org/10.3390/math9101157

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Journal: Mathematics	Publication Date: May 20, 2021
Citations: 6	License type: CC BY 4.0

Affiliation: University of Valladolid, University of La Laguna

Abstract

This paper presents the optimal policy for an inventory model where the demand rate potentially depends on both selling price and stock level. The goal is the maximization of the profitability index, defined as the ratio income/expense. A numerical algorithm is proposed to calculate the optimal selling price. The optimal values for the depletion time, the cycle time, the maximum profitability index, and the lot size are evaluated from the selling price. The solution shows that the inventory must be replenished when the stock is depleted, i.e., the depletion time is always equal to the cycle time. The optimal policy is obtained with a suitable balance between ordering cost and holding cost. A condition that ensures the profitability of the financial investment in the inventory is established from the initial parameters. Profitability thresholds for several parameters, including the scale and the non-centrality parameters, keeping all the others fixed, are evaluated. The model with an isoelastic price-dependent demand is solved as a particular case. In this last model, all the optimal values are given in a closed form, and a sensitivity analysis is performed for several parameters, including the scale parameter. The results are illustrated with numerical examples.

Highlights

The majority of the deterministic inventory models in the literature consider the selling price of the item as a fixed parameter of the model
That is why this paper focuses on the maximization of the profitability index PI, which is equivalent to maximizing return on investment (ROI) ME
Denoting by t the elapsed time in the inventory, and I(t) the inventory level at time t, this paper aims to consider a broad frame for the demand of the item, depending on the selling price, p > c, and the stock level I(t)

Summary

Introduction

The majority of the deterministic inventory models in the literature consider the selling price of the item as a fixed parameter of the model. In most real practical situations, it is common for the demand of the item to depend on its selling price. This circumstance happens today, especially in such competitive business markets as exist today. Inventory managers are interested in knowing the optimal ordering policy for their warehouses, and in the optimal selling price to improve business profitability. For this reason, it is necessary to consider the selling price of the item as a decision variable in the model.

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