An Inventory Model with Stock-Dependent Demand Rate and Maximization of the Return on Investment

Valentín Pando, Luis A. San-José and Joaquín Sicilia
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Valentín Pando: Departamento de Estadística e Investigación Operativa, Universidad de Valladolid, 47002 Valladolid, Spain
Luis A. San-José: IMUVA-Instituto de Investigación en Matemáticas, Universidad de Valladolid, 47002 Valladolid, Spain
Joaquín Sicilia: Departamento de Matemáticas, Estadística e Investigación Operativa, Universidad de La Laguna, 38200 San Cristóbal de La Laguna, Spain

Mathematics, 2021, vol. 9, issue 8, 1-18

Abstract: This work presents an inventory model for a single item where the demand rate is stock-dependent. Three fixed costs are considered in the model: purchasing cost, ordering cost and holding cost. A new approach focused on maximizing the return on investment (ROI) is used to determine the optimal policy. It is proved that maximizing profitability is equivalent to minimizing the average inventory cost per item. The global optimum of the objective function is obtained, proving that the zero ending policy at the final of a cycle is optimal. Closed expressions for the lot size and the maximum ROI are determined. The optimal policy for minimizing the inventory cost per unit time is also obtained with a zero-order point, but the optimal lot size is different. Both solutions are not equal to the one that provides the maximum profit per unit time. The optimal lot size for the maximum ROI policy does not change if the purchasing cost or the selling price vary. A sensitivity analysis for the optimal values regarding the initial parameters is performed by using partial derivatives. The maximum ROI is more sensitive regarding the selling price or the purchasing cost than regarding the other parameters. Some useful managerial insights are deduced for decision-makers. Numerical examples are solved to illustrate the obtained results.

Keywords: EOQ models; return on investment maximization; stock-dependent demand rate; minimizing average inventory cost per item (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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