An Inventory Model for Imperfect Quality Products with Rework, Distinct Holding Costs, and Nonlinear Demand Dependent on Price

Leopoldo Eduardo Cárdenas-Barrón (), María José Lea Plaza-Makowsky, María Alejandra Sevilla-Roca, José María Núñez-Baumert and Buddhadev Mandal
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María José Lea Plaza-Makowsky: Universidad Privada de Santa Cruz de la Sierra, Faculty of Engineering, Industrial and Systems Engineering, Av. Paraguá y 4to. Anillo, Santa Cruz de la Sierra 2944, Bolivia
María Alejandra Sevilla-Roca: Universidad Privada de Santa Cruz de la Sierra, Faculty of Engineering, Industrial and Systems Engineering, Av. Paraguá y 4to. Anillo, Santa Cruz de la Sierra 2944, Bolivia
José María Núñez-Baumert: Universidad Privada de Santa Cruz de la Sierra, Faculty of Engineering, Industrial and Systems Engineering, Av. Paraguá y 4to. Anillo, Santa Cruz de la Sierra 2944, Bolivia
Buddhadev Mandal: Tecnologico de Monterrey, School of Engineering and Sciences, Ave. Eugenio Garza Sada 2501, Monterrey 64849, Mexico

Mathematics, 2021, vol. 9, issue 12, 1-20

Abstract: Traditionally, the inventory models available in the literature assume that all articles in the purchased lot are perfect and the demand is constant. However, there are many causes that provoke the presence of defective goods and the demand is dependent on some factors. In this direction, this paper develops an economic order quantity (EOQ) inventory model for imperfect and perfect quality items, taking into account that the imperfect ones are sent as a single lot to a repair shop for reworking. After reparation, the items return to the inventory system and are inspected again. Depending on the moment at which the reworked lot arrives to the inventory system, two scenarios can occur: Case 1: The reworked lot enters when there still exists inventory; and Case 2: The reworked lot comes into when the inventory level is zero. Furthermore, it is considered that the holding costs of perfect and imperfect items are distinct. The demand of the products is nonlinear and dependent on price, which follows a polynomial function. The main goal is to optimize jointly the lot size and the selling price such that the expected total profit per unit of time is maximized. Some theoretic results are derived and algorithms are developed for determining the optimal solution for each modeled case. It is worth mentioning that the proposed inventory model is a general model due to the fact that this contains some published inventory models as particular cases. With the aim to illustrate the use of the proposed inventory model, some numerical examples are solved.

Keywords: pricing; inventory model; lot size; imperfect quality; non-linear demand (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 (2)

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