Optimal production-inventory policy for products with time-dependent demand pattern and backlogged shortages

Abstract

In this work, a production-inventory system for items with a time-dependent demand pattern is studied. Shortages are allowed and these are met with the arrival of the next production run. Fluctuations of the net inventory level are analysed and the costs related with the production and inventory management are calculated. The aim is to maximise the profit per unit time. That profit is equal to the difference between sale revenue and production-inventory costs. In the analysis of this system, different scenarios can occur. All these possible cases are studied in detail and, for each scenario, the optimal production-inventory policy and the maximum profit per unit time are determined. Moreover, several numerical examples to illustrate the solution methodology are presented. Finally, a sensitivity analysis of the optimal inventory policy with respect to several parameters of the system and some useful managerial insights derived from the results are given.

Keywords:

• Production-inventory systems
• time-dependent demand
• backlogged shortages
• profit maximisation

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work is partially supported by the Spanish Ministry of Science, Innovation and Universities [Ministerio de Ciencia, Innovación y Universidades] through [research project MTM2017-84150-P] and by the Spanish Ministry of Science and Innovation [Ministerio de Ciencia e Innovación] [project PID2021-125042NB-I00], which are co-financed by the European Community under European Regional Development Fund (ERDF).

Notes on contributors

Luis A. San-José

Luis A. San-José is currently an Associated Professor at the Department of Applied Mathematics, University of Valladolid, Spain. He obtained his BS degree in Mathematics and a PhD in Operations Research, from Valladolid University. He has published several papers in journals, such as Annals of Operations Research, Applied Mathematical Modelling, Applied Mathematics and Computation, Asia-Pacific Journal of Operational Research, Computers and Industrial Engineering, Computers and Operations Research, Engineering Optimization, European Journal of Operational Research, International Journal of Production Economics, International Journal of Systems Science, Mathematics, Omega and TOP (an official Journal of the Spanish Society of Statistics and Operations Research). His research interest areas include inventory control, logistics and data envelopment analysis.

Joaquín Sicilia

Joaquín Sicilia is a Full Professor in the Department of Mathematics, Statistics and Operational Research, Faculty of Mathematics, La Laguna University, Tenerife, Spain. He received a Bachelor Science from the Complutense University of Madrid in 1979 and his PhD in Mathematics in 1987 from the Faculty of Mathematics at La Laguna University, Spain. He has published several papers in different journals such as Annals of Operations Research, Applied Mathematical Modelling, Applied Mathematics and Computation, Asia-Pacific Journal of Operational Research, Computers & Industrial Engineering, Computers & Operations Research, Engineering Optimization, European Journal of Industrial Engineering, European Journal of Operational Research, International Journal of Production Economics, International Journal of Production Research, International Journal of Systems Science, Omega and TOP. His teaching and research interests include inventory systems, location theory, scheduling, supply chain management and applied operations research.

Manuel González-de-la-Rosa

Manuel González-De la Rosa is an Associate Professor in the Department of Economy and Business Management, Faculty of Economics and Business Sciences, La Laguna University, Tenerife, Spain. He received a Bachelor in Social Sciences from the Faculty of Economics and Business Sciences at La Laguna University, Spain, in 1991. He has published some papers in journals such as Applied Mathematical Modelling, Asia-Pacific Journal of Operational Research, European Journal of Industrial Engineering, International Journal of Production Economics and International Journal of Production Research. His teaching and research interests include business management, marketing, inventory systems, international trade and supply chain management.

Jaime Febles-Acosta

Jaime Febles-Acosta is an Associate Professor in the Department of Economy and Business Management, Faculty of Economics and Business Sciences, La Laguna University, Tenerife, Spain. He received a Bachelor Science in 1987 and his PhD in Economics in 2002 from the Faculty of Economics and Business Sciences at La Laguna University, Spain. He has published some papers in journals such as Applied Mathematical Modelling, Asia-Pacific Journal of Operational Research, European Journal of Industrial Engineering, International Journal of Production Economics and International Journal of Production Research. His teaching and research interests include business management, business organization, inventory systems, scheduling and corporate culture.