Effects of all-units discount on pricing and replenishment policies of an inventory model under power demand pattern

Abstract

A profit optimisation inventory problem is studied for the products whose demand is interconnected with the per unit selling price and products’ consumption duration as a multiplicative form of the impacts of the selling price as a logit-function and time as a power function. A reduction opportunity of the unit purchase price is offered to the retailer against an order quantity-based prepayment schedule. This study identifies when an inventory procedure is profitable or non-profitable by examining all possibilities of the optimum order quantity under an order quantity-based advance and discount scheme. Combining all the derived theoretical results, an efficacious solution algorithm is established to determine the optimal solution to the problem. Several numerical problems of businesses are solved in order to clarify the algorithm and derive results as well. Finally, the effects of the all-units discount and prepayment system on the retailer's best pricing and replenishing strategies are explored by implementing sensitivity analyses.

KEYWORDS:

• Inventory
• profit optimisation
• price-logit and time-power multiplicative demand
• order-based all-units discount and prepayment structure

Disclosure statement

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

Additional information

Notes on contributors

Md. Al-Amin Khan

Md. Al-Amin Khan is a Ph.D. student at Tecnológico de Monterrey. He also is an Assistant Professor in the Department of Mathematics at Jahangirnagar University, Savar, Dhaka. Mr. Khan received an MS degree in Mathematics from Jahangirnagar University in Bangladesh. He joined the Department of Mathematics at Jahangirnagar University in Bangladesh in 2014. Moreover, he received SHARFUDDIN GOLD MEDAL for outstanding results in the Master’s examination and for securing the highest marks among all faculties of Jahangirnagar University in the MS Examination 2012 from the Department of Mathematics. He is working on supply chain management, inventory control theory, computational optimization, soft computing, and interval mathematics. He has published articles in Omega, International Journal of Production Economics, Expert Systems with Applications, Knowledge-Based Systems, Computers & Industrial Engineering, Artificial Intelligence Review, International Journal of Systems Science: Operations and Logistics, Annals of Operations Research, International Transactions in Operational Research, Soft Computing, RAIRO-Operations Research, and others.

Leopoldo Eduardo Cárdenas-Barrón

Leopoldo Eduardo Cárdenas-Barrón received the B.S. degree in industrial and systems engineering, the M.S. degree in manufacturing systems, the M.S. degree in industrial engineering, the Ph.D. in industrial engineering; all degrees from Tecnológico de Monterrey. In 1996, Leopoldo Eduardo Cárdenas-Barrón joined the Industrial and Systems Engineering Department at Tecnológico de Monterrey, where he was appointed assistant professor in 1997, associate professor in 2001, and professor in 2007. At present, he is a researcher of the research group in Smart supply chain and logistics research. He is a member of the Mexican Research National System since 2015. His research activities include inventory theory, optimization, and supply chain. He has published 165 papers in JCR journals. His academic and research leadership at Tecnológico de Monterrey has been awarded several awards such as the Teaching and Research Award in 2007, the Rómulo Garza Prize for Research and Technology Development in 2011, and the award to the “professor who left a mark” from the Community of Former Students of Tecnológico de Monterrey in 2013 and 2018.

Neale R. Smith

Neale R. Smith is an associate professor at the Tecnológico de Monterey within the National School of Engineering and Sciences where he currently directs the Doctoral Program in Engineering Sciences. He holds an undergraduate degree in Industrial Engineering from the University of Arizona and M.S. and Ph.D. degrees in Industrial Engineering from Georgia Tech. He has taught both undergraduate and graduate level courses in operations research, logistics and supply chain management. His research interests are in the areas of applied optimization and logistics, and he has advised 29 M.S. and eight Ph.D. theses. He has over 50 peer reviewed publications and a Mexican patent. Before pursuing an academic career, he was a consultant and implemented logistics-related solutions for numerous companies.

Rafael Ernesto Bourguet-Díaz

Rafael Ernesto Bourguet-Díaz Full-time professor since 2000 in the Department of Industrial and Systems Engineering at Tecnológico de Monterrey. Research since 1996 on the reuse of knowledge in corporate complex projects that interweave engineering, business, and public policy using Systems Dynamics and Systems Methodologies. Consulting to CEMEX Global Analytics 2019–2020 training data scientists in Systems Dynamics to integrate simulators to “Machine Learning” technologies in concrete operational planning in Monterrey. Research in Knowledge Management CEMEX-ITESM, 2010–2013, project leader: Business Dynamics, with recognition as the best project, among 10 participating projects, in three consecutive years. Also carries out research in educational innovation: evaluator of educational innovation projects in virtual reality and development of computer applications in 2020 and developing research on hybrid environments for the teaching and learning of mathematics and Systems thinking. He has published several papers in JCR journals. Advisor for Master thesis in Engineering Schools; Business and Administration, and Government and Public Transformation. Dissertation committee member in Ph.D. thesis and member on more than 60 master’s thesis committees.

Imelda de Jesús Loera-Hernández

Imelda de Jesús Loera-Hernández is a full-time professor since 1999 in the Industrial and Systems engineering department at Tecnológico de Monterrey, Campus Monterrey. She holds an undergraduate degree in Industrial and Management Engineering and Master on General Management from Universidad Autónoma de Nuevo León. She graduated with a Master of Science in Industrial Engineering from the Tecnológico de Monterrey, Campus Monterrey and obtained a Ph.D. in Project Engineering from the Universidad Politécnica de Cataluña. She has more of 30 years of teaching experience on undergraduate and graduate levels in different courses such as: Production management, Ergonomics, Process improvement, Optimization, Project management and Feasibility of Projects. Imelda is coauthor in more of 20 research papers in international journals. Her lines of research are related decontaminate of mercury in water by bioadsorbents materials, production, inventory, and supply chain. She is coinventor in 2 patents with register in México.

Rodrigo Ernesto Peimbert-García

Rodrigo Ernesto Peimbert-García is the Director of the International Liaison Office of Tecnológico de Monterrey in Sydney, Australia. He is also an Honorary Research Fellow in the School of Engineering at Macquarie University. Dr. Peimbert-García holds a Ph.D. in Engineering Management from Texas Tech University (TTU), and he is a certified Lean Six Sigma Master Black Belt. In addition, he belongs to the Engineering Honor Society Tau Beta Pi and Industrial Engineering Honor Society Alpha Pi Mu in the United States. He has published several articles in Scopus Q1/Q2 scientific journals. On one hand, he has participated in more than 20 consulting projects in companies such as: ARC Automotive, Bayer Health Care, Gonher de México, Earth Tech, Continental, Frisa Aerospace, Methode Electronics, Xertix Metronet, Cornelius, Vitro, and Excel Dura Auto Parts, Federal Electricity Commission (CFE), and Aeromexico Group at the Mexico City International Airport. On the other hand, he has teaching and research experience in countries such as Mexico, Ecuador, Puerto Rico, the U.S., and Australia, and he has partaken in other areas like executive education and international affairs. Finally, his research interests include Lean Six Sigma, Industry 4.0, Cost of Quality, Inventory Models, and Healthcare Engineering.

Gerardo Treviño-Garza

Gerardo Treviño-Garza is an International Guest Professor at the Tecnológico de Monterey. He holds an undergraduate degree in Industrial and Systems Engineering and a M.S. in Computer Science from Tecnológico de Monterrey and a Ph.D. in Industrial Engineering from Arizona State University. He is a member of the Mexican Research National System. He has published several papers in JCR journals. He has taught undergraduate and graduate courses in optimization and decision science models. His research interests are in the areas of applying optimization techniques to solve real world problems. He has been awarded by Tecnológico de Monterrey with Teaching Excellence 2012 and Professor who left a mark 2018.

Armando Céspedes-Mota

Armando Céspedes-Mota holds a Ph.D. in Information and Communication Technologies with a major in Telecommunications from the Tecnológico de Monterrey, Campus Monterrey, May 2016. He received also the Bachelor of Science in Electronic and Communication Engineering, a master’s degree in electrical engineering, and a master’s degree in Telecommunications Engineering, from the Tecnológico de Monterrey, Campus Monterrey, México in 1983, 1986, and 2009 respectively. He also realized a professional perfecting in Germany in the areas of microelectronics, process automation, and industrial networks at the University of Applied Science Furtwangen in Furtwangen, Germany, and the Siemens Company in Karlsruhe, Germany, supported by the Carl Duisberg Gesellschaft e.v. (CDG) from February 1992 to September 1993. He has been working with wireless sensor networks and industrial networks projects at ITESM and industry and has an international patent. His research interests are focused on the topology control techniques and coverage area optimization of ad hoc wireless sensor networks with industrial applications and how can be integrated into the Internet of things (IoT) and enterprise architectures, lean manufacturing, inventory, production and manufacturing models, and supply chain. He has published several papers in JCR journals.