Incorporating non-empty initial states into MRP Theory

Abstract

MRP theory is a theoretical body treating production-inventory systems, in which produced items are made up of sets of produced or purchased sub-items, required to be available a lead-time before each product is completed. The hierarchical dependence between items is captured using input matrices from input-output-analysis, the necessary advanced timing by employing Laplace transform methodology, and the economic consequences by applying the net present value. Little attention has hitherto been given to aspects of a non-empty initial state, e.g. an initial inventory position. Since such states are common in industry, there is a strong need for this theory to include such aspects, in order to gain further practical acceptance. In this paper, theoretical consequences from having a non-empty initial state are investigated. A method for finding the Lot-for-Lot solution is developed using the concept of a truncated monotonically non-decreasing time function, generalising the approach of the generalised Leontief inverse and instrumental for designing plans meeting the necessary inner-corner requirement for optimality. Also the definition of inventory-related costs needs a modification for this concept to be consistent with NPV. These findings are applied in an extensive numerical example. Immediate future research concerns investigating principles for the optimal removal of initial backlogs.

KEYWORDS:

• MRP theory
• input-output-analysis
• Laplace transform methodology
• net present value
• inventory-related costs

Acknowledgements

The author is indebted to Professor Ou Tang, Division of Production Economics, Linköping Institute of Technology, for valuable comments on an early draft of this manuscript.

Disclosure statement

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

Data availability statement

The data that support the findings of this study are available from the corresponding author, Grubbström, R.W., upon request.

Additional information

Notes on contributors

Robert W. Grubbström

Robert W. Grubbström has been Professor of Production Economics at Linköping Institute of Technology, Sweden, since 1972, and is now Emeritus Professor. He is Licentiate of Technology and Doctor of Economics, and has received honorary doctoral degrees from Lappeenranta University of Technology, Finland, Corvinus University, Budapest, Hungary, and Leopold-Franzens-Universität, Innsbruck, Austria. He has Master’s degrees from the Royal Institute of Technology, Stockholm, and the Stockholm School of Economics. Among the recognitions awarded him are Knight (First Class) of the Order of the White Rose of Finland, Commander of the Order of the Lion of Finland, Award of Recognition for Outstanding Contributions to the Development of the Faculty, University of Ljubljana, Slovenia, (also Honorary Visiting Professor) and Honorary Corporal, Kungl. Svea Trängregemente, Sweden. He has been Honorary Research Fellow, Lancaster University, and Honorary Professor, University of Nottingham Business School. He is Honorary President of the Economic Club of Linköping. He is Past President and Fellow of the International Society for Inventory Research (ISIR) and Fellow of the Royal Academy of Engineering Sciences. He is Co-Founder and Honorary Council Member of Young Enterprise Sweden, currently educating per annum around 36,000 Swedish youths in the rôle that entrepreneurship plays in contemporary society, and Co-Founder of Young Enterprise Europe. He has been an Editorial Board Member of the International Journal of Production Research, for 30 years. He has been Editor-in-Chief of the International Journal of Production Economics (Elsevier) 1979–2018, and is now Honorary Editor. He has authored articles in the International Journal of Production Research, Management Science, International Journal of Production Economics, The Mathematical Scientist, European Journal of Operational Research, Omega, Applied Energy, Annual Reviews in Control, and several other international journals. His current scientific interests are focussed on the development of a general theory for multi-level, multi-stage production-inventory systems applying the Laplace transform and input-output analysis (MRP Theory).