Advanced Inventory Theory fall 2023


8 November, 6 December 2023, 17 January, 31 January 2024


10.00 – 16.00 h.




Prof. Rommert Dekker & Prof. Geert-Jan van Houtum




1 (participating only) – 4 (participating + passing the assignment)

Course fee:

free for TRAIL/Beta/OML/ERIM members, others please contact the TRAIL office


see below.


  • Students will learn fundamental inventory models
  • Students will be exposed to recent papers in FT50 journals which build on fundamental inventory models
  • Students will be exposed to open research problems.

Course description:

Inventory theory is one of the key theories within operations management. In a lot of state-of-the-art research, inventories play an important role (see e.g. Song, Van Houtum, and Van Mieghem, M&SOM 22, pp. 36-46, 2020, who found that inventories play a role in 33% of the papers published in M&SOM in the years 1999-2018). Hence, knowledge on fundamental inventory models is important for every scholar in the field of operations management. In this course, we discuss two types of inventory models:

  1. Single-location inventory models for inventories in general,
  2. Spare parts inventory models.

The first part starts with a review of chapters of the book of Axsäter (2015) on single-item, single-location inventory policies. Next, we consider several extensions, viz. the joint replenishment problem, multiple demand classes, short-term control and reverse logistics. We discuss the classic papers on these topics and we show how these papers fit in a whole line of research. Apart from presenting theory on these topics, including optimization aspects, exact as well as heuristic approaches, we also pay attention to the problems when trying to use these models in practice. Quite often several extensions of existing theory have to be made to arrive at solutions. Several examples will be given.

The second part will be based on Chapters 3 and 5 of the book of Van Houtum and Kranenburg (2015). In spare parts inventory problems, the focus is generally on the system availabilities of the machines for which spare parts are taken on stock. This leads to multi-item inventory models with various types of system-oriented service level constraints. We show how to derive efficient solutions in a single-location setting with one type of customers, and we formulate heuristics. Next, we study a single-echelon, multi-location setting with lateral transshipments, We also show how these models can be and actually are applied in practice. Finally, we connect the single-echelon, multi-location model to settings for internet sales, library books, and ambulance services.

We use two course days per part. Per part, the first course day is used to present the existing theory, while the second course day is focused on recent papers and open research problems. For the recent papers, we look explicitly at papers published in FT50 journals (OR, MS, M&SOM, POM, JOM) and we discuss why these papers are so good that they deserved to be published in a top journal.

Connection with the course “Quantitative Modelling and Analysis of Supply Chains QMASC)”:

The latter course is about inventories in general and as such mainly related to our first part. In our first part, we focus on single-location models, and especially in settings with multiple items, joint replenishment costs and multiple demand classes. The course QMASC has a focus on multi-echelon production/inventory systems.


Two sets of homework exercises and presentations of papers.


  • First and second lecture day: First type of inventory models, by prof. Dekker.

Participants without background in inventory control should study Chapter 3 (cost structure and concepts) and Chapter 5 (Sections 5.1 to 5.10) of the book of Axsäter (2015).

  • Third and fourth lecture day: Second type of inventory models, by prof. Van Houtum.

Participants who did not have any inventory theory course until now, can prepare themselves for this part by studying Sections 2.1-2.5 of Van Houtum and Kranenburg (2015); this part of the book can be downloaded as free sample pages at  In these sections, the basic multi-item spare parts model is analyzed. This basic model forms a basis for the models of Chapters 3 and 5, and is relatively easy for participants who had an inventory theory course during their master program; this model will be discussed only briefly at the third lecture day.



In this course, various quantitative/mathematical models for inventory problems are discussed.

Course material:

  • Axsäter, S., Inventory Control, 3rd edition, Springer, 2015. (Chapters 3-7)
  • Van Houtum, G.J., and Kranenburg, A.A., Spare Parts Inventory Control under System Availability Constraints, Springer, 2015. (Chapter 1, Sections 2.1-2.5, Chapters 3, 5, and 6)
  • Handouts


Basic probability theory. Basic knowledge of Markov processes and queueing theory (M|M|1, M|G|, M|G|c|c queue). If you miss this part of the prerequisite, you can study chapters on these topics in a standard text book on Operations Research; see e.g. Chapter 17 on “Markov Chains” (up to and including Section 17.6, pp. 923-950) and Chapter 20 on “Queueing Theory” (up to and including Section 20.8, pp. 1051-1098) of Winston [2004], “Operations Research: Applications and Algorithms” (4-th edition), Brooks/Cole-Thomson Learning, Bement, CA, U.S.A.

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