Operations Education

Impact in practice

Since 1985 we have used quantitative modelling to develop solutions to real-world problems in Operations Management. End of 2011 we did an assessment of the financial impact of research at the Operations Planning, Accounting, and Control group of Technische Universiteit Eindhoven. We limited ourselves to impact reported in the public domain. Much to our surprise we found that in the preceding decade, i.e. 2001-2011, the financial impact of our research totaled close to one billion US dollars.

Billion dollar models

Advanced Planning and Scheduling Systems

Since 1998 I have been working together with several companies on the understanding, selection, and implementation of Advanced Planning and Scheduling systems. These systems support planners and schedulers to take decisions in a complex and uncertain world. My research on inventory management in real-life supply chains (see below for more details) enabled to get a deeper understanding of the foundations of the so-called engines of these APS systems. These engines use algorithms to derive decision advice. Most APS systems assume a perfect forecast of the future and derive an “optimal” decision from there. Using both real-world data and discrete event simulation experiments, we could show that an uncertain world needs different algorithms than the ones most commonly used in APS systems. We implemented such an algorithm at Philips Semiconductors, and the so-called SCOP model has been used as the basis for the development of a Master Planning tool at ASML.

link to Springer

Together with Vincent Wiers we developed a course on APS system development and implementation for MSc students at TU Eindhoven. This course led to the publication of our APS book.

Inventory Management: Modelling Real-life Supply Chains and Empirical Validity

End of 2016 I started to write a chapter on Inventory Management for an edited book of a colleague. Unfortunately, I missed the deadlines set for completing the chapter: writing single-authored papers is nowadays a challenge at a Dutch university. In any case it was a challenge for me. But as I wanted to write something different than, or complementary to, existing reviews of inventory management, and I was on 60% of the road towards completion, I decided to continue researching (as I created some new stuff as I progressed) and writing. To my great fortune, Charles Corbett, Editor-In-Chief of Foundations and Trends® in Technology, Information and Operations Management expressed his interest in my work when I sent him a 90% version. With the support of an anonymous referee the monograph has been completed and is published as “hyperlink-when-published”. A preliminary version is available here.

In parallel I got the opportunity to contribute to the special issue celebrating the 55th anniversary of the International Journal of Production Research. For a long time, I had been pondering on writing a paper on my experiences with success and failure of the application of inventory models. A main insight was that human interventions corrupt the application of most mathematical models that allow for tractable analysis. This led to the concept of Intervention-Independent Performance Indicators, which allows for application and calibration of mathematical models. A preliminary version of the paper in IJPR can be found here.

The two papers mentioned here can be seen as the foundation for the papers and tools shared below. But conversely, the tools shared allowed for experimentation and implementation of the concepts, so that the above papers have a strong empirical foundation. Indeed, an example of cross-fertilization of science and practice.

Analysis and optimization of basic inventory models

Since the nineteen-fifties virtually any text book on Operations Management has a number of chapters devoted to single-item single-echelon inventory models. These models assume various control rules that trigger inventory replenishment orders. Extensive application of these inventory models in practice since 1985 has revealed three main findings:

1. The inventory models are valid descriptions of inventory control principles in practice.
2. If such a valid inventory model is mathematically rigorously analyzed, then the quantitative analysis yields empirically valid results for relevant performance measures such as average inventory levels and customer service levels.
3. The majority of formulas presented in standard text books yield quantitatively invalid results, as they are based on assumptions that are not valid in practice and erroneous mathematical analysis.

The impact of the above empirical findings should not be underestimated. Even in 2013 ERP systems such as SAP have inventory management modules that provide safety stock calculation functionality which are based on standard text book formulas explained by standard text book reasoning, without carefully assessing the assumptions underlying this reasoning. In any case, the results are invalid, which implies that users of inventory management modules set target service levels at 95%, and later on find out that the actual results are as displayed in the figure below.

The above figure shows that using the standard formulas prohibits a fundamental necessity for controlling a process that is assumed to be similar for thousands of instances (sku’s): a consistent bias between initial target outcome set to feed a model of a process and the actual measurement of the outcome.

The second finding tells us that the only modification necessary is using correct mathematics. Regarding the third finding, unfortunately, the correct mathematics is beyond the capability of most Operations Management textbook readers. But this is not relevant: for OM textbook readers the control principles and qualitative insights are vastly more important than the mathematical analysis. Nowadays the mathematical analysis can be packaged in user-friendly software that can be downloaded from the internet and interfaced with ERP systems. This is similar to common practice in textbooks on mechanical and process engineering: models expressed in partial differential equations are presented, the numerical solutions of which are left to Matlab or other off-the-shelf packages.

Below we provide an Excel spreadsheet that contains the analysis of almost all basic inventory models. The underlying assumptions are only:

i. The demand process is probabilistically stationary.
ii. Customer demand is backordered.

As stated above the results computed have proven to be valid is a wide range of business environments, including retail and spare parts. Furthermore, we provide a basic manual of the spreadsheet and a document that provides further explanation on the above statements.

Classical Inventory Models

Manual Classical Inventory Models

Analysis of basic inventory models

Basics of Inventory Management

Expecting to lose contact with academia after a career switch, I spent three months at Catholic University Brabant (now University of Tilburg) to write down my work on the analysis of the basic inventory models under the assumption of compound renewal demand. The intention was to publish a book on inventory management. While developing the manuscript it became clear that the material would not be accessible to a wide audience: it was too technical. After the career switch to Logistics Innovation Manager at Philips Consumer Electronics, it was impossible to continue working on the manuscript and we decided to publish the material as 6 research reports. This material has been the basis for much of my work on inventory management since my return to academia in 1992. The formulas used in the Classical Inventory Models Excel spreadsheet are derived in the research reports. The book on inventory management has never been published …

Part 1: Renewal theoretic background

Part 2: The (R,S)-model

Part 3: The (b,Q)-model

Part 4: The (s,S)-model

Part 5: The (R,b,Q)-model

Part 6: The (R,s,S)-model

History of inventory management research

On the occasion of the 40th anniversary of the Dutch Logistics Association (vLm) I contributed a brief history on the milestones of inventory management research on basic inventory models. To my surprise I found that Edgeworth in 1888 was the first to publish on the Newsvendor problem, thereby showing that this problem with stochastic demand precedes the EOQ model of Harris in 1913!

100 years of inventory management research (this is the original version in Dutch, an English version using Microsoft Translate is also available)

Lost-sales models

In inventory management research, assuming that unsatisfied demand is backlogged is dominant, because it yields mathematically tractable results, including optimal policy structures under various cost structures. However, in quite some inventory management situations, it is more realistic to assume that unsatisfied demand is lost. This is typical for supermarkets and other retail stores, and in upstream commodity businesses. There is no hope to find the optimal policy using numerical methods, due to the fact that we must take into account net stock and each individual outstanding order when deciding how much to order. Fortunately, there has been considerable progress on periodic-review policies under linear holding and penalty costs, which is quite relevant for practice. We can safely say we solved the lost-sales model in that case, implying that results can be made available for practice. In fact, that is my intention with the tool I provide for download.

The tool provides simulation-based optimization of three policies

• Base stock policies that are asymptotically optimal for penalty costs to infinity
• Fixed order quantity policies that are asymptotically optimal for lead time to infinity
• Fixed P3 policy, where P3 is defined as the non-stockout probability at the end of an arbitrary period

An extensive experimental study shows that the fixed P3 policy dominates the other two policies. For most real-life situation the cost reduction is substantial. An important auxiliary benefit of the fixed P3 policy is that it shows a low replenishment order volatility, even for volatile demand. This implies that upstream suppliers can benefit from low demand volatility. Our experiments show that asymptotically the P3 policy behaves like the asymptotically optimal policies, both for high penalty costs and long lead times.

The tool is self-explanatory, assuming the user is familiar with basic inventory models. Next to policy parameter simulation, the tool allows the user to simulate period-by-period to see the difference in order quantities and the consequential evolution of inventory over time. The tool also provides a finite horizon simulation to show these differences between the policies under more realistic conditions, realizing that infinite horizon behavior and short-term behavior of control policies may be different. We created an instruction video:

Please note that we assume that the review period is equal to a time unit, and the lead time is a constant multiple of the review period. It is rather straightforward to extend to the situation where the review period and lead time are multiples of some basic time unit. This is left for the future.

Lost-sales model analysis tool

We continued our research on the lost-sales model, driven by the excellent performance of the fixed non-stockout probability policy. We found that this policy outperforms all recently proposed policies for the lost-sales model and even produces the same costs as the optimal policy for cases introduced in the literature by Paul Zipkin, one of the giants in inventory management theory. Eventually this lead to a paper that has been submitted to Operations Research, a revised version of this paper and a tool that enables researchers and students to get a deeper understanding of the behaviour of the inventory process for the lost-sales model under different control policies and how this behaviour differs from that of the inventory process under backlogging. The tool is available here: Analysis and optimization of various policies for the lost-sales model. An example input file is available here:Example input file for lost-sales analysis tool

The Stochastic Economic Lot Sizing Problem (SELSP)

The classical economic lot sizing problem under constant demand rate was solved by Harris in 1913, while the economic lot sizing problem (ELSP) under known dynamic demand was solved by Wagner and Whitin in 1958. The obvious extension to the economic lot sizing problem under stochastic dynamic demand, linear holding and penalty costs, fixed ordering costs, and positive lead time, has not been solved, due to its mathematical intricacies. Like many others, we resort to the application of a rolling scheduling formulation, where each period we solve an ESLP and implement the immediate decisions (no order or order some quantity). Uncertainty is taken into account by setting a safety stock. Thanks to the so-called net stock translation property, discussed in De Kok (2018), we can find the long-run optimal safety stock for any lot sizing heuristic by discrete event simulation, requiring only two runs. Under any lot sizing heuristic, the optimal safety stock ensures that the non-stockout probability satisfies the Newsvendor fractile. In that way we can determine the range of parameter values for which a particular heuristic performs best.

We developed an assignment that challenges students to develop a computer program that allows for comparison of different heuristics to solve the SELSP. To reduce the workload we developed the SELSP tool that allows for determining the performance of a number of lot sizing rules under a given safety stock, allows for optimizing the safety stock parameter under a given lot sizing rule, and allows for batch input, according to some input format, generating a semicolon separated file that can be imported into Excel. We created an instruction video with the SELSP tool:

Concepts for multi-item multi-echelon models

A major development concerning operational management of companies and networks of companies is the concept of Synchronized Base Stock (SBS) policies. This concept has been implemented at Philips Semiconductors, generating over € 100 million additional profits over a six year period compared to the situation before implementation. This amounts to an additional yearly profit equal to 7.5% of yearly turnover. The SBS concept not only enables far more effective operational material management, it also enabled the development of ChainScope, a tool for supply chain optimization. ChainScope determines the optimal control parameters, such as safety times and stocks, and lot sizes, that drive all existing manufacturing planning and control concepts, including MRP and APS systems. ChainScope has been extensively tested in a wide variety of production environments, ranging from process industries, to FMCG, to low volume high tech. ChainScope explains your current operational performance and provides detailed directions for improvement.

On June 30, 2014, Ton de Kok gave a keynote on multi-item multi-echelon systems at the StochMod 2014 conference in Mannheim. In the video below he discusses Newsvendor equations at the basis for efficient optimization of such systems. The principles and results presented are the foundation for the ChainScope software.

Recently, I was invited by the editors of StatOR, the journal of the Dutch society of Statistics and Operations Research, to tell something about my research on Supply Chain Management and its relevance for practice. The published Dutch version can be found here, the extended Dutch version can be found here, and an English version derived using Microsoft Translate can be found here

Tools

Until recently I allowed for the download of the ChainScope tool, which allows to optimize multi-item multi-echelon supply chains. To get an idea of its functionality, the ChainScope manual can still be downloaded.

ChainScope manual

As soon as the website of my startup company ChainStock is live, I will put here a link to the website.

Case

Together with Logixperience we developed the L-Pad case. Martijn Schmit developed an introduction slide show video.

Safety lead times in Configure-To-Order environments and Project Management

We recently developed a tool to set so-called planned lead-times for order-driven manufacturing with stochastic cycle times. The tool can be downloaded here as well as a sample input file (Note that the file has an extension .xls, but it is not a spreadsheet file. Normally I use the extension .dat and edit with Notepad. But the server does not accept hyperlinks to files with a .dat extension). There is no manual available, but this paper may provide sufficient context information.

The model can be applied to project management situations where each activity has at most one succeeding activity. We are currently extending our research to more general situations. For recent seminal work on modelling project management situations we refer to the work of Dan Trietsch and Ken Baker.

Contact information

Ton de Kok: ton.de.kok@kpnmail.nl

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