Inventory Models in Service of Practice

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Rue-La-La. Rent-the-Runway.

Onera Commerce. SmartOps. Bain Capital.

Boeing. Nike. Apple. Amazon.

Caterpillar. Deere. IBM. GM.

Every other year, I teach a PhD course, Foundations of Operations Management I, that covers elementary inventory models and selected topics in supply chain management. 

As I updated the syllabus for Fall 2019 (7 week mini-semester) teaching, I thought (again) how to best select 12 papers out of thousands that have been published. How to balance between the fundamental models (developed in 1950s and 1960s, or even before, in 1880s and 1920s!) and contemporary topics?

I am not going back to Taylor (1911), Veinott et al (1965) or even my own edited volume (1998)!

Of course, I have to cover stochastic dynamic programming (DP). 

So, I open with single stage, single product models, of the type studied by Arrow, Karlin and Scarf (AKS) in the 1950s. 

I feel it is important not to get sucked into the black-hole of academic research (1960-) that largely mimicked this DP approach through a plethora of minor variations that did not advance the core technique (or thinking) in any significant way, and more importantly, did not contribute to any noticeable change in the practice of managing inventories.

Solving practical problems requires a general-purpose computational technique that is (a) scalable, (b) comprehensive in its ability to accommodate a variety of practical considerations simultaneously, (c) easy to implement utilizing data and systems that are reasonably available and, importantly, (d) generates outputs that are easy to understand.

How? Infinitesimal Perturbation Analysis (IPA) derivative method for inventory models!

To cover these two techniques (DP and IPA) quickly, I chose three papers.

The first is a reflection of the early models (and times and collaborators) by Herb Scarf (which covers stochastic DP and so introduces base-stock policy; backlogging and lost sales; K-convexity, and so (s,S) policy; multi-echelon serial system; dynamically learning demand distribution via Bayesian updating; and min-max analysis, and other topics).

The second paper introduces IPA for inventory models (on a generalization of the serial multi-echelon model of Clark and Scarf). The third paper illustrates both techniques applied to a model that is a generalization of AKS.

H. Scarf. Inventory Theory. Operations Research. 2002.

P. Glasserman and S. Tayur. Sensitivity Analysis of Base Stock Levels for Capacitated Multi-stage Production-Inventory Models. Management Science. 1995.

R. Kapuscinski and S. Tayur. A Capacitated Production-Inventory Model with Periodic Demand. Operations Research. 1998.

How are these techniques actually applied to tackle practical problems in operations management (PPOM)?

Two PPOMs are (a) Designing a responsive supply chain (at Caterpillar) and (b) managing product variety using postponement through the use of vanilla boxes (at IBM). 

The solutions of these PPOMs utilize IPA in important ways. These two papers also serve the purpose of (a) understanding the various real-world complexities that are necessary to incorporate simultaneously, (b) how IPA is part of an over-all solution methodology that uses other techniques (notably from Linear programming, Stochastic programming, Network flows) and (c) the many what-if (or scenario) analyses that need to be conducted to get a solution implemented

Flexibility, indeed the design of it to enable responsiveness, can also be provided through manufacturing processes. An example is the paper by Jordan and Graves (Management Science, 1995).

Let us enter the 21stCentury.

We cover two papers in each of the following two current-day PPOMs: (a) Omni-Channel and (b) On-line retail.

In Omni-channel, we consider (i) strategic consumer behavior in choosing a channel (using a Game Theory framing) and (ii) use of IPA to calculate optimal parameters for effectively fulfilling omni-channel demand.

This allows students to see how game theory is incorporated in stylized models of supply chain OM research and another modern day illustration of the use of IPA (for actually solving a PPOM, in this case, through software developed by a startup Onera Commerce whose customers include Dick’s Sporting Goods and Saks Fifth Avenue).

In On-line retail, we consider (i) Forecasting and Pricing using Machine Learning (at Rue-La-La) and (ii) Managing rental inventories that have usage-based loss (using methods of sample path comparisons) motivated by Rent-the-Runway.

The Rue La-La paper further illustrates how analytics are incorporated within enterprise software systems for on-going operations, different from one-off consulting projects (such as responsive network design at Caterpillar).

There is a fundamental difference between consulting projects (that may use desk-top software), and enterprise software that is the backbone of on-going execution in a company.

The algorithms imbedded in enterprise software can be custom (like at Amazon or Rue La-La), or can be based on implementing a packaged product (like SmartOps EIO).

In previous years, to illustrate the imbedding of OM algorithms in enterprise software, I used Deere as an example, where more than $1Billion of savings were created with SmartOps (Enterprise Inventory Optimization (EIO) software), my software startup that was acquired by SAP (in 2013).

The rental paper illustrates how sample path methods can be used to derive the structure of optimal policies, a technique different from the mainstream use of stochastic DP in discrete-time stochastic inventory models.

Fun fact: The lead venture capitalist (VC) investor in Onera (where I am an angel investor) and Rent-the-Runway is the same, Bain Capital.

I suppose I did the predictable thing, after selling SmartOps, by becoming an angel investor and limited partner (LP) in a VC firm!

If you want to know my thoughts on venture capital (and venture capitalists!), see my recent interviews with Business Insider: Retail Unicorns and Series A financing.

We close the mini-semester with two papers that both use game theory to study contemporary multi-enterprise supply chains: (i) Trust and Trustworthiness in Forecasting and (ii) Combating Child Labor, an example of OM research in ethical supply chains.

An additional purpose of the second of the above papers is also to illustrate that not all OM problems have inventories in them!

There are great papers from service supply chains that could have been in the syllabus, especially in healthcare operations. As I teach a PhD course on Healthcare, the alternate years when I do not teach this one, I cover them there.

I wish I could discuss other contemporary topics like strategic counterfeiters, role of automation (and robotics) or the impact of tariffs (and trade wars) on supply chain operations.

Certainly, I have been asked about these topics in recent media interviews: Amazon’s attempts at managing fakes, Bootleg alcohol in Dominican Republic, Nike supply chain and Apple Supply Chain. And, of course, what is happening at Boeing. Will drones change operations? Oh, so many cool PPOMs to study!

So at the end of this course, the expectation is that the students have: (a) familiarity with techniques such as DP, IPA, Game Theory, Sample Path Comparisons and ML; and (b) knowledge of, and ability to model and analyze (and help implement improved solutions at companies), PPOMs such as responsive supply chains, managing product variety, omni-channel fulfillment, operating on-line operations, understanding nuances in multi-enterprise decision making and ethical supply chains.

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