Nonlinear dynamics in the Beer Distribution Game – A high-throughput computing analysis

Nathan J Patterson, Purdue University

Abstract

Since the early 1960s, the Beer Distribution Game (BDG) has been used to characterize the various instabilities that arise in multi-stage supply chains. Although an appreciable body of research exists for the BDG and its inherent nonlinear instabilities, there are three apparent technical voids in literature that have been addressed in this dissertation, including: characterizing the difference between discrete- and continuous-valued BDG implementations, characterizing various aspects of the transient behavior of the BDG, and characterizing the impact of both heterogeneously- and homogeneously-implemented Electronic Data Interchange (EDI) and Radio Frequency Identification (RFID) technologies on the nonlinear dynamics of the BDG. This dissertation utilizes numerical simulations, previously-validated data sifting methods, and an ordering heuristic known to mimic human decision making behavior to examine each topic. A high-throughput computing approach to the BDG allowed for, what is believed to be, the most computationally intensive investigation of the BDG to date. This dissertation seeks to fill the first apparent void by examining the nonlinear behavior of four distinct BDG models: a continuous-variable implementation and three discrete implementations, incorporating conventional, nearest-integer rounding, floor functions, and ceiling functions, respectively. Specifically, numerical simulations and previous-validated data sifting methods are utilized to detail the cost and system response characteristics associated with each game implementation. The acquired results are subsequently compared to one another and used to derive refined ordering policies, which have distinct applicability to the operation of low volume supply chains of indivisible products. The in-depth numerical investigation is followed by a set of agent based simulations that utilize a reinforcement learning technique to learn optimal rounding methods. These rounding methods consist of various combinations of the aforementioned rounding functions and easily defined agent system states, which are based on ordering characteristics and operating costs. These simulations illustrate the effectiveness of reinforcement learning techniques in learning optimal behaviors for a highly nonlinear, often aperiodic, multi-stage supply chain model. This dissertation seeks to address the second apparent void by examining the transient performance metrics (e.g. settling time, average settling time cost, total setting time cost, and number of stock outages) associated with the prototypical supply chain model – the BDG. Managerial insights, which both support and contradict common practice, were derived from the data distributions created through extensive simulations. Process automation and information sharing are becoming increasingly important to the successful operation of supply chains. While previous works have investigated the effects of RFID, EDI, and other transparency technologies on multi-stage supply chain models, the studies completed to date have not fully examined the implications of these technologies on the dynamic behavior of the BDG. This is especially true for supply chains which feature heterogeneously-implemented transparency technologies. This dissertation seeks to fill this apparent technical void, by characterizing the impact of both heterogeneously- and homogeneously-implemented EDI and RFID technologies on the nonlinear dynamics of the BDG. To achieve this, the high-throughput numerical simulations are utilized to characterize the effects of EDI and RFID on the aforementioned transient performance metrics to form a series of succinct conclusions on the relative utility of these technologies.

Degree

Ph.D.

Advisors

Kim, Purdue University.

Subject Area

Mechanical engineering|Operations research

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