The DASCh Experience: How to Model a Supply Chain

Nonlinear dynamical systems have been a fertile field for the application of simulation techniques. Since the 1960's, System Dynamics has studied such problems by integrating systems of ordinary differential equations (ODE's) over time. More recently, increases in computer power have permitted the broad application of agent-based (or individual-based) modeling. In our work on supply chain modeling, we have found agent-based modeling to be more flexible than ODE models for basic exploration. One phenomenon we discovered, the inventory oscillator, can also be modeled in ODE's, an approach that permits more rapid manipulation in a spreadsheet environment. Further study permits derivation of a closed-form analytical model as well, which makes explicit a number of interesting structural features of the oscillator. This paper does not pretend to enrich the repertoire of nontrivial behaviors known to complexity researchers. Mathematically, the behavior we observe is not particularly sophisticated: the inventory oscillator turns out to be computing a modulus function. Its intended contribution is twofold. First, and primarily, we seek to highlight the differences among agent-based, equation-based, and analytical system modeling, in terms of when they can be applied and the results one can expect to derive. The comparative simplicity of our system is what makes the analytical treatment possible at all. Second, manufacturing engineers find the potential for inventory fluctuation under stable boundary conditions counterintuitive and of great practical import. Its reducibility to the modulus function, far from making the results trivial, suggests that similar threshold nonlinearities may be responsible for other unexpected time-varying manufacturing measurements, and thus points the way to stabilize these important commercial systems. Section 2 of this paper describes the supply chain problem. Section 3 reports the three models that we constructed. Section 4 reviews the roles of each model and recommendations for their deployment. Section 5 summarizes our conclusions.