Contributions to a supply chain’s overall cost function (such as the bullwhip effect) are sensitive to the different players’ ordering policies. This chapter addresses the problem of developing ordering policies which minimise the overall supply chain cost. Evolutionary Algorithms have been used to evolve such ordering policies. The authors of this chapter extend existing research in a number of ways. They apply two more recent evolutionary algorithms to the problem: Grammatical Evolution (GE), using a standard Genetic Algorithm (GA) search engine; and Quantum Inspired Genetic Algorithm (QIGA), used both as a standalone algorithm, and as an alternative search engine for GE. The authors benchmark these against previous work on the linear Beer Game supply chain, and extend our approaches to arborescent supply chains (without gaming), and capacitated inventory. The ordering-policy-generating grammars investigated range from simple — only using the demand presented at that point — to complex — which may incorporate lagged demands, forecasting approaches such as Moving Average or Simple Exponential Smoothing, conditional statements and other operators. The different grammars and search engines are compared for deterministic demand, and various stochastic demand distributions. Overall, GE outperforms other approaches by discovering more efficient ordering policies. However, its performance is sensitive to the choice of grammar: simple grammars do best on deterministic demand, while grammars using conditionals, information sharing and forecasting do better on stochastic demand. GE with a QIGA search engine has similar performance overall to GE with a standard GA search engine: typically QIGA is better if demand follows a Poisson distribution, with GA better for Normal demand.
