An agent-based simulator for quantifying the cost of uncertainty in production systems

Abstract

Product-mix problems, where a range of products that generate different incomes compete for a limited set of production resources, are key to the success of many organisations. In their deterministic forms, these are simple optimisation problems; however, the consideration of stochasticity may turn them into analytically and/or computationally intractable problems. Thus, simulation becomes a powerful approach for providing efficient solutions to real-world productmix problems. In this paper, we develop a simulator for exploring the cost of uncertainty in these production systems using Petri nets and agent-based techniques. Specifically, we implement a stochastic version of Goldratt’s PQ problem that incorporates uncertainty in the volume and mix of customer demand. Through statistics, we derive regression models that link the net profit to the level of variability in the volume and mix. While the net profit decreases as uncertainty grows, we find that the system is able to effectively accommodate a certain level of variability when using a Drum-Buffer-Rope mechanism. In this regard, we reveal that the system is more robust to mix than to volume uncertainty. Later, we analyse the cost-benefit trade-off of uncertainty reduction, which has important implications for professionals. This analysis may help them optimise the profitability of investments. In this regard, we observe that mitigating volume uncertainty should be given higher consideration when the costs of reducing variability are low, while the efforts are best concentrated on alleviating mix uncertainty under high costs.