How can you optimize manufacturing systems with uncertainty?

1 What is optimization?

Optimization is the process of finding the best solution or decision for a given problem or objective. In manufacturing systems, optimization can involve various aspects, such as production planning, scheduling, inventory management, quality control, maintenance, or logistics. Optimization can help you improve the productivity, quality, flexibility, and sustainability of your manufacturing systems. However, optimization is not a one-time activity, but a continuous and iterative process that requires constant monitoring, evaluation, and adjustment.

2 Why is uncertainty important?

Uncertainty is the lack of complete or accurate information about the current or future state of a system or its environment. Uncertainty can affect the feasibility, validity, and robustness of your optimization solutions or decisions. For example, if you optimize your production schedule based on a deterministic demand forecast, but the actual demand is different, you may face overproduction or underproduction, which can increase your inventory costs or harm your customer service. Therefore, you need to consider uncertainty in your optimization models and methods, and use appropriate tools and techniques to handle it.

3 How can you model uncertainty?

Modeling uncertainty means representing the possible values and probabilities of uncertain parameters or variables in your optimization problem. Depending on the type and degree of uncertainty, and the available data and information, there are various methods to consider. Scenario-based modeling assumes a finite number of possible scenarios for each uncertain parameter or variable and assigns a probability to each. Stochastic programming relies on known probability distributions, such as normal, uniform, or Poisson. Fuzzy logic uses fuzzy sets and fuzzy rules to capture imprecision and vagueness in human language and reasoning. For example, one can model demand uncertainty by using historical data or expert opinions to estimate the probability distribution of demand in each period, machine failure uncertainty by using a Poisson distribution to describe frequency and duration of breakdowns, or quality uncertainty by using fuzzy sets to define linguistic terms of good, acceptable, or defective.

4 How can you solve uncertainty?

Solving uncertainty involves finding the optimal solution or decision that achieves the best expected performance or outcome under uncertainty. The approach you use to solve uncertainty depends on the objective and constraints of your optimization problem. Robust optimization seeks to minimize the worst-case deviation from the desired performance or outcome, such as finding a production schedule that minimizes the maximum tardiness of orders under demand uncertainty. Stochastic optimization maximizes the expected value or utility of the performance or outcome, such as finding an inventory policy that maximizes expected profit under demand and supply uncertainty. Fuzzy optimization looks to satisfy the fuzzy goals and constraints of an optimization problem, like finding a quality control plan that satisfies fuzzy customer and regulator requirements under quality uncertainty.

5 How can you evaluate uncertainty?

Evaluating uncertainty involves measuring and comparing the performance or outcome of your optimization solutions or decisions under uncertainty. There are various metrics and methods to evaluate uncertainty, based on the criteria and perspective of your evaluation. Such metrics and methods include risk, which measures the variability or dispersion of the performance or outcome; reliability, which measures the probability or frequency of achieving a desired performance or outcome; sensitivity analysis, which measures the impact of changes in uncertain parameters or variables; and scenario analysis, which measures the performance or outcome under different scenarios. For example, you can use standard deviation to measure risk, service level to measure reliability, sensitivity analysis to measure changes in production schedule, and scenario analysis to measure inventory policy performance.

6 Here’s what else to consider

This is a space to share examples, stories, or insights that don’t fit into any of the previous sections. What else would you like to add?