# Manufacturing Optimization: It's about Time

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Executive Summary

The author reintroduces the concept of optimization and shows how manufacturing companies should use the concept and the techniques that flow from it to enhance their business operations.

The term optimization has been used in operations management, operations research, and engineering for decades. The idea is to use mathematical techniques to arrive at the best solution, given what is being optimized (cost, profit, or time, for instance). To optimize a manufacturing system means that the effort to find best solutions focuses on finding the most effective use of resources over time.

The term optimization is now being used incorrectly, however. Many people, especially consultants, are using it without regard to what optimization is or to how manufacturing companies should apply the concept to their own operations. Optimization has become a catch-all term, and this is dangerous for two reasons. First, those who use the term do not usually know whether the systems they propose are truly optimal solutions or not. And second, the lack of rigor they use to develop and articulate their proposed solutions means that failure is inevitable - not exactly good advertisement for the benefits of optimization.

Optimizing

Finding the optimal solution relates to a specific problem such as minimizing the cost associated with purchasing materials, minimizing the amount of wasted material created when punching shapes from a piece of sheet metal, or maximizing throughput at an operation. So the first step is to understand what your problem is - that is, what you want to optimize. You might try, for example, to minimize costs, maximize profit, minimize time, or maximize throughput. Objectives like these are often referred to as objectives in prose form. In the performance of a mathematical analysis leading to an optimal solution, the objective takes on a mathematical form and becomes an objective function (Figure 1).

After defining the objective, you must then define what constraints act on the model being optimized. Time may be a constraint, in that only one shift may be operating and therefore all activities must be completed within that one shift. Additionally, a manufacturing facility that is seeking to optimize profit via an optimal product mix may find that a daily, repetitive schedule must be adhered to. The shift policies and the repetitive schedule will shape what's being modeled and influence the optimal solution. Whereas the optimal solution might be, for example, to meet the entire market demand for a particularly desirable product, shift requirements or the need to meet the demand created by the repetitive schedule could limit the ability to maximize profitability After applying constraints to the objective, you have the basis for an optimization problem, the general form of which is as follows: optimize the objective function subject to the constraints acting on the system.

Applying constraints

The power of optimization is in the application of constraints to the model. Applying constraints may create optimal solutions that are not intuitive, especially to those without formal training in optimization. This is because the dynamics of the model are not fully understood, and the models themselves are sufficiently complex that optimization through observation (or foresight) is not possible. Consider the following example.

A company produces two products. The 830 has a unit margin of \$35, whereas the 930 has a unit margin of \$30. Markets for the products are large enough that the company cannot meet the demand for either product. Considering this information only without regard to the constraints acting on the system that will be used to manufacture the items, it is clear that the company should use all of its capacity to meet the demand for the 830 market.

Taking account of the constraints, however, may lead to a different result. …