Production problems with multiple criteria

Production managers seek to attain low production costs, high quality of products, quick response to demand, and the flexibility to produce a variety of goods that match customers’ tastes and specifications. These multiple concerns, useful in enhancing a firm’s competitive position and profitability, must be considered in the design of a production system and in determining numerous planning and control decisions. Unfortunately, a factory or an operating system is seldom able to produce optimal results for all criteria simultaneously. Trade offs must be made. Although the necessity of making trade offs among multiple conflicting objectives or criteria has been recognized in the literature, few formal methods have been proposed to aid a manager in making such trade offs. Almost all of the literature in production management deals with optimization on a single criterion, whereas nearly all real world decisions involve balancing multiple concerns and criteria. In this article, we provide a framework for analyzing production problems that incorporates multiple criteria and we discuss several methods that are useful in obtaining solutions for these problems.


Consider a scheduling problem in which a manager must determine the sequence for the manufacture of some customized products with a common set of labor and facilities. In selecting a sequence, the manager may wish to balance machine utilization, work-in-progress inventory, and on-time deliveries. Often, a sequence that is optimal (produces the best results) for one criterion may produce an unacceptable level for some other criterion. In fact, a manager may finally select a sequence that is not optimal with respect to any single criterion but provides a good solution for all the criteria of interest.

In materials management, at an aggregate level, a manager may be interested in balancing investment in inventory, the cost of running the department, and the service level provided. For example, a simple annual ordering of parts and components to satisfy the anticipated demand and adequate buffer stock may result in low cost of running the purchasing department and excellent service level but may require unacceptably high investment in inventory.

In selecting the location for a new plant, a manager may wish to balance land and building costs, delivery time to customers, labor availability, ability to attract professional and technical personnel, among other factors. The economic considerations alone may not be sufficient, as managers have other qualitative but strategically important concerns for location, capacity expansion, and technology choice decisions.

Finally, in formulating a manufacturing strategy, trade offs among cost, quality, dependability, and flexibility must be explicitly considered. These trade offs determine the unique positioning of a firm within the industry. A company may place a high weight on the cost criterion and gear its manufacturing organization and plant to low cost production. Another company may emphasize customization and therefore will choose a flexible process and emphasize flexibility in its production planning methods. The relative weights placed on different criteria will determine many other intermediate manufacturing positions.

No single method of analysis will be sufficient to deal with all of the different types of decision problems that occur in production and operations. Based on the nature of the decision problem and the type of information available, different methods may be suitable for different problems.

Problem Statement and defining criteria:

Consider a simple situation in which there are N decision alternatives denoted a1, a2 …., aN. The desirability of each alternative is measured on m criteria. The performance of the alternative aj on the ith criterion is denoted fji. The table depicts this notation. To illustrate the notation, consider a site location problem. Each site is denoted by aj; for example, a1=Cleveland, a2 = Detroit and so on. The criteria that are relevant in selecting a site may be capital costs (land, plant, equipment, and construction), labor availability, operating costs (determined by wages, electricity, water, taxes etc) and availability of transportation. Further, suppose that the capital costs are measured in million of dollars, labor availability is measured as the percentage of factory labor requirements that can be met from the local labor pool, operating costs are measured by per unit cost of production, and the availability of transportation is measured on a subjective scale as excellent, very good, good, fair and poor.

The mathematical solution derived for various alternatives is beyond the scope of this article as such it is not shown in this article.