Response to 'Theory of constraints and linear programming: A re-examination'

The thrust of `Theory of constraints and linear programming’ (Luebbe and Finch 1992) was to compare and contrast linear programming with the theory of constrains (TOC). This comparison examined the ® ve step TOC process with the intent to demonstrate that TOC’s contributions are di€ erent from linear programming. The Balakrishnan and Cheng paper, according to their abstract, focuses on comparing the results of linear programming with the $ return/per unit of constraint consumed approach sometimes used in TOC. It is important to recognize that this is not a comparison of linear programming with TOC. It is a comparison of linear programming with one of many techniques sometimes incorporated in TOC. TOC employs a 5-step focusing process designed to help managers improve throughput. The second step (exploit the constraint) can be accomplished, in some situations, by utilizing the return/unit of constraint consumed technique. It makes intuitive sense that when exploiting the constraint, or getting the most out of it in terms of system goals, it would be useful to know what the return (in terms of system goals) per unit of constraint consumed would be. Given a constrained resource, the product mix that provided the greatest return per unit of the constraint would be the one that exploits the constraint the best. It is important to recognize that product mix is only one of many ways to exploit a constraint. Constraints can also be exploited through preventive maintenance, quality inspections, scheduling, etc. In many situations, such as a make-to-order environment, the product mix is not in the hands of management, thus determining the product mix that best utilizes the constraint would not be possible. Sometimes in make-to-order environments the constraint actually shifts as changes in order proportions change the mix. The issue of LP being a technique and TOC being a focusing process consisting of many di€ erent techniques was an important conclusion of the Finch and Luebbe article. The failure of the return/unit of constraint consumed technique that the Balakrishnan and Cheng paper focuses is a valid concern and has been recognize for some time. For example, Finch and Luebbe, (1995) identify that there are di culties with the methodology when multiple constraints are present. The ® rst scenario presented in the 1992 Finch and Luebbe article (P, Px, Q, Qx) had multiple constraints. Both A and B required over-utilization. However, by adding more processing time to machine A for all of the products, the over-utilization of A increased, creating the possibility for constrains to interact as production occurs. The issue of changing or interacting constraints is a familiar problem, especially in make-to-order environments or other environments with very dynamic demands or product mixes. The constraints may change on a weekly, daily or even as often as an hourly basis.