Finding optimum product-mix for production systems is an important decision. Several researchers have developed algorithms to determine the product-mix under the Theory of Constraints (TOC). Literature reveals failure of the traditional TOC heuristic in determining product-mix when multiple constrained resources exist. In this paper, a Mixed Integer Linear Goal Programming (MILGP) model is proposed to deal with product-mix problem when multiple constrained resources exist. The proposed MILGP model emphasizes utilization of all bottlenecks as the primary goal and maximization of throughput as the secondary goal. The proposed model is experimented on problems cited in literature and the randomly generated ones, and the optimum results are reported by the proposed model.

The Theory of Constraints (TOC), a relatively new management philosophy, proposed by Goldratt and Cox (1992), is based on effective use of system’s constraints. The TOC’ philosophy stresses that a system’s outputs are determined by its constraint(s). Goldratt proposed Five Focusing Steps (FFS) process for managing constraints and continuously improving any system. The TOC FFS are:

1. IDENTIFY the system’s constraint(s), whether physical or policy constraint.
2. Decide how to EXPLOIT the system’s constraint(s), i.e., get the best possible from the limit of the current constraint(s); reduce the effects of the current constraint(s); and make everyone aware of the constraint(s) and its effects on the performance of the system.
3. SUBORDINATE everything else to the above decision, i.e., avoid keeping non-constraint resources busy doing unneeded work.
4. ELEVATE the system’s constraint(s), i.e., offload some demand or expand capability.
5. If in the previous steps a constraint has been broken, go back to Step 1, but do not allow INERTIA to cause a system constraint.

Determining the product-mix for a given period of time is one of the important production decisions. The objective is to utilize the limited resources to maximize the net value of the output from the production facilities. The product-mix decision is dependent upon the production capacities of facilities, demand for various products, and the sales revenue and costs associated with each product. Traditionally, Linear Programming (LP) is used to solve the product-mix problem. The product-mix problem has been discussed in the TOC literature since Goldratt (1990) first reported it with the example of the simple P’s and Q’s problem (where P and Q are products in productmix). Many researchers have compared the TOC heuristic with LP and found that the former gives optimal results (Luebbe and Finch, 1992; and Patterson, 1992). The TOC heuristic uses the ratio of Contribution Margin (CM) to the processing time on the bottleneck as the production priority (Patterson, 1992). Plenert (1993) concluded that the TOC heuristic did not provide an optimal or even feasible solution for product-mix problems with multiple constrained resources. Fredendall and Lea (1997) revised the traditional TOC algorithm for multiple constrained resources product-mix problem. Aryanezhad and Komijan (2004) showed disadvantages of the revised algorithm of Fredendall and Lea (1997) and proposed an improved algorithm for multiple constrained resources product-mix problem. They concluded that multiple resource constrained product-mix problem is like a Multiple Objective Decision-Making (MODM) problem and each bottleneck contributes to the decision-making process. This study tries to further extend the conclusions of Aryanezhad and Komijan (2004) and proposes a Mixed Integer Linear Goal Programming (MILGP) model for solving multiple constrained resources product-mix problem.

Operations Management Journal, Theory of Constraints (TOC), Mixed Integer Linear Goal Programming (MILGP), Optimizing Multiple Constrained Resources, Product-Mix Problem, Theory of Constraints.