Mathematical modeling of multi-plant order allocation problem and solving by genetic algorithm with matrix representation

As many enterprises deal with orders of various products everyday and attend to maximize total profit or minimize total cost, a quick automatic dispatching tool is required for higher efficiency. In practical, the dispatching is not an easy task even for experienced experts; it is often determined depending on empirical knowledge, but usually would not be the optimal solution. It is due to the complex nature of the so-called “multi-plant order allocation problem”, which can be modeled as a typical mixed-integer programming problem. Considering companies with multiple plants, the large quantity of orders need to be distributed within a short time and the due dates of various orders shall be met such that the total costs can be minimized. In this research, an order allocation scheme for multi-plant to produce a variety of products is developed. The objective is to minimize total cost, including operation cost, setup cost, transportation cost, and the penalty cost of order delay under the constraint of capacity load. A mixed-integer programming model, named model of quasi-transportation problem, is proposed and solved. Several examples are presented and solved and compared by a general software LINDO and a genetic algorithm. Proposed genetic algorithm is demonstrated to be more efficient as the dimension of problem increases.