Production planning models for a central factory with multiple satellite factories

The production planning problem of minimizing total cost, which consists of transportation cost, processing cost, raw material holding cost, and finished product inventory holding cost in a network of factories involving a central factory and multiple satellite factories is investigated in this paper. Based on two different raw material purchase plans, two non-linear mathematical programming models are formulated. In the first model, the material ordering policy at any given factory is based on the aggregation of each raw material type demanded over all items to be manufactured in the factory during a given production period. In the second model, lot consolidation for ordering is not done. The raw materials for each item produced by a factory are ordered separately. These two models integrate the raw material supply factory selection problem, order size determination, order processing sequence, and material handling functions to define a cost-effective production plan. The results from the model define a production plan, material purchase policy between factories, and selection of factory site (producing or purchasing factory) to hold items in inventory in order to minimize total factory network cost. Heuristics which used two linear mixed-integer programming submodels, are developed to solve the models. An example problem and several test results are given to demonstrate the use of the developed models and algorithms.