6B3 A UNIFIED MODELING AND SOLUTION PRINCIPLE FOR FINE SCHEDULING(Technical session 6B: General model for scheduling and assignment problem)

This paper presents a unified method for formulating a multi-item multi-process dynamic lot size scheduling problem and its extensions into fine mathematical models. Then, the paper refers to its global optimization oriented solution principle, which is based on Lagrangian decomposition coordination method together with heuristics. In modeling, first, we derive a dynamic equation of processing of an item and the accompanied work-in-process stock transition. It is described by use of "echelon inventory" so as to ensure additively separable property of the model and enable its decomposition. Then, we guarantee feasibility of processing on a machine. Placing the inequality constraint to interdict machine interference attains it. Last, we integrate all of the processing over the whole processes. Placing the one to interdict work-in-process stock shortage also attains it. Further, in the extended problem, our finding is that besides the constraints stated above there exists some additional restrictions unique to the problem, which specify the operation, whether it is real processing or set up, and yet define relative states among multiple system elements. Then, instead of formulating those directly, we introduce imaginary items and their work-in-process once and then place the constraints to interdict excess and shortage of them under some additional assumptions. This gives a means for solution.