Abstract
This paper investigates the problem of clarifying a method to obtain a feasible production schedule for multiple products on a single machine over a finite planning horizon. The paper takes into consideration four types of transportation method from the machine's location to each place of consumption, which are derived from the possible combinations on the two factors ; supply timing and transportation lot consolidation. The paper deals with a general case in which the four types are specified under arbitrary mixture for all products. First, the "demand and supply quantity balance equation" in each production cycle is derived. Then, when the planning horizon is sufficiently long, a property is presented that the solution for this balance equation converges to the "balanced lot size, " which is proportional to the demand rate of each product. This property holds irrelevant to the production sequence and the mixture of the transportation types. The paper then presents two scheduling methods, direct application of the solution for the balance equation and utilization of the balanced lot size, for both cases where demand rate for each product is constant, or varies a finite number of times, over the given planning horizon. Furthermore, pros and cons of the two methods are examined from the practical viewpoint of their applications.
