The optimal production plan under limited production capacity at any point in time

For the production planning decision maker needing to fit new orders into a pre-existing production plan with limited production capacity, he must estimate how much unused capacity exists at any given point in time in the prearranged production plan. In this study, we assume that the available production capacity at each point in time is estimated and known, and it is intended to build this issue into a mathematical model that is concrete for discussion with the purpose of minimizing total costs, where the total costs is the sum of production operating costs and inventory costs at any given point in time during the production process. Seeking an optimal solution and a sensitivity analysis of optimal solutions are the main parts of this study. From the results of this study, we can provide a decision procedure for an optimal production control plan for a new order for the production planners as a decision reference.