In production planning and logistics planning, there are multiple purposes which are to reduce cost of procurement and to shorten transportation time, and so on. These are sometimes contrary to each other and have different units. To adjust the balance of these purposes is important to the satisfaction of operators for the plan. Although various methods have been proposed in these multi-objective optimizations, there exists a problem it is impossible to derive the satisfactory result for operators, because the reason for the difficulty of judging for each purpose. Therefore, in this paper, we consider the achievement as operators’ preferred solution and aim to obtain a satisfactory plan for operators by proposing a method to estimate the importance of each objective to obtain this preferred solution. In the proposed method, the weighting coefficient of the problem is estimated as an inverse problem. In the cases the preferred solution is a Pareto optimal solution and a base solution, or the preferred solution is not a Pareto optimal solution or a basis solution, but a Pareto optimal constraint is given, it was confirmed that we can estimate the weighting coefficient to make the optimal solution is consistent with the preferred solution.

In this paper, we deal with a cooperative production planning model in which multiple firms mutually pool a part of resources procured by themselves. Although the firms are cooperative in the sense that pooling of the resources is allowed, we consider an equilibrium model in which the firms maximize their own profits and a Nash equilibrium point with respect to their profits is calculated. Finally, we show allocation schemes based on a cooperative game arising from the cooperative linear production planning with pooling of the resources because the total profit of all the firms in the cooperative production planning model is larger than that in the independent production planning model without pooling. Calculating the Nash equilibrium points of a numerical example with various pooling rates and the corresponding profit allocations, we demonstrate the validity of the proposed cooperative production planning model.

Much attention has been paid on CMGs (Control Moment Gyros) as a large torque generator of spacecraft. There are many studies on singularities of CMGs. However, the steering law in their studies has achieved only singularity avoidance in most cases. In this paper, we propose a multi-objective steering law which achieves complete 3-axis attitude control while considering not only singularity avoidance but also another function. First, we introduce a steering law for both singularity avoidance and power optimization. Second, we propose another steering law for both singularity avoidance and achieving preferred gimbal angles. Regarding the control law, we apply a GS (Gain-Scheduled) controller via LPV control theory while introducing a Parameter-Dependent Coordinate Transformation.