Planning coordination for multiple companies has received much attention from viewpoints of global supply chain management. In practical situations, a plausible plan for multiple companies should be created by mutual negotiation and coordination without sharing such confidential information as inventory costs, setup costs, and due date penalties for each company. In this paper, we propose a framework for distributed optimization of supply chain planning using an augmented Lagrangian decomposition and coordination approach. A feature of the proposed method is that it can derive a near-optimal solution without requiring all of the information. The proposed method is applied to supply chain planning problems for a petroleum complex, and a midterm planning problem for multiple companies. Computational experiments demonstrate that the average gap between a solution derived by the proposed method and the optimal solution is within 3% of the performance index, even though only local information is used to derive a solution for each company.

In this paper, we propose a distributed routing method for multiple mobile robots under uncertain motion delays. The feature of the proposed method is that each AGV subsystem creates the routing to minimize the sum of the transportation time and the penalty for collision avoidance constraints taking into account motion delay disturbances for other AGVs. The computational results show that the total transportation time obtained by the proposed method is shorter than that of the conventional method under various type of motion delay disturbances.

We propose a distributed routing system for multi-robot cooperative transportation using parallel multiple processors with asynchronous data exchange. In the proposed method, each robot generates a routing to minimize each objective function comprising of traveling time and the penalty for violating constraints of cooperation with other robots. A near optimal routing is generated by repeating the generation of each routing and data exchange among the robots. Asynchronous data exchange is adopted to reduce the computation time. In order for the solution not to be trapped in a local optimum, the weighting factors violating the constraints are updated with a time-dependent method during parallel computation. The proposed method is applied to motion planning for cooperative transportation of an experimental 4 real robots system. The effectiveness of the proposed method is investigated on various types of experimental conditions.

Coordination and optimization of supply chain planning among multiple companies have widely been received much attention from viewpoints of global supply chain management. Conventional system for supply chain planning is configured on the assumption that correct information for entire company is available by sharing the detailed information among multiple companies. It is required to generate a near optimal plan for multiple companies without sharing the confidential information such as inventory costs, set up costs and due date penalties among competing companies. In this paper, we propose a framework of a distributed supply chain planning for multiple companies by using an augmented Lagrangian relaxation approach. The proposed method features that a feasible solution can be derived without using the entire information by exchanging the data which is not directly related to cost data. From the computational experiments, it has been shown that the average gap between the solution derived by the proposed method and an optimal solution is within 1% of the performance index even though only the local information is used to derive a solution for each company

To enable efficient transportation in semiconductor fabrication bays, it is necessary to generate route planning of multiple automated guided vehicles (AGVs) efficiently to minimize the total transportation time without collision among AGVs. In this paper, we propose a distributed route-planning method for multiple mobile robots using an augmented Lagrangian decomposition and coordination technique. The proposed method features a characteristic that each AGV individually creates a near-optimal routing plan through repetitive data exchange among the AGVs and local optimization for each AGV. Dijkstra's algorithm is used for local optimization. The optimality of the solution generated by the proposed method is evaluated by comparing the solution with an optimal solution derived by solving integer linear programming problems. A near-optimal solution, within 3% of the average gap from the optimal solution for an example transportation system consisting of 143 nodes and 14 AGVs, can be derived in less than 5 s of computation time for 100 types of requests. The proposed method is implemented in an experimental system with three AGVs, and the routing plan is derived in the configuration space, taking the motion of the robot into account. It is experimentally demonstrated that the proposed method is effective for various problems, despite the fact that each route for an AGV is created without minimizing the entire objective function.

Coordination of planning among several companies has been widely received much attention from the viewpoint of global supply chain management. In a practical situations, a plausible plan for several companies should be created by the negotiation and coordination among the companies without sharing the confidential information such as inventory costs, set up costs and due date penalties for each company. In this paper, we propose a framework of a distributed optimization of supply chain planning using a new augmented Lagrangian relaxation method. The feature of the proposed method is that a feasible solution can be derived without using the procedure of heuristic generation of feasible solutions. From the computational experiments, it has been shown that the average gap between the solution derived by the proposed method and an optimal solution is within 1% of the performance index even though only the local information is used to derive a solution for each company.

For the transportation in semiconductor fabricating bay, route planning of multiple AGVs (Automated Guided Vehicles) is expected to minimize the total transportation time without collision and deadlock among AGVs. In this paper, we propose a distributed route planning method for multiple mobile robots using Lagrangian decomposition technique. The proposed method has a characteristic that each mobile robot individually creates a near optimal route through the repetitive data exchange among the AGVs and the local optimization of its route using Dijkstra's algorithm. The proposed method is successively applied to transportation route planning problem in semiconductor fabricating bay. The optimality of the solution generated by the proposed method is evaluated by using the duality gap derived by using Lagrangian relaxation method. A near optimal solution within 5% of duality gap for a large scale transportation system consisting of 143 nodes and 15 AGVs can be obtained only within five seconds of computation time. The proposed method is implemented on 3 AGVs system and the route plan is derived taking the size of AGV into account. It is experimentally shown that the proposed method can be found to be effective for various types of problems despite the fact that each route for AGV is created without considering the entire objective function.

In the conventional Lagrangian relaxation approach, the scheduling problems are decomposed into job-level sub-problems or operation-level sub-problems. However, these approaches are not applicable to the flowshop problems with the changeover cost which depends on the sequence of operations. In this paper, we propose a machine-oriented decomposition method for the flowshop problems using the Lagrangian decomposition and coordination technique. In the proposed method, each sub-problem for single machine is solved by the simulated annealing method. The solutions of the sub-problems are used to generate a feasible schedule by a heuristic procedure. The effectiveness of the proposed method is verified by comparing the results of the example problems solved by the proposed method with those solved by the conventional method. Furthermore, it has been shown that the proposed approach is easily applicable to the flow hop problem with resource constrains minimizing the changeover costs and due date penalties.