Tatsushi Nishi

Petri Net Decomposition Approach to Optimization of Route Planning Problems for AGV Systems

In this paper, we propose a Petri Net (PN) decomposition approach to the optimization of route planning problems for automated guided vehicles (AGVs) in semiconductor fabrication bays. An augmented PN is developed to model the concurrent dynamics for multiple AGVs. The route planning problem to minimize the total transportation time is formulated as an optimal transition firing sequence problem for the PN. The PN is decomposed into several subnets such that the subnets are made independent by removing the original shared places and creating its own set of resource places for each subnet with the appropriate connections. The partial solution derived at each subnet is not usually making a feasible solution for the entire PN. The penalty function algorithm is used to integrate the solutions derived at the decomposed subnets. The optimal solution for each subnet is repeatedly generated by using the shortest-path algorithm in polynomial time with a penalty function embedded in the objective function. The effectiveness of the proposed method is demonstrated for a practical-sized route planning problem in semiconductor fabrication bay from computational experiments.

A distributed decision making system for integrated optimization of production scheduling and distribution for aluminum production line

A distributed decision making system for integrated optimization of production scheduling and distribution planning is proposed. The system consists of several subsystems that individually derive the solution of its own subproblem to minimize the objective function obtained by decomposing the problem using an augmented Lagrangian decomposition and coordination technique. The proposed approach is applied to planning and scheduling for an aluminum rolling processing line. Decision variables such as arrival date of raw materials, lot-sizing, production scheduling, and allocation of products to warehouses are optimized simultaneously by repeating local optimization in material resource planning, and scheduling subsystem for each production process and warehouse planning subsystem. The effectiveness of the proposed approach is demonstrated.

Lagrangian relaxation with cut generation for hybrid flowshop scheduling problems to minimize the total weighted tardiness

In this paper, we address a new Lagrangian relaxation (LR) method for solving the hybrid flowshop scheduling problem to minimize the total weighted tardiness. For the conventional LR, the problem relaxing machine capacity constraints can be decomposed into individual job-level subproblems which can be solved by dynamic programming. The Lagrangian dual problem is solved by the subgradient method. In this paper, a Lagrangian relaxation with cut generation is proposed to improve the Lagrangian bounds for the conventional LR. The lower bound is strengthened by imposing additional constraints for the relaxed problem. The state space reductions for dynamic programming for subproblems are also incorporated. Computational results demonstrate that the proposed method outperforms the conventional LR method without significantly increasing the total computing time.

Petri Net Decomposition Approach for Dispatching and Conflict-Free Routing of Bidirectional Automated Guided Vehicle Systems

In this paper, we address a Petri net decomposition approach for simultaneous dispatching and conflict-free routing for bidirectional automated guided vehicle (AGV) systems in dynamic environments. To solve the dynamic problem, static problems for finding near-optimal dispatching and conflict-free routing are solved each time when transportation requests are given. The static problem is converted to an optimal firing sequence problem for a timed Petri net. A Petri net decomposition approach is applied to solve the problem efficiently. In the algorithm, the entire Petri net is decomposed into task and AGV subnets. The penalty function method is used to derive a solution for all subnets. A deadlock avoidance method is embedded in the proposed methodology to ensure the feasibility and the quality of the solution. Computational results show that the proposed method with a deadlock avoidance algorithm efficiently maximizes the throughput for dynamic situations.

A bilevel decomposition algorithm for simultaneous production scheduling and conflict-free routing for automated guided vehicles

We address a bilevel decomposition algorithm for solving the simultaneous scheduling and conflict-free routing problems for automated guided vehicles. The overall objective is to minimize the total weighted tardiness of the set of jobs related to these tasks. A mixed integer formulation is decomposed into two levels: the upper level master problem of task assignment and scheduling; and the lower level routing subproblem. The master problem is solved by using Lagrangian relaxation and a lower bound is obtained. Either the solution turns out to be feasible for the lower level or a feasible solution for the problem is constructed, and an upper bound is obtained. If the convergence is not satisfied, cuts are generated to exclude previous feasible solutions before solving the master problem again. Two types of cuts are proposed to reduce the duality gap. The effectiveness of the proposed method is investigated from computational experiments.

An autonomous decentralized supply chain planning system for multi-stage production processes

In this paper, we propose an autonomous decentralized optimization system for multi-stage production processes. The proposed system consists of a Material Requirement Planning subsystem, a Distribution Planning subsystem and Decentralized Scheduling subsystems belonging to each production stage that constitute the entire plant. In the proposed system, each subsystem repeats both optimization of the schedule at each subsystem and data exchange among the subsystems. Computational results demonstrate that the results of the proposed planning system are superior to those of the hierarchical planning system, despite the fact that the proposed system has wide flexibility for adding the constraints and modifying the criterion of performance evaluation.

Distributed route planning for multiple mobile robots using an augmented Lagrangian decomposition and coordination technique

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. Dijkstras 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.

Column generation heuristics for ship routing and scheduling problems in crude oil transportation with split deliveries

Abstract We propose a column generation based heuristic algorithm to solve a ship routing and scheduling problem for crude oil transportation with split deliveries. The problem is to find an optimal assignment and sequence and loading volume of demand simultaneously in order to minimize the total distance satisfying the capacity of tankers. The problem can be considered as a multi-product heterogeneous fleet split pickup ship routing problem with finite capacity and loading constraints. An efficient heuristic algorithm based on the column generation method is developed to generate a feasible solution taking into account of practical constraints. The performance of the proposed method is compared with the branch and bound algorithm and that of human operators. Computational results demonstrate the effectiveness of the proposed algorithm for a real case.

An Augmented Lagrangian Approach for Distributed Supply Chain Planning for Multiple Companies

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.

A distributed route planning method for multiple mobile robots using Lagrangian decomposition technique

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 Dijkstras 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.