Number Of Side Constraints Research Articles

Computational complexity of convoy movement planning problems

Convoy movement planning problems arise in a number of important logistical contexts, including military planning, railroad optimization and automated guided vehicle routing. In the convoy movement problem (CMP), a set of convoys, with specified origins and destinations, are to be routed with the objective of minimizing either makespan or total flow time, while observing a number of side constraints. This paper characterizes the computational complexity of several restricted classes of CMPs. The principal objective is to identify the most parsimonious set of problem features that make the CMP intractable. A polynomial-time algorithm is provided for the single criterion two-convoy movement problem. The performance of a simple prioritization–idling approximation algorithm is also analyzed for the K-convoy movement problem. Error bounds are developed for the makespan and flow time objectives.

A Network Simplex Algorithm for the Equal Flow Problem on a Generalized Network

A network simplex algorithm is described for the minimum-cost network flow problem on a generalized network, with the additional constraint that there exist sets of arcs that must carry equal amounts of flow. This problem can be modeled as a linear programming problem and solved using the standard simplex algorithm. However, because of the structure of the problem, more efficient algorithms are possible that solve the problem by operating directly on the network itself. One such algorithm is described that leads to improved asymptotic performance per iteration over the standard simplex algorithm, as long as the number of side constraints is small relative to the size of the network. Computational results are given comparing this algorithm to CPLEX's primal simplex solver on randomly generated graphs.

The Distribution Problem with Carrier Service: A Dual Based Penalty Approach

The distribution problem with carrier service is an important optimization problem that often arises in vehicle routing. The problem arises in the distribution of commodities from a central facility to a set of geographically distributed locations. Each location has a certain demand, the distribution vehicle has a load capacity, and the entire operation should be completed within a certain time. An outside carrier is available for direct service of locations from the central facility. The problem is to determine a feasible tour for the company vehicle and the locations to be served by the outside carrier such that the total cost of the operations is minimized. We model this problem and develop a solution technique using valid inequalities. A key feature of the solution approach is that it can easily be extended to solve similar problems with any type and number of side constraints as encountered in the current model. The algorithm has been extensively tested and computational results for problems having up to 200 locations are presented. The results show that the proposed approach is efficient and viable for solving problems of medium to large size. We also present a real-world application, and show how the model is implemented within the framework of an order scheduling and vehicle routing system. We present performance results with real-world data and demonstrate the operational efficiency achieved by using the proposed approach. INFORMS Journal on Computing, ISSN 1091-9856, was published as ORSA Journal on Computing from 1989 to 1995 under ISSN 0899-1499.