A dynamic version for the Network Simplex Algorithm

Simulation and Evaluation of Network Simplex Algorithm and its Extensions for Vehicle Scheduling Problems in Ports

“…When S (as the dynamic stage) is zero, the procedure Generate Initial BFS is called. Otherwise, the Reconstruct New BFS procedure repairs the current solution and spanning tree at time t; (Tt, Lt, Ut) is reconstructed (See [5] for more detail). The main body of the algorithms, NSA and DNSA, are the same.…”

“…For the arcs and nodes in the graph model, an Identification flag has been considered. The Identification flag associated with each arc identifies whether the arc is in the Tt set, Lt set, Ut set, or Dt set (see [5]) at time t. There is the one-to-one mapping between every location in the Job Buffer and the nodes associated with the job in the graph model. When a job is fulfilled, the nodes associated with this job are marked for deletion.…”

“…The algorithm iterates towards an optimal solution by exchanging basic and non-basic arcs in the graph. NSA has three extensions, namely network simplex plus algorithm (see [4]), dynamic network simplex algorithm and dynamic network simplex plus algorithm (see [5]). To compare the advantages and disadvantages of those algorithms, we choose one of the challenging problems in transportation area.…”

“…Given a number of AGVs and their availability, the task is to schedule the AGVs to meet the transportation requirements. In order to determine to what extent NSA and its extensions can be applied in practice, this paper followed the research done in [5]. The structure of the remaining parts is as follows: Next section is a brief description of the related works over algorithms and problems.…”

The syntax and semantics of a domain-specific language for flow-network design

“…Ours are in fact identical to linear constraints (but not necessarily the linear objective function) that arise in the network simplex method [24], i.e., linear programming applied to problems of network flows. There is still on-going research to improve network-simplex algorithms (e.g., [25]), which will undoubtedly have a bearing on the efficiency of typing inference for our DSL.…”