ABSTRACT
This chapter explains a new version of Network Simplex Algorithm (NSA), which avoids cycling and is faster. The arcs in the graph are divided into several blocks with the same size. At each iteration, a packet of the violated arcs are collected. The capacity of the packet is more than the block's size, and the most violated arcs are kept at the top of the packet. The memory technique uses a few elements at the top of the packet for the next iteration. At the beginning of the entering arc procedure, the reduced costs of the most violated arcs in the previous stage are recalculated. At the beginning, based on the solution to the current problem, a job is assigned to each vehicle and crane. The main features of NSA+ deal with the entering arc and leaving arc. In order to find an entering arc, the algorithm uses a mixture of memory techniques and heuristic method.
