Parallel branch and bound algorithm for scheduling problem with retooling

The paper deals with parallelization of a branch-and-bound (BB) algorithm for one-machine scheduling with retooling. A one-machine shop is to produce n different items, requiring retooling whenever the produced item is changed. The retooling time depends on the items. It may be assumed infinite for some pairs of items when retooling is difficult. The retooling times and the times to produce each of the items are known: One must find the production sequence so that the total time to produce all the items is minimal and the retooling time between last and first items is not infinite. In network theory terms, the problem is to find a minimum-weight cycle of length n in a given weighted graph G of n nodes. G is given in the form of the matrix A, where the element a[ijl denotes the weight of [ijl arc. The nodes represent items to be performed and the element a[ij] is the sum of the j-th item processing time and the retooling time between i-th and j-th items. This is the travelling salesman problem (TSP). The paper presents 3 parallel algorithms based on the sequential BB algorithm. They are implemented in C and have been examined with use of package PVM (Parallel Virtual Machine). The results are given and discussed.