A local search framework for the (undirected) Rural Postman Problem (RPP) is presented in this paper. The framework allows local search approaches that have been applied successfully to the well-known Travelling Salesman Problem also to be applied to the RPP. New heuristics for the RPP, based on this framework, are introduced and these are capable of solving significantly larger instances of the RPP than have been reported in the literature. Test results are presented for a number of benchmark RPP instances in a bid to compare efficiency and solution quality against known methods.

Practical vehicle routing problems generally have both routing and scheduling aspects to consider. However, few heuristic methods exist that address both these complicated aspects simultaneously. We present heuristics to determine an efficient circular traversal of a weighted graph that requires a subset of its edges to be traversed, each a specified (potentially different) number of times. Consecutive time instances at which the same edge has to be traversed should additionally be spaced through a scheduling time window as evenly as possible, thus introducing a scheduling consideration to the problem. We present a route construction heuristic for the problem, based on well-known graph theoretic algorithms, as well as a route improvement heuristic, that accepts the solution generated by the construction heuristic as input and attempts to improve it in an iterative fashion. We apply the heuristics to various randomly generated problem instances, and interpret these test results.

Real-life vehicle routing problems generally have both routing and scheduling aspects to consider. Although this fact is well acknowledged, few heuristic methods exist that address both these complicated aspects simultaneously. We present a graph theoretic heuristic to determine an efficient service route for a single service vehicle through a transportation network that requires a subset of its edges to be serviced, each a specified ( potentially different) number of times. The times at which each of these edges are to be serviced should additionally be as evenly spaced over the scheduling time window as possible, thus introducing a scheduling consideration to the problem. Our heuristic is based on the tabu search method, used in conjunction with various well-known graph theoretic algorithms, such as those of Floyd (for determining shortest routes) and Frederickson (for solving the rural postman problem). This heuristic forms the backbone of a decision support system that prompts the user for certain parameters from the physical situation (such as the service frequencies and travel times for each network link as well as bounds in terms of acceptability of results) after which a service routing schedule is suggested as output. The decision support system is applied to a special case study, where a service routing schedule is sought for the South African national railway system by SPOORNET (the semi-privatised South African national railways authority and service provider) as part of their rationalisation effort, in order to remain a lucrative company.

Hierdie artikel beskryf 'n familie van probleem-oplossingstegnieke bekend as " Constraint Programming", wat al hoe meer gebruik word om groot-skaalse industriële probleme op te los.Die nut van hierdie tegnieke word gedemonstreer deur die beskrywing van 'n skeduleringsisteem om die roosters vir 'n universiteit te genereer.Roosterskeduleringsprobleme is in praktiese gevalle NP-volledig en deel baie eienskappe met industriële skeduleringsprobleme. Die sisteem wat hier beskryf word maak gebruik van beide harde beperkings (wat altyd bevredig moet word) en sagte beperkings (bevrediging hiervan is wel voordelig maar dit is opsioneel.) http://sajie.journals.ac.za