Conditions for the discovery of solution horizons

We present necessary and sufficient conditions for discrete infinite horizon optimization problems with unique solutions to be solvable. These problems can be equivalently viewed as the task of finding a shortest path in an infinite directed network. We provide general forward algorithms with stopping rules for their solution. The key condition required is that of weak reachability, which roughly requires that for any sequence of nodes or states, it must be possible from optimal states to reach states close in cost to states along this sequence. Moreover the costs to reach these states must converge to zero. Applications are considered in optimal search, undiscounted Markov decision processes, and deterministic infinite horizon optimization.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/47927/1/10107_2005_Article_BF01581244.pd

A decision support model to improve rolling stock maintenance scheduling based on reliability and cost

Thesis (MEng)--Stellenbosch University, 2014.ENGLISH ABSTRACT: The demand for rail travel has increased over the years. As a result, it is becoming mandatory for railway industries to maintain very high availability of their assets to ensure that service levels are high. Railway industries require both their infrastructure and rolling stock assets maintained efficiently to sustain reliability. There has been on-going research on how maintenance can be carried out in a cost effective manner. However, the majority of this research has been done for infrastructure and the rolling stock maintenance has not been properly covered. The purpose of this research is to contribute to the maintenance sector of rolling stock for railway industries by developing a decision support model for rolling stock based on reliability and cost. The model is developed as an optimization problem of a system containing several components dependent on each other with different reliability characteristics. In this model, a mixed integer nonlinear problem is developed and solved using an exact method and metaheuristics methods. The Metrorail facility in Cape Town was chosen as a case study. Failure history and cost data were gathered from the facility and the information was applied to the model developed. The case study was investigated and different results were achieved using both exact and metaheuristics methods. The final result from the study is an optimal maintenance schedule based on reliability and cost. The developed model serves as a practical tool railway companies can adopt to schedule rolling stock maintenance to achieve a high level of reliability and at the same time maintaining minimum cost expenditure.AFRIKAANSE OPSOMMING: Die vraag na spoorvervoer het oor die jare toegeneem. Dus het dit belangrik geword dat die spoorweg se bates hoogs toeganklik moet wees om te verseker dat die vlak van dienslewering hoog bly. Die spoorweg industrie besef dat hulle infrastruktuur, lokomotiewe, waens ens. effektief in stand gehou moet word sodat dit betroubaar kan wees. Navorsing word nog steeds gedoen oor hoe instandhouding op ’n koste-effektiewe wyse gedoen kan word. Die meeste van hierdie navorsing gaan egter oor infrastruktuur en instandhouding word nie ordentlik gedek nie. Die doel met hierdie navorsing is om by te dra tot die instandhoudingsektor van die spoorweg deur om ’n besluit-ondersteunende model vir lokomotiewe, waens, ens wat op betroubaarheid en koste gegrond is, te ontwikkel. Die model is ontwikkel as ’n optimasie probleem van ’n sisteem wat verskillende komponente wat van mekaar afhanklik is maar oor verskillende betroubaarheidskenmerke beskik, inluit. In hierdie model word ’n gemengde, heeltal nie-lineêre probleem ontwikkel en met ’n eksakte metode en metaheuristiese metodes opgelos. Die Metrorail fasiliteit in Kaapstad is vir die gevalle studie gekies. Die geskiedenis van mislukkings en koste data is by die fasiliteit versamel en die inligting is op die model wat ontwikkel is, toegepas. Die gevalle studie is ondersoek, en verskillende resultate is met eksakte en metaheuristiese metodes bereik. Die finale uitkomste van die studie is ’n optimale instandhoudingskedule wat op betroubaarheid en koste gegrond is. Die model wat ontwikkel is dien as ’n praktiese instrument wat spoormaatskappye kan gebruik om die instandhouding van lokomotiewe, waens ens. te reël sodat ’n hoë vlak van betroubaarheid bereik kan word en kostes terselfdertyd tot ’n minimum beperk kan word