Browsing by Author "Visagie, Stephan E."
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- ItemAlgoritmes vir die maksimering van konvekse en verwante knapsakprobleme(Stellenbosch : University of Stellenbosch, 2007-03) Visagie, Stephan E.; De Kock, H. C.; University of Stellenbosch. Faculty of Economic and Management Sciences. Dept. of Logistics.In this dissertation original algorithms are introduced to solve separable resource allocation problems (RAPs) with increasing nonlinear functions in the objective function, and lower and upper bounds on each variable. Algorithms are introduced in three special cases. The first case arises when the objective function of the RAP consists of the sum of convex functions and all the variables for these functions range over the same interval. In the second case RAPs with the sum of convex functions in the objective function are considered, but the variables of these functions can range over different intervals. In the last special case RAPs with an objective function comprising the sum of convex and concave functions are considered. In this case the intervals of the variables can range over different values. In the first case two new algorithms, namely the fraction and the slope algorithm are presented to solve the RAPs adhering to the conditions of the case. Both these algorithms yield far better solution times than the existing branch and bound algorithm. A new heuristic and three new algorithms are presented to solve RAPs falling into the second case. The iso-bound heuristic yields, on average, good solutions relative to the optimal objective function value in faster times than exact algorithms. The three algorithms, namely the iso-bound algorithm, the branch and cut algorithm and the iso-bound branch and cut algorithm also yield considerably beter solution times than the existing branch and bound algorithm. It is shown that, on average, the iso-bound branch and cut algorithm yields the fastest solution times, followed by the iso-bound algorithm and then by die branch and cut algorithm. In the third case the necessary and sufficient conditions for optimality are considered. From this, the conclusion is drawn that search techniques for points complying with the necessary conditions will take too long relative to branch and bound techniques. Thus three new algorithms, namely the KL, SKL and IKL algorithms are introduced to solve RAPs falling into this case. These algorithms are generalisations of the branch and bound, branch and cut, and iso-bound algorithms respectively. The KL algorithm was then used as a benchmark. Only the IKL algorithm yields a considerable improvement on the KL algorithm.
- ItemAssignment of stock keeping units to parallel unidirectional picking(SAIIE, 2015-05) Matthews, Jason; Visagie, Stephan E.An order picking system consisting of a number of parallel unidirectional picking lines is investigated. Stock keeping units (SKUs) that are grouped by product type into distributions (DBNs) are assigned daily to available picking lines. A mathematical programming formulation and its relaxations is presented. A greedy insertion and a greedy phased insertion are further introduced to obtain feasible results within usable computation times for all test cases. The walking distance of the pickers was shown to decrease by about 22 per cent compared with the current assignment approach. However, product handling and operational risk increases.
- ItemFairness of seat allocation methods in proportional representation(Operations Research Society of South Africa, 2005) Van Eck, L.; Visagie, Stephan E.; De Kock, H. C.ENGLISH SUMMARY : In this paper the fairness of some methods of allocating seats in a proportional representation (PR) voting system is investigated. Different PR systems are in use throughout the democratic world, but the primary focus here is the method used in South Africa, namely the largest remainder method with a Droop quota. It is shown that as the number of parties increases, the number of lost votes (votes not used to allocate seats) increases when using this method. Other existing allocation methods are discussed and compared with each other as well as with three optimisation methods (based on mathematical programming) introduced in this paper. Applying these mathematical programming methods results in allocations that are more fair than the existing methods of seat allocation, if South African voting data are used. These mathematical models attempt to minimise a number of different measures of the deviation between the actual percentage of votes received and the percentage of seats allocated to a certain party. Ideally this deviation should be zero, but due to the discrete nature of seats this is virtually impossible to achieve.
- ItemGuidelines for the economic choice of transport infrastructure projects.(Southern African Association of Departments and Schools of Public Administration and Development (ASSADPAM)) c/o Prof. H.F Wissink, P.E. Technikon, Private Bag X 6011, Port Elizabeth, 6000, South Africa, 2000) Pienaar WJ; Visagie, Stephan E.
- ItemIntroducing Stellenbosch University Open Access Journals(Stellenbosch : Stellenbosch University, 2011-10) Simon, Carol; Thom, Johan; Botma, Gabriël; Botha, Willem; Brand, Gerrit; Visagie, Stephan E.; Van der Walt, Christa; Vrey, Francois; Khondowe, Oswell
- ItemOn the efficient solvability of a simple class of nonlinear knapsack problems(Operations Research Society of South Africa, 2008) Visagie, Stephan E.ENGLISH SUMMARY : In this paper the e cient solvability of a class of nonlinear knapsack problems are investigated by means of the problem's necessary and su cient conditions. It is shown that, from the general theory, it is impossible to determine su cient conditions for a solution to be globally optimal. Furthermore, it is shown that even for the smallest possible instance of this problem it is, in general, possible to have an arbitrary large number of solutions for which the necessary conditions hold. These results are then generalised to larger instances of the problem. A possible solution approach is applied to sets of randomly generated problems that utilises the necessary conditions together with the branch-and-bound technique in an attempt to limit the search space. This approach solves mixed 0/1 knapsack problems in order to nd all possible solutions satisfying the necessary conditions. Due to the large number of solutions satisfying the necessary conditions the proposed solution approach takes substantially longer than existing branch-and-bound algorithms together with linear enveloping when applied to the same set of problems. This result renders the proposed approach not very e cient.
- ItemOptimale toewysing en skedulering van werkers en take op 'n monteerbaan(AOSIS OpenJournals, 2009-03) Venter, L.; Visagie, Stephan E.Die optimale aanwending van kruisopgeleide werkslui in ’n produksielyn word ondersoek. Kruisopgeleide werkslui het die vermo¨e om haas enige taak in die produksieproses te verrig. ’n Wiskundige model om die optimale toewysing van werkers aan take te bepaal, word geformuleer. Die invloed van vaardige of onvaardige tydelike werkslui op die produksielyn word ook ondersoek. Die finale model neem verskeie doelwitte in ag. In die eerste fase word ’n nutsfunksie van produksie gemaksimeer terwyl werkers aan take toegewys word. Daarmee saam word die verbetering van die werkers se vaardigheidsvlakke gemaksimeer terwyl die effek van die leer en vergeet van vaardighede in ag geneem word. Die arbeidskoste van produksie word ook geminimeer terwyl die tipe werkers en die manier waarop hulle aangestel en afgelˆe moet word, bepaal word. Laastens word die totale produksietyd geminimeer terwyl die optimale volgorde van die take in die produksieproses bepaal word. Die praktiese bruikbaarheid van die model word ook met behulp van ’n gevallestudie gedemonstreer.
- ItemOptimising an integrated crop-livestock farm using risk programming(Operations Research Society of South Africa, 2004) Visagie, Stephan E.; De Kock, H. C.; Ghebretsadik, A. H.ENGLISH SUMMARY : Numerous studies have analysed farm planning decisions focusing on producer risk preferences. Few studies have focussed on the farm planning decisions in an integrated croplivestock farm context. Income variability and means of managing risk continues to receive much attention in farm planning research. Different risk programming models have attempted to focus on minimising the income variability of farm activities. This study attempts to identify the optimal mix of crops and the number of animals the farm needs to keep in the presence of crop production risk for a range of risk levels. A mixed integer linear programming model was developed to model the decision environment faced by an integrated crop-livestock farmer. The deviation of income from the expected value was used as a measure of risk. A case study is presented with representative data from a farm in the Swartland area. An investigation of the results of the model under different constraints shows that, in general, strategies that depend on crop rotation principles are preferred to strategies that follow mono-crop production practices.
- ItemPicking location metrics for order batching on a unidirectional cyclical picking line(Operations Research Society of South Africa, 2019-12-20) Hofmann, F. M.; Visagie, Stephan E.In this paper order batching is extended to a picking system with the layout of a unidirectional cyclical picking line. The objective is to minimise the walking distance of pickers in the picking line. The setup of the picking system under consideration is related to unidirectional carousel systems. Three order-to-route closeness metrics are introduced to approximate walking distance, since the orders will be batched before the pickers are routed. All metrics are based on the picking location describing when a picker has to stop at a location to collect the items for an order. These metrics comprise a number of stops, a number of non-identical stops and a stops ratio measurement. Besides exact solution approaches, four greedy heuristics as well as six metaheuristics are applied to combine similar orders in batches. All metrics are tested using real life data of 50 sample picking lines in a distribution centre of a prominent South African retailer. The capacity of the picking device is restricted, thus the maximum batch size of two orders per batch is allowed. The best combination of metric and solution approach is identified. A regression analysis supports the idea that the introduced metrics can be used to approximate walking distance. The combination of stops ratio metric and the greedy random heuristic generate the best results in terms of minimum number of total cycles traversed as well as computational time to find the solution.
- ItemPrysverlagings op voorraad met ’n dalende vraag(Operations Research Society of South Africa, 2004) Visagie, Stephan E.AFRIKAANSE OPSOMMING : Hierdie artikel stel ’n heuristiese benadering voor om die verliese op voorraad met ’n dalende vraag en onbekende tydshorison te minimeer. Die twee metodes wat voorgestel word, gebruik ’n benaderde vraagkromme om die verwagte verliese te voorspel. Albei heuristieke gebruik hierdie vooruitskatting om te bepaal wanneer die prys van items in voorraad afgemerk moet word ten einde verkope te versnel om verliese te vermy wat as gevolg van lang omsettye ontstaan. ’n Gevallestudie wat die werklike data van ’n CD-winkel simuleer, word gebruik om die twee heuristieke se prestasie relatief tot die huidige afmerkstrategie van die bestuur te meet.
- ItemSelection and scheduling of jobs with time-dependent duration(Operations Research Society of South Africa, 2007) Seegmuller, D. M.; Visagie, Stephan E.; De Kock, H. C.; Pienaar, W. J.ENGLISH SUMMARY : In this paper two mathematical programming models, both with multiple objective functions, are proposed to solve four related categories of job scheduling problems. All four of these categories have the property that the duration of the jobs is dependent on the time of implementation and in some cases the preceding job. Furthermore, some jobs (restricted to subsets of the total pool of jobs) can, to different extents, run in parallel. In addition, not all the jobs need necessarily be implemented during the given time period.