SUNScholar - Browsing by Author "Visagie, Stephan E."

Browsing by Author "Visagie, Stephan E."

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Algoritmes 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.
Assignment 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.
Fairness 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.
Introducing 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
On 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.
Optimale toewysing en skedulering van werkers en take op 'n monteerbaan
(AOSIS, 2009-03) Venter, Lieschen; Visagie, Stephan E.
In this paper the assignment of cross-trained and temporary workers to tasks on an assembly line is investigated. Cross-trained workers are skilled to perform more than one task on the assembly line in the production process. Temporary workers are viewed as either trained or untrained and may be hired or laid oﬀ as required. The solution procedure may be divided into three parts. During the ﬁrst part a model is formulated to determine an optimal assignment of the workers to the production tasks. During the second part the model is extended to determine the eﬀect of the assignment of both trained and untrained temporary workers to the tasks on the assembly line. During the ﬁnal part of the model an optimal sequence of tasks in the assembly line is determined that minimises the resulting execution times of these tasks. During the ﬁrst part the objective is to maximise the total production utility. This is achieved by implementing a two-phase model. The ﬁrst phase maximises the utility of pro-duction by minimising labour shortage in the assembly line. During the second phase the improvement of the workers’ levels of skill is maximised while the eﬀect of the learning and forgetting of skills is taken into consideration. A learn-forget-curve model (LFCM) is implemented to model the eﬀect of this human characteristic on the master model. This approach ensures that the advantageous cross-trained nature of the workers is maintained and optimized, without a large deviation from the solution determined by the ﬁrst phase. The objective of the second part is to minimise the labour cost of production by determin-ing the best type of workers for a certain task as well as the manner in which they should be hired or laid oﬀ. A worker is classiﬁed as either permanently or temporarily employed. Tem-porarily employed workers are further classiﬁed as either untrained or cross-trained workers. The assignment of workers to tasks on the assembly line is achieved by means of a Master Production Scheduling (MPS) model. The MPS has as its objective the minimisation of the total labour cost of performing all the tasks. The labour cost is deﬁned as the sum of the temporary workers’ daily wages, the overtime cost of permanent workers, the overtime cost of temporary workers and the cost of employing and laying oﬀ temporary workers. Finally, during the third part an optimal sequence of tasks is determined in the production process in order to minimise the total production time. This is achieved by means of a two-phase dynamic assembly line balancing model, which is adjusted to incorporate the critical path method. During the ﬁrst phase, an optimal task sequence is determined, while during the second phase, an optimal assignment of tasks to workstations and the timing thereof, is determined. The practical applicability of the model is demonstrated by means of a real life case study. The production of various styles of shoes in a leatherworks factory is considered. The production of each style requires a diﬀerent set of tasks and each task requires a diﬀerent level of skill. The factory under consideration employs both cross-trained and temporary workers and data sets were obtained empirically by observation, interviews and questionnaires. Upon execution of the ﬁrst phase of the assignment model, an optimal utility is found and the second phase is able to maximise the increase of the workers’ skill level without deviation from this optimum. Upon execution of the employment model, it is found that labour costs are minimized by increasing the use of temporary workers and by assigning the maximum allowable number of overtime hours to them. Upon application of the scheduling model, an improved time is obtained compared to the standard execution time of each style. The results obtained from the case study indicate that the application of the model presented in this paper shows a substantial improvement in production, while reducing the cost of labour as well as improving the overall level of workers’ skills. A multi-objective model is thus developed which successfully maximises production utility, maximises skill development of workers, minimises labour costs and the occurrence of idle workers as well as minimises total execution time.
Optimising 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.
Petrochemical blending problem instances
(2013-06-27) Venter, Lieschen; Visagie, Stephan E.
This file supplies the input data for four petrochemical blending problems.
Picking line data set A
(2014-02-13) Visagie, Stephan E.; Matthews, Jason
This is a data set of picking lines that can by used for the comparison of the performance of different algorithms
Picking 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.
Prysverlagings 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.
Selection 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.
Wisselboustelsels in kleingraangebiede
(Stellenbosch : Stellenbosch University, 1997) Visagie, Stephan E.; Stellenbosch University. Faculty of . Dept. of .

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