This paper is concerned with wastage reduction in constrained two-dimensional guillotine-cut cutting stock problems, often called trim loss problems. A number of researchers report in the literature on algorithmic approaches to find exact solutions for the trim loss problem. Alternative heuristic functions are investigated and applied to the modified Wang method. This involves the sharpening of underestimates used in the methods heuristic function. Two aspects of these solution approaches are considered and some empirical results are given. The first part considers the feasibility to construct more informed heuristic functions. The second part investigates the role of more informedness on the computational cost of these search processes.
{"title":"Efficient waste reduction algorithms based on alternative underestimates for the modified Wang method","authors":"Jan A. Oberholzer, J. Hattingh, T. Steyn","doi":"10.5784/30-2-143","DOIUrl":"https://doi.org/10.5784/30-2-143","url":null,"abstract":"This paper is concerned with wastage reduction in constrained two-dimensional guillotine-cut cutting stock problems, often called trim loss problems. A number of researchers report in the literature on algorithmic approaches to find exact solutions for the trim loss problem. Alternative heuristic functions are investigated and applied to the modified Wang method. This involves the sharpening of underestimates used in the methods heuristic function. Two aspects of these solution approaches are considered and some empirical results are given. The first part considers the feasibility to construct more informed heuristic functions. The second part investigates the role of more informedness on the computational cost of these search processes.","PeriodicalId":30587,"journal":{"name":"ORiON","volume":"14 1","pages":"73-83"},"PeriodicalIF":0.0,"publicationDate":"2014-11-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84972216","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
A large South African retailer (hereafter referred to as the Retailer) faces the problem of selling out inventory within a specified finite time horizon by dynamically adjusting product prices, and simultaneously maximising revenue. Consumer demand for the Retailer's fashion merchandise is uncertain and the identification of products eligible for markdown is therefore problematic. In order to identify products that should be marked down, the Retailer forecasts future sales of new products. With the aim of improving on the Retailer's current sales forecasting method, this study investigates statistical techniques, viz. classical time series analysis (Holt's smoothing method) and survival analysis. Forecasts are made early in the product life cycle and results are compared to the Retailer's existing forecasting method. Based on the mean squared errors of predictions resulting from each method, the most accurate of the methods investigated is survival analysis.
{"title":"In-season retail sales forecasting using survival models","authors":"M. Hattingh, DW Uys","doi":"10.5784/30-2-153","DOIUrl":"https://doi.org/10.5784/30-2-153","url":null,"abstract":"A large South African retailer (hereafter referred to as the Retailer) faces the problem of selling out inventory within a specified finite time horizon by dynamically adjusting product prices, and simultaneously maximising revenue. Consumer demand for the Retailer's fashion merchandise is uncertain and the identification of products eligible for markdown is therefore problematic. In order to identify products that should be marked down, the Retailer forecasts future sales of new products. With the aim of improving on the Retailer's current sales forecasting method, this study investigates statistical techniques, viz. classical time series analysis (Holt's smoothing method) and survival analysis. Forecasts are made early in the product life cycle and results are compared to the Retailer's existing forecasting method. Based on the mean squared errors of predictions resulting from each method, the most accurate of the methods investigated is survival analysis.","PeriodicalId":30587,"journal":{"name":"ORiON","volume":"101 1","pages":"59-71"},"PeriodicalIF":0.0,"publicationDate":"2014-11-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76196708","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
A novel primal-dual path-following interior-point algorithm for the Cartesian P*(k)-linear complementarity problem over symmetric cones is presented. The algorithm is based on a reformulation of the central path for finding the search directions. For a full Nesterov-Todd step feasible interior-point algorithm based on the new search directions, the complexity bound of the algorithm with small-update approach is the best-available bound.
{"title":"An interior-point method for the Cartesian P * ( Κ )-linear complementarity problem over symmetric cones","authors":"B. Kheirfam","doi":"10.5784/30-1-140","DOIUrl":"https://doi.org/10.5784/30-1-140","url":null,"abstract":"A novel primal-dual path-following interior-point algorithm for the Cartesian P*(k)-linear complementarity problem over symmetric cones is presented. The algorithm is based on a reformulation of the central path for finding the search directions. For a full Nesterov-Todd step feasible interior-point algorithm based on the new search directions, the complexity bound of the algorithm with small-update approach is the best-available bound.","PeriodicalId":30587,"journal":{"name":"ORiON","volume":"443 1","pages":"41-58"},"PeriodicalIF":0.0,"publicationDate":"2014-06-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77349006","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This paper employs a combined 'soft-hard' OR approach to aid decision making in the area of allocation at a not-for-profit organization, Foodbank South Africa (FBSA), that represents the largest hunger-relief network in South Africa. Two problem-structuring tools, causal mapping and root definitions (RDs) are utilized. Causal mapping is used to identify areas for useful research within FBSA, and gain a greater understanding of the organization in terms of its goals and consequently a good appreciation of the context in which decisions are made. Root definitions are employed to acquire a better understanding of the 'decision-issues' within the allocation system at the Cape Town warehouse. A simulation model is developed to imitate daily allocation decisions, with the end-objective of assisting decision-making by developing a range of allocation policies. A decision support system (DSS) is developed to help FBSA manage their agency database, automate some of the daily allocation decisions and simulate allocation policies.
{"title":"Decision support for Foodbank South Africa","authors":"Nm Watson, T. Stewart, L. Scott","doi":"10.5784/30-1-142","DOIUrl":"https://doi.org/10.5784/30-1-142","url":null,"abstract":"This paper employs a combined 'soft-hard' OR approach to aid decision making in the area of allocation at a not-for-profit organization, Foodbank South Africa (FBSA), that represents the largest hunger-relief network in South Africa. Two problem-structuring tools, causal mapping and root definitions (RDs) are utilized. Causal mapping is used to identify areas for useful research within FBSA, and gain a greater understanding of the organization in terms of its goals and consequently a good appreciation of the context in which decisions are made. Root definitions are employed to acquire a better understanding of the 'decision-issues' within the allocation system at the Cape Town warehouse. A simulation model is developed to imitate daily allocation decisions, with the end-objective of assisting decision-making by developing a range of allocation policies. A decision support system (DSS) is developed to help FBSA manage their agency database, automate some of the daily allocation decisions and simulate allocation policies.","PeriodicalId":30587,"journal":{"name":"ORiON","volume":"67 1","pages":"1-18"},"PeriodicalIF":0.0,"publicationDate":"2014-06-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90442388","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
CITATION: Hauman, C. & Bekker, J. F. 2014. Application of the multi-objective cross-entropy method to the vehicle routing problem with soft time windows. Orion, 30 (1):19-40, doi:10.5784/30-1-127.
引用本文:Hauman, C. & Bekker, J. F. 2014。多目标交叉熵方法在带软时间窗车辆路径问题中的应用。猎户座，30 (1):19-40,doi:10.5784/30-1-127。
{"title":"Application of the multi-objective cross-entropy method to the vehicle routing problem with soft time windows","authors":"C. Hauman, J. Bekker","doi":"10.5784/30-1-127","DOIUrl":"https://doi.org/10.5784/30-1-127","url":null,"abstract":"CITATION: Hauman, C. & Bekker, J. F. 2014. Application of the multi-objective cross-entropy method to the vehicle routing problem with soft time windows. Orion, 30 (1):19-40, doi:10.5784/30-1-127.","PeriodicalId":30587,"journal":{"name":"ORiON","volume":"26 1","pages":"19-40"},"PeriodicalIF":0.0,"publicationDate":"2014-06-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80687198","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Editorial to Volume 30(1)","authors":"S. E. Visagie","doi":"10.5784/30-1-519","DOIUrl":"https://doi.org/10.5784/30-1-519","url":null,"abstract":"","PeriodicalId":30587,"journal":{"name":"ORiON","volume":"51 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2014-06-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72839089","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
A new course entitled "Methods of Operations Research (OR)" was introduced at the Department of Applied Mathematics of Stellenbosch University during the second half of 2001. The aim of this course was to introduce students of OR to the trauma of mathematical modelling in real-world scenarios, instead of merely teaching them a number of theoretical OR-related topics in the form of a lecture-driven course with an examination at the end. Therefore this project-driven course, which is offered in collaboration with a number of partners in industry, is assessed on a continued evaluation basis, by means of written reports and oral presentations by students, after having physically, or at least virtually, visited real-world OR application sites. The objectives of the course, its structure and contents, as well as lessons learnt and some student feedback are described in this paper. A selection of projects used in the course are described in some detail in an appendix.
{"title":"Methods of OR: A new graduate course","authors":"P. Fourie, I. Nieuwoudt, Jh van Vuuren","doi":"10.5784/19-0-178","DOIUrl":"https://doi.org/10.5784/19-0-178","url":null,"abstract":"A new course entitled \"Methods of Operations Research (OR)\" was introduced at the Department of Applied Mathematics of Stellenbosch University during the second half of 2001. The aim of this course was to introduce students of OR to the trauma of mathematical modelling in real-world scenarios, instead of merely teaching them a number of theoretical OR-related topics in the form of a lecture-driven course with an examination at the end. Therefore this project-driven course, which is offered in collaboration with a number of partners in industry, is assessed on a continued evaluation basis, by means of written reports and oral presentations by students, after having physically, or at least virtually, visited real-world OR application sites. The objectives of the course, its structure and contents, as well as lessons learnt and some student feedback are described in this paper. A selection of projects used in the course are described in some detail in an appendix.","PeriodicalId":30587,"journal":{"name":"ORiON","volume":"19 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2014-01-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85256393","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The application of valid inequalities to provide relaxations which can produce tight bounds, is now common practice in Combinatorial Optimisation. This paper attempts to complement current theoretical investigations in this regard. We experimentally search for "valid" equalities which have the potential of strengthening the problem's formulation. Recently, Martello and Toth included cardinality constraints to derive tight upper bounds for the 0-1 Knapsack Problem. Encouraged by their results, we partition the search space by using equality cardinality constraints. Instead of solving the original problem, an equivalent problem, which consists of one or more 0-1 Knapsack Problem with an exact cardinality bound, is solved. By explicitly including a bound on the cardinality, one is able to reduce the size of each subproblem and compute tight upper bounds. Good feasible solutions found along the way are employed to reduce the computational effort by reducing the number of trees searched and the size of the subsequent search trees. We give a brief description of two Lagrangian-based Branch-and-Bound algorithms proposed in Kruger for solving the exact cardinality bounded subproblems and report on results of numerical experiments with a sequential implementation. Implications for and strategies towards parallel implementation are also given.
{"title":"A partitioning scheme for solving the 0-1 knapsack problem","authors":"M. Kruger, J. Hattingh","doi":"10.5784/19-0-179","DOIUrl":"https://doi.org/10.5784/19-0-179","url":null,"abstract":"The application of valid inequalities to provide relaxations which can produce tight bounds, is now common practice in Combinatorial Optimisation. This paper attempts to complement current theoretical investigations in this regard. We experimentally search for \"valid\" equalities which have the potential of strengthening the problem's formulation. Recently, Martello and Toth included cardinality constraints to derive tight upper bounds for the 0-1 Knapsack Problem. Encouraged by their results, we partition the search space by using equality cardinality constraints. Instead of solving the original problem, an equivalent problem, which consists of one or more 0-1 Knapsack Problem with an exact cardinality bound, is solved. By explicitly including a bound on the cardinality, one is able to reduce the size of each subproblem and compute tight upper bounds. Good feasible solutions found along the way are employed to reduce the computational effort by reducing the number of trees searched and the size of the subsequent search trees. We give a brief description of two Lagrangian-based Branch-and-Bound algorithms proposed in Kruger for solving the exact cardinality bounded subproblems and report on results of numerical experiments with a sequential implementation. Implications for and strategies towards parallel implementation are also given.","PeriodicalId":30587,"journal":{"name":"ORiON","volume":"45 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2014-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74974311","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
International portfolio diversification is often advocated as a way of enhancing portfolio performance particularly through the reduction of portfolio risk. Portfolio managers in Europe have for decades routinely invested a substantial portion of their portfolios in securities that were issued in other countries. During the last decade US investors have held a significant amount of foreign securities with over a trillion dollars invested in foreign assets by 1994. South African institutions have been allowed some freedom to diversify internationally since mid 1995 and individual investors since July 1997. In this paper the potential diversification benefits for South African investors are considered. The stability over time of the correlation structure is investigated and simple ex-ante investment strategies are formulated and evaluated.
{"title":"Optimising investment performance through international diversification","authors":"J. Swart","doi":"10.5784/15-0-414","DOIUrl":"https://doi.org/10.5784/15-0-414","url":null,"abstract":"International portfolio diversification is often advocated as a way of enhancing portfolio performance particularly through the reduction of portfolio risk. Portfolio managers in Europe have for decades routinely invested a substantial portion of their portfolios in securities that were issued in other countries. During the last decade US investors have held a significant amount of foreign securities with over a trillion dollars invested in foreign assets by 1994. South African institutions have been allowed some freedom to diversify internationally since mid 1995 and individual investors since July 1997. In this paper the potential diversification benefits for South African investors are considered. The stability over time of the correlation structure is investigated and simple ex-ante investment strategies are formulated and evaluated.","PeriodicalId":30587,"journal":{"name":"ORiON","volume":"40 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2014-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80057655","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In the Swartland region farmers do not plant wheat exclusively. There are a lot of reasons for this. The main reason is that farmers who plant only one crop will end up with a situation where they will have to buy so much fertiliser that they would not be able to make any money. Every crop influences the crops on the same land later on. It is up to the farmer to decide what the influence will be. That means it is up to the farmer to decide what crop to plant on what land. The farmer ends up rotating a certain number of crops on his land. This rotation of crops is called a rotary crop system. In this situation arises the problem of what sequence of crops should be planted to ensure an optimal income to the farmer without exhausting the land. The problem could be solved by means of linear programming (LP). This problem, however, seem to get very large as the number of crops as well as the number of years over which the problem is solved is increased. By assuming that the influence of crops are only for three years and by restricting the number of years over which the problem is solved the problem is greatly reduced. If we look at the dual of the problem we find a further reduction. The solution of the dual problem also leads to the formulation of strategies. If we formulate the problem by means of the above mentioned strategies the problem reduces to a linear programming problem with only on constraint (which is the knapsack problem). The solution of this knapsack problem with help of a little game theory is then used in a computer program to assist farmers in deciding which crops to plant.
{"title":"Wisselboustelsels in die Swartland","authors":"H. Kock, Stephan E. Visagie","doi":"10.5784/14-0-420","DOIUrl":"https://doi.org/10.5784/14-0-420","url":null,"abstract":"In the Swartland region farmers do not plant wheat exclusively. There are a lot of reasons for this. The main reason is that farmers who plant only one crop will end up with a situation where they will have to buy so much fertiliser that they would not be able to make any money. Every crop influences the crops on the same land later on. It is up to the farmer to decide what the influence will be. That means it is up to the farmer to decide what crop to plant on what land. The farmer ends up rotating a certain number of crops on his land. This rotation of crops is called a rotary crop system. In this situation arises the problem of what sequence of crops should be planted to ensure an optimal income to the farmer without exhausting the land. The problem could be solved by means of linear programming (LP). This problem, however, seem to get very large as the number of crops as well as the number of years over which the problem is solved is increased. By assuming that the influence of crops are only for three years and by restricting the number of years over which the problem is solved the problem is greatly reduced. If we look at the dual of the problem we find a further reduction. The solution of the dual problem also leads to the formulation of strategies. If we formulate the problem by means of the above mentioned strategies the problem reduces to a linear programming problem with only on constraint (which is the knapsack problem). The solution of this knapsack problem with help of a little game theory is then used in a computer program to assist farmers in deciding which crops to plant.","PeriodicalId":30587,"journal":{"name":"ORiON","volume":"18 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2014-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75739157","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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