Simulating realistic set covering problems with known optimal solutions

Sapkota, Nabin; Reilly, Charles H.

doi:10.1016/j.cie.2011.02.008

Cited by 6 publications

(3 citation statements)

References 28 publications

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“…Another potential limitation of proposed approach appears when solving a large dimension problem, since schemes definition and solving the problem with many binary variables can be time-consuming. This issue opens an area for further research and the development of constructive heuristics (Sapkota & Reilly, 2011).…”

Section: Discussionmentioning

confidence: 99%

Staff Assignment to Multiple Projects Based on DEA Efficiency

Martinovic¹,

Savić

2019

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An adequate staff assignment plan is recognized as one of the most important factor for fulfilling the foreseeable delivery of multiple projects with restrictions on available budget, time and quality. This problem is very complex and becomes more complicated as the number of projects, tasks and staff members increases. Decision makers need to find a single unique performance measure as the primary criterion for making a balanced and efficient staff assignment plan. The efficiency of an assignment plan depends on different input and output criteria related to staff member performances which can be economic, qualitative or quantitative by nature. Therefore, the main question is how to make the most efficient assignment plan in multi-project, multi-task environment if several staff members can carry out different tasks at the different level of performance. This paper proposes an integration of all input-output criteria, regardless of their type through a DEA-based mixed-integer programming model. It evaluates the efficiency of staff members as a unique criterion, based on their past performances, together with making an assignment plan. Practical examples with different restrictions empirically demonstrate the possibilities of the decision model. The results show that the fulfilling of maximum efficiency criteria of all staff members in implementing the required tasks provides balanced efficiency in the implementation of all ongoing projects, which makes this model a useful tool for decision makers.

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Section: Discussionmentioning

confidence: 99%

Staff Assignment to Multiple Projects Based on DEA Efficiency

Martinovic¹,

Savić

2019

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“…Даже при относительно небольшой размерности для таких примеров известны лишь минимальные из полученных решений, но не доказана их оптимальность. Предлагаемые подходы, основанные на интегрировании различных идей, позволяют сократить время вычисления и лишь улучшить известные решения [28,31,33,35]. Численные эксперименты также показывают, что основные затраты приходятся на доказательство оптимальности решения [8].…”

Section: Introductionunclassified

Boolean functions minimization problem: conditions of minimality and the probabilistic method

Chukhrov

2022

MVK

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The article is written on the basis of reports presented at the XII International Seminar. Discrete mathematics and its applications named after academician O. B. Lupanov (Moscow, Moscow State University, June 20–25, 2016) and contains a survey of results for the problem of minimizing Boolean functions, in which methods are considered for proving the minimality and nonconstructive approaches to obtaining estimates of parameters that characterize the complexity of minimization with respect to classes of measures difficulties.

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“…The set covering problem is a zero-one linear programming model known as an NP-complete optimization problem (as Karp believes) (Sapkota & Reilly, 2011;Karp, 1972). This problem is discussed when it is necessary that a number of customers exist and each one is served by, at least, one facility with the least possible costs; therefore, the problem investigated in this research will be NP-complete by adding proximity to and the presence in the goods' stock exchange.…”

Section: Fig 2 General Pattern Of the Problem Modelmentioning

confidence: 99%

Locating distribution/service centers based on multi objective decision making using set covering and proximity to stock market

Dabibi

Moghaddam²,

Kazemi³

2016

10.5267/j.ijiec

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In the present competitive world, facility location is an important aspect of the supply chain (sc) optimization. It involves selecting specific locations for facility construction and allocation of the distribution channel among different SC levels. In fact, it is a strategic issue which directly affects many operational/tactical decisions. Besides the accessibility, which results in customer satisfaction, the present paper optimizes the establishment costs of a number of distribution channels by considering their proximity to the stock market of the goods they distribute, and proposes mathematical models for two objective functions using the set covering problem. Then, two objective functions are proposed into one through the ε-constraint method and solved by the metaheuristic Genetic Algorithm (GA). To test the resulted model, a smaller scale problem is solved. Results from running the algorithm with different ε-values show that, on average, a 10% increase in ε, which increases the value of the second objective function -distance covered by customers will cause a 2% decrease in the value of the first objective function including the costs of establishing distribution centers). The repeatability and solution convergence of the twoobjective model presented by the GA are other results obtained in this study.

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Simulating realistic set covering problems with known optimal solutions

Cited by 6 publications

References 28 publications

Staff Assignment to Multiple Projects Based on DEA Efficiency

Staff Assignment to Multiple Projects Based on DEA Efficiency

Boolean functions minimization problem: conditions of minimality and the probabilistic method

Locating distribution/service centers based on multi objective decision making using set covering and proximity to stock market

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