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1
Content available remote An application of facility location problem for electricity supply cost minimization at the stage of preliminary high voltage network development planning
Kapler Piotr
Przegląd Elektrotechniczny
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2020
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R. 96, nr 11
170--172
EN
The article deals with minimizing the costs of electricity supply at the preliminary network planning stage. It presents selected information on costs in power engineering. The facility location problem and Mixed-Integer Linear Programming has been also described. A computational example of the application of this method is presented to solve the problem of minimizing the costs of electricity supply between high voltage / 110 kV power stations and 110 kV urban stations.
PL
Artykuł dotyczy minimalizacji kosztów dostaw energii elektrycznej na etapie wstępnego planowania sieci. Przedstawiono w nim wybrane informacje dotyczące kosztów w elektroenergetyce. Opisano zagadnienie lokalizacji obiektów oraz metodę optymalizacji mieszanej całkowitoliczbowej liniowej. Zaprezentowano przykład obliczeniowy zastosowania tych metod do rozwiązania problemu zminimalizowania kosztów dostaw energii elektrycznej pomiędzy stacjami NN / 110 kV a stacjami miejskimi 110 kV.
2
Content available Robust p-median problem in changing networks
Peško Š., Majer T.
Transport Problems
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2015
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T. 10, z. 3
125--130
EN
The robust p-median problem in changing networks is a version of known discrete p-median problem in network with uncertain edge lengths where uncertainty is characterised by given interval. The uncertainty in edge lengths may appear in travel time along the edges in any network location problem. Several possible future scenarios with respect to the lengths of edges are presented. The planner will want a strategy of positioning p medians that will be working "as well as possible" over the future scenarios. We present MILP formulation of the problem and the solution method based on exchange MILP heuristic. The cluster of each median is presented by rooted tree with the median as root. The performance of the proposed heuristic is compared to the optimal solution found via Gurobi solver for MILP models through some illustrative instances of Slovak road network in Zilina.
DE
Das Problem des P-Medians in den sich wechselnden Netzen ist eines der Versionen des bekannten diskreten Problems über P-Median im Netz mit nicht gewissen Abschnittlängen, wo die Unbestimmheit durch das gegebene Intervall angesetzt wird.Nicht gewisse Länge der Abschitte kann sich als Fahrtlänge in dem Gebiet des jeweiligen Lokationsproblem bestimmen. Wir führen einige Szenare mit Rücksicht auf Kantenlänge ein. Der Planer sucht die Strategie "möglichst guter" Plazierung von P-Medianen mit Rücksicht auf zukünftige Szenare. Wir stellen MILP-Formulierung des Problems und Lösungsverfahren vor, die auf der Tausch-Heuristik gegründet werden. Die zu jedem Median gehörende Ansammlung wird als der Baum mit Würzeln als Median präsentiert. Die Qualität der vorgeschlagenen Heuristik vergleichen wir mit der optimalen Lösung der erworbenen Gurobi-Solver für MILP-Modelle auf einigen Illustrationsinstanzen der Strassennetze in der Slowakischen Republik im Region Zilina.
3
Content available Optymalizacja kosztów w łańcuchu dostaw - implementacja modelu matematycznego
Sitek P., Wikarek J.
Pomiary Automatyka Robotyka
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2012
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R. 16, nr 2
141-146
PL
W artykule przedstawiono implementację autorskiego modelu optymalizacji kosztów w łańcuchu dostaw. Model został sformułowany w postaci zagadnienia programowania liniowego całkowitoliczbowego z funkcją celu określającą koszty dystrybutora, producenta oraz transportu. Implementacji dokonano w środowisku pakietu optymalizacji LINGO firmy LINDO Systems Inc. Po dokonaniu implementacji zostały przeprowadzone eksperymenty obliczeniowe dla przykładowych zbiorów danych.
EN
The paper presents the implementation of the supply chain cost optimization model. The model was formulated as a linear integer programming problem with objective function specifies the cost of distribution, manufacturing and transportation. Implementation took place in an environment optimization package "LINGO". After the implementation the computational experiments were carried out for sample data sets.
4
Content available Model matematyczny optymalizacji kosztów w łańcuchu dostaw
Sitek P., Wikarek J.
Pomiary Automatyka Robotyka
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2012
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R. 16, nr 2
137-140
PL
W artykule przedstawiono autorski model optymalizacji łańcucha dostaw z punktu widzenia operatora logistycznego. Model został sformułowany w postaci zagadnienia programowania liniowego całkowitoliczbowego z funkcją celu określającą koszty dystrybutora, producenta oraz transportu. Przeprowadzono szczegółową dyskusję modelu z omówieniem ograniczeń, parametrów i zmiennych decyzyjnych. Dodatkowo w artykule zaprezentowano aktualny stan outsourcingu usług logistycznych.
EN
The article presents the author’s model of supply chain optimization in terms of logistics operator. The model was formulated as an integer linear programming problem with objective function specifies the cost of a distributor, manufacturer, and transportation. A detailed discussion of the discussion of model constraints, parameters and decision variables. In addition, the article presents the current state of logistics outsourcing.
5
Content available Mathematical programming model of cost optimization for supply chain from perspective of logistics provider
Sitek P., Wikarek J.
Management and Production Engineering Review
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2012
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Vol. 3, No. 2
49-61
EN
The article presents the problem of optimizing the supply chain from the perspective of a logistics provider and includes a mathematical model of multilevel cost optimization for a supply chain in the form of MILP (Mixed Integer Linear Programming). The costs of production, transport and distribution were adopted as an optimization criterion. Timing, volume, capacity and mode of transport were also taken into account. The model was implemented in the environment of LINGO ver. 12 package. The implementation details, the basics of LINGO as well as the results of the numerical tests are presented and discussed. The numerical experiments were carried out using sample data to show the possibilities of practical decision support and optimization of the supply chain. In addition, the article presents the current state of logistics outsourcing.
6
Content available On MILP Models for the OWA Optimization
Ogryczak W., Olender P.
Journal of Telecommunications and Information Technology
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2012
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nr 2
5-12
EN
The problem of aggregating multiple outcomes to form overall objective functions is of considerable importance in many applications. The ordered weighted averaging (OWA) aggregation uses the weights assigned to the ordered values (i.e., to the largest value, the second largest and so on) rather than to the specific coordinates. It allows to evaluate solutions impartially, when distribution of outcomes is more important than assignments these outcomes to the specific criteria. This applies to systems with multiple independent users or agents, whose objectives correspond to the criteria. The ordering operator causes that the OWA optimization problem is nonlinear. Several MILP models have been developed for the OWA optimization. They are built with different numbers of binary variables and auxiliary constraints. In this paper we analyze and compare computational performances of the different MILP model formulations.
7
Content available remote A tabu search algorithm for the cell formation problem with part machine sequencing
Papaioannou G., Wilson J. M.
Foundations of Computing and Decision Sciences
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2012
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Vol. 37, No. 2
97--127
EN
This paper presents extensions of the IP model where part-machine assignment and cell formation are addressed simultaneously and part machine utilisation is considered. More specifically, an integration of inter-cell movements of parts and machine set-up costs within the objective function, and also a combination of machine set-up costs associated with parts revisiting a cell when the part machine operation sequence is taken into account are examined and an enhanced model is formulated. Based upon this model’s requirements, an initial three stage approach is proposed and a tabu search iterative procedure is designed to produce a solution. The initial approach consists of the allocation of machines to cells, the allocation of parts to machines in cells and the evaluation of the objective function’s value. Special care has been taken when allocating parts to machine cells as part machine operation sequence is preserved making the system more complex but more realistic. The proposed tabu search algorithm integrates short term memory and an overall iterative searching strategy where two move types, single and exchange, are considered. Computational experiments verified both the algorithm’s robustness where promising solutions in reasonably short computational effort are produced and also the algorithm’s effectiveness for large scale data sets.
8
Content available Extended model formulation of the Proportional Lot-sizing and Scheduling Problem with lost demand costs
Kaczmarczyk W.
Decision Making in Manufacturing and Services
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2011
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Vol. 5, no. 1-2
49-56
EN
We consider mixed-integer linear programming (MIP) models of production planning problems known as the small bucket lot-sizing and scheduling problems. We present an application of a class of valid inequalities to the case with lost demand (stock-out) costs. Presented results of numerical experiments made for the the Proportional Lot-sizing and Scheduling Problem (PLSP) confirm benefits of such extended model formulation.
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