Step fixed-charge solid transportation problem: a Lagrangian relaxation heuristic approach

Sanei, Masoud; Mahmoodirad, Ali; Niroomand, Sadegh; Jamalian, Ali; Gelareh, Shahin

doi:10.1007/s40314-015-0293-5

Cited by 20 publications

(19 citation statements)

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“…where, p is the number of objective functions, where, each of them is defined as below,   Each of the fixed charges rj F and rj f is of a step function (see [24,25,26]) with l steps defined as below,…”

Section: Fuzzy Multi-objective Fractional Fixed Charge Problem (Fmffcp)mentioning

confidence: 99%

An effective solution approach for multi-objective fractional fixed charge problem with fuzzy parameters

2018

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A multi-objective fixed charge problem in existence of several fractional objective functions with triangular fuzzy parameters is considered in this study. The problem previously has been tackled only by Upmanyu and Saxena [1] with a method containing wrong mathematical concepts (see the commentary of Kaur and Kumar [2]). To overcome the shortcomings of the literature, an effective solution approach based on a typical goal programming approach is proposed to solve the problem for obtaining a Paretooptimal solution. The proposed approach considers the shortcomings of the method of Upmanyu and Saxena [1] and applies no ranking function of fuzzy numbers. In addition, the goal programming stage considers no preference from decision maker. The computational experiments provided by an example of the literature, prove the effectiveness of the proposed approach. Conflicts of interest: noneRemainder of the paper is organized by five sections. Section 2, describes some basic definitions and concepts of fuzzy theory and optimization theory. Section 3, introduces the FMFFCP, analyzes its formulation and deals with its non-linearity. Section 4, organizes the goal programming based solution approach proposed for the FMFFCP. Section 6, contains an illustrative numerical example from the literature to analyze the performance of the proposed solution approach provided by Section 4. Finally, the paper is ended by remarking some conclusions in Section 6. Basic conceptsSome basic definitions from fuzzy theory which will be applied later in this paper are explained in this sub-section. fuzzy theory, exact and meta-heuristic solution approaches.

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Section: Fuzzy Multi-objective Fractional Fixed Charge Problem (Fmffcp)mentioning

confidence: 99%

An effective solution approach for multi-objective fractional fixed charge problem with fuzzy parameters

2018

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“…Similar to the simple plant location problem, the simple Transportation Problem (TP), usually solved using the transportation tableau of which no fixed charges are considered has also been extended into several variants to capture real-world distribution scenarios such as indicated by [31,23]. Among the variants which are currently being explored by researchers are the Fixed Charge Transportation Problem (FCTP), Fixed Charge Solid Transportation problem (FCSTP) studied by [33,5,39] and recently the Step Fixed Charge Solid transportation problem (SFC-STP) as captured in the works of [35]. Furthermore, the raw material blending and transportation problem modeled by [21] is also another variant of STP and a practical application in the field of manufacturing.…”

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confidence: 99%

“…Both the FCSTP and SFCSTP are distribution problems which involve m-sources, n-destinations and k-conveyances. [35] Indicated that both FCSTP and SFCSTP seek to determine the quantities that the chosen capacitated k-conveyances will be able to ship from the m-sources to ndestinations under a mix of route fixed charges at minimum cost. They also showed that the FCSTP and the SFCSTP were NP-hard problems in which exact methods may be deficient in tackling certain problem sizes and structure in a reasonable time.…”

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confidence: 99%

“…Following relaxation of the hard constraints, the new model obtained which is the Lagrange Relaxation of the Original Problem (LR of OP) is thus decomposed into simpler Sub-Problems (SP) based on either the continuous or integer decision variables of the OP. Solving the SP separately and subsequently adding their objective values result in a lower bound (LB) for a minimization problem as shown by [35]. Moreover, as indicated by [38,26] the methods of coupling the decomposed solutions would determine how the optimal solutions or upper bounds of the OP can be formed.…”

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Solving the facility location and fixed charge solid transportation problem

Oyewole¹,

Adetunji²

2021

JIMO

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In this paper, a new variant of the Solid Transportation Problem (STP) that incorporates both facility location and Fixed Charge Solid Transportation Problem (FCSTP) is presented with significant applications in logistics. It integrates decisions of diverse planning horizons: operational, tactical and strategic. The problem is termed Fixed Charge Solid Location and Transportation Problem (FCSLTP). Benchmark data obtained from the literature was extended for experimentation purposes. Solution to the FCSLTP was obtained using CPLEX commercial optimization solver. A Lagrange Relaxation Heuristic (LRH) was developed as an alternative solution for users not possibly having access to CPLEX. We further defined an equivalent FC-SLTP in the main paper and termed this as FCSTP-EQ. The FCSTP-EQ was compared to our FCSLTP to investigate possible cost savings with both formulations. Results obtained showed CPLEX outperforming the Lagrange relaxation heuristic developed both in the upper bound and lower bound generation for the problem sizes considered. Additionally, the cost savings obtained using the FCSLTP was consistently better than the FCSTP-EQ. The upper bound generation capability of Lagrange relaxation could possibly be improved by using better search methods such as metaheuristics. Under certain conditions, the FCSTP could feasibly be used as a starting solution to solve the FCSLTP.

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“…There are three main factors involved with the profit maximization of the company: waste minimization, surplus minimization, and cost minimization. Therefore, a multiobjective modelling and optimization (Boros, Fehér, Lakner, Niroomand, & Vizvári, 2016;Cardillo, Cascini, Frillici, & Rotini, 2013;Franco, Jablonsky, Leopold-Wildburger, & Montibeller, 2009;Ghasemi & Varaee, 2017;Gholizadeh & Baghchevan, 2017;Gutiérrez, Huerga, & Novo, 2018;Jablonsky, 2014;Jiménez, Bilbao-Terol, & Arenas-Parra, 2018;Kovács & Marian, 2002;Özmen, Karakaya, & Köksalan, 2018;Sanei, Mahmoodirad, Niroomand, Jamalian, & Gelareh, 2017;Taassori et al, 2015) is a suitable approach for incorporating the above-mentioned objectives. Furthermore, when some parameters of the problem have uncertain nature, it must be reflected in the model as well (Fullér, Canós-Darós, & Canós-Darós, 2012;Fullér & Majlender, 2004;Moloudzadeh, Allahviranloo, & Darabi, 2013;Niroomand, Mahmoodirad, Heydari, Kardani, & Hadi-Vencheh, 2017;Salahshour & Allahviranloo, 2013;Salmasnia, Khatami, Baradaran Kazemzadeh, & Zegordi, 2015;Taassori, Niroomand, Uysal, Hadi-Vencheh, & Vizvari, 2016;Wang, Zhou, Li, Zhang, & Chen, 2014).…”

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A hybrid solution approach for fuzzy multiobjective dual supplier and material selection problem of carton box production systems

Niroomand¹,

Mahmoodirad

Mosallaeipour

2018

Expert Systems

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A novel optimization problem of carton box manufacturing industries is introduced in this paper. A mixed integer linear formulation with multiple objective functions is developed in order to determine the value of some criteria of carton raw sheets such as size, amount, and supplier under simultaneous minimization of multiple goals such as purchasing cost of raw sheets under discount policy, wastage remained from raw sheets, and quantity of surplus of carton boxes. In order to cope with the unstable market of this sector, some parameters of the proposed formulation such as demand value of the products and price given for raw sheets are assumed to be fuzzy numbers. To tackle such fuzzy multiobjective problem, first, the fuzzy problem is converted to a crisp form using the concepts of necessity‐based chance‐constrained modelling approach. Then a new hybrid form of the fuzzy programming approach is proposed to solve the obtained crisp multiobjective problem effectively. Computational experiments on a real case given by a carton box factory show the superior result of the proposed solution approach compared with the well‐known multiobjective solution methods taken from the literature.

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Step fixed-charge solid transportation problem: a Lagrangian relaxation heuristic approach

Cited by 20 publications

References 47 publications

An effective solution approach for multi-objective fractional fixed charge problem with fuzzy parameters

An effective solution approach for multi-objective fractional fixed charge problem with fuzzy parameters

Solving the facility location and fixed charge solid transportation problem

A hybrid solution approach for fuzzy multiobjective dual supplier and material selection problem of carton box production systems

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