The noncooperative fixed charge transportation problem

Sagratella, Simone; Schmidt, Marcel; Sudermann‐Merx, Nathan

doi:10.1016/j.ejor.2019.12.024

Cited by 15 publications

(12 citation statements)

References 28 publications

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“…A i : the maximum amount at source i, B j : the minimum demand at destination j, V k : the maximum transportation capacity of conveyance k, λ j : return rate at destination j η j : exchange rate at destination j, c ijk : direct transportation cost from source i to destination j via conveyance k, e j : direct transportation cost from destination j back to the manufacture, f ijk : the fixed charge from source i to destination j via conveyance k. (11) Decision variables:…”

Section: Parametersmentioning

confidence: 99%

“…Farley and Richardson [10] studied a particular case of identical fixed charges during the transportation period. Sagratella et al [11] introduced a noncooperative FCTP with several competing players and made discussions on three versions about it. A simple but effective heuristic procedure was designed in [12] to solve a series of small FCTPs, and the best solution was achieved via several steps.…”

Section: Introductionmentioning

confidence: 99%

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An Uncertain Programming Model for Fixed Charge Transportation Problem with After‐Sale Service

Zhu

Fan²,

Shen

et al. 2022

Journal of Mathematics

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This paper constructs an uncertain mathematical model for the fixed charge transportation problem in which several kinds of items are transported from different sources to various destinations via different methods. In addition, after-sale service such as product return and exchange that help to raise the customer’s satisfaction is considered during the trade to meet the reality. Meanwhile, some indeterministic factors may occur during the transportation process; probability theory is not the best option due to the lack of adequate historical data. In the light of this statement, some parameters like supplies, demands, return rate, and exchange rate are all defined as uncertain variables to formulate the uncertain programming model. After that, the equivalent deterministic models are derived with the help of uncertainty theory. Finally, some numerical experiments are implemented via three algorithms; the optimal values are displayed and compared to show the application of this problem. The study of this paper provides an applicable method for the decision maker.

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Section: Parametersmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

An Uncertain Programming Model for Fixed Charge Transportation Problem with After‐Sale Service

Zhu

Fan²,

Shen

et al. 2022

Journal of Mathematics

View full text Add to dashboard Cite

show abstract

“…Mixed delivery approach, which combines attended home delivery (AHD) and shared delivery locations (SDL) usage in an innovative way, was proposed in [4]. In real-life situations, the traditional transportation problems deals with issues such as transportation costs, selection of delivery routes, selection of production places, or reduction of carbon emissions [5][6][7][8]. Indeed, it is necessary to plan the transportation of materials within the supply network rationally and optimally [9].…”

Section: Transportation Of Materials In Supply Networkmentioning

confidence: 99%

Mathematical Programming and Solution Approaches for Transportation Optimisation in Supply Network

et al. 2021

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The problem of transport is a special type of mathematical programming designed to search for the optimal distribution network, taking into account the set of suppliers and the set of recipients. This article proposes an innovative approach to solving the transportation problem and devises source codes in GNU Octave (version 3.4.3) to avoid the necessity of carrying out enormous calculations in traditional methods and to minimize transportation costs, fuel consumption, and CO2 emission. The paper presents a numerical example of a solution to the transportation problem using: the northwest corner, the least cost in the matrix, the row minimum, and Vogel’s Approximation Methods (VAM). The joint use of mathematical programming and optimization was applicable to real conditions. The transport was carried out with medium load trucks. Both suppliers and recipients of materials were located geographically within the territory of the Republic of Poland. The presented model was supported by a numerical example with interpretation and visualization of the obtained results. The implementation of the proposed solution enables the user to develop an optimal transport plan for individually defined criteria.

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“…Roy et al [37] presented a conic scalarization technique to solve multiple objective TP under multi-choice ground. Sagratella et al [41] designed a noncooperative FCTP by introducing a game-theoretic extension. Tao & Xu [45] developed rough programming to tackle multiple objective solid TP, whereby they discovered that the feasible domain was not fixed but more workable due to impreciseness of parameters.…”

Section: Literature Surveymentioning

confidence: 99%

Fuzzy multiple objective fractional optimization in rough approximation and its aptness to the fixed-charge transportation problem

2021

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This article presents a multiple objective fractional fixed-charge transportation problem (MFFTP) in a rough decision-making framework. A transformation procedure is modified to convert non-linear multi-objective transportation problem to its linear version. The parameters of the designed model are considered to be fuzzy. We employ separate kinds of fuzzy scale, i.e., possibility, credibility and necessity measures, to deal with the fuzzy parameters. Using the fuzzy chance-constrained rough approximation (FCRA) technique, we extract the more preferable optimal solution from our suggested MFFTP. The initial result is compared with that of the robust ranking (RR) technique. We also use the theory of rough sets for expanding as well as dividing the feasible domain of the MFFTP to accommodate more information by considering two approximations. Employing these approximations, we introduce two variants, namely, the lower approximation (LA) and the upper approximation (UA), of the suggested MFFTP. Finally, by using these models, we provide the optimal solutions for our proposedproblem. We also associate our MFFTP with a real-world example to showcase its applicability as well as performance. Our core concept of this article is that it tackles an MFFTP using two separate kinds of uncertainty and expands its feasible domain for optimal solutions. Optimal solutions of the designed model (obtained from FCRA technique) belong to two separate regions, namely, “surely region” and “possible region”. The optimal solution which belongs to the “surely region” is better (as these are minimum values) than the one in the “possible region” and other cases. An interpretation of our approach along with offers about the intended future research work are provided at last.

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The noncooperative fixed charge transportation problem

Cited by 15 publications

References 28 publications

An Uncertain Programming Model for Fixed Charge Transportation Problem with After‐Sale Service

An Uncertain Programming Model for Fixed Charge Transportation Problem with After‐Sale Service

Mathematical Programming and Solution Approaches for Transportation Optimisation in Supply Network

Fuzzy multiple objective fractional optimization in rough approximation and its aptness to the fixed-charge transportation problem

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