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Goal programming (GP) is one of the widely used and effective method of solving real-world multi-objective decision-making problems. The term "multi-objective transportation problem" (MOTP) covers a specific class of vector maximum (minimum) linear programming problem that typically has multiple, competing, and incompatible objective functions. In this article, GP and weighted goal programming (WGP) are summarized in MOTP. Furthermore, its advantages over GP are illustrated by a theorem. Additionally, by utilizing WGP, a solution procedure is articulated for MOTP. Finally, an application on screen-panels of mobile devices is presented to explore the applicability. The paper ends with a conclusion and including an outlook to future studies, whereby we address internal and external transportation, and view the internal one with a broader understanding of logistics. [ABSTRACT FROM AUTHOR]

Congestion is one of the problems that often occurs in several areas, such as the Damage Circle Line Intersection. This research aims to identify the causes of traffic problems, the characteristics of traffic movements, and the level of service in the area. The research method was carried out by collecting related data from the results of literature studies, agency surveys, and observations. There are several transportation problems at the Damage Circle Line Intersection. The Damage Circle Line Intersection has transportation problems because of the road capacity and vehicle and other commonly known as conflict points. In addition, the traffic light is not functioning properly, and the level of road service is quite low, indicating that road service is quite high, while the travel speed is low. This study concludes that the traffic problem at the Dramaga Ring Road Intersection is triggered by several factors, including the intersection between the flow of vehicle traffic and others which is commonly known as a conflict point. In addition, the traffic lights on site are not working properly, and the area is a congested commercial area. [ABSTRACT FROM AUTHOR]

The neutrosophic fuzzy set offers us a broad outline for combining several existing sets into one. Indeterminate and unpredictable data cannot be dealt with by either the fuzzy set theory or intuitionistic fuzzy set theory. The computing techniques of neutrosophic sets are valid for software development for many uses. The transportation problem profoundly depends on the neutrosophic fuzzy set. Most of the time, the data provided is indeterminate and inconsistent. At this point of time, we cannot make use of the fuzzy set and intutionistic fuzzy set to get deal with this indeterminacy. Here, we have solved numerically to reflect the impact of neutrosophic pentagonal numbers and neutrosophic octagonal numbers. The efficiency of the method is applied is also compared with the other methods. [ABSTRACT FROM AUTHOR]

A study is conducted on solving stochastic transportation linear programming problems with fuzzy uncertainty information on probability distribution space (STLPPFI) model problems. A proposed method utilizes the concepts of alpha-cut technique with truth degrees technique on probability distribution, linear fuzzy membership function (LFMF), linear fuzzy ranking function (LFRF), trapezoidal fuzzy number, triangular fuzzy number and expectation weighted summation (EWS) technique. Those are used to convert STLPPFI into its corresponding equivalent deterministic transportation linear programming problem (DTLPP) via defuzzifying fuzziness on probability distribution and derandomization randomness of problem formulation respectively. Although, matrix minima cost method (MMCM) with modify distribution method (MODI) respectively are used on obtained DTLPP to get optimal solution. In addition, decision maker (DM) manually decides which of resulting solution is a post optimal solution via choosing a solution that has suitable situation to DM. A proposed algorithm along with numerical example on electricity field illustrating the practicability of it. The obtained results with existing methods show the efficiency of strategy proposed solution method based on the analysis that from results performed. [ABSTRACT FROM AUTHOR]

Transportation Problem is a specific type of linear programming problem (LPP). Today, in the real world, the decision maker handles the multi-objectives at the same time. Fuzzy Concepts are used in LPP to handle the uncertainty and vagueness of data. This paper presents a new algorithm to solve a special type of fuzzy transportation problem (FTP) with the generalized trapezoidal fuzzy numbers (GTpFN) in which the decision maker is not certain about the exact value of transportation charge and the availabilities and requirements are the real numbers. In this Proposed Algorithm first, the fuzzy multi-objective transportation problem (FMOTP) is converted into a Crisp multi-objective transportation problem (MOTP) by the Proposed ranking function, and then the Crisp MOTP is transformed into a single objective transportation problem using the sum of objective functions values. The proposed algorithm gives an efficient compromise solution of FMOTP. To elaborate the proposed algorithm, one numerical example is solved. [ABSTRACT FROM AUTHOR]

This paper presents a solution approach for the transportation problem (TP) in an uncertain environment using trapezoidal intuitionistic fuzzy numbers (TrIFNs). We introduces a new approach to solving Transportation Problems (TP) in uncertain environments, focusing on the Trapezoidal Fermatean Fuzzy Number (TrFFN). The Fermatean Fuzzy TP (FFTP) treats transportation cost, supply, and demand as TrFFN, offering superior performance and feasibility compared to existing methods. It also highlights its advantages in uncertain environments. Using standard LP algorithms, the IFTP is converted into a deterministic linear programming (LP) problem. The quadratic fuzzy transportation problem is a significant problem in operations research and optimization, involving finding the best feasible solution for a transportation problem with quadratic function cost coefficients. The paper presents a new method for solving the fully generalized quadratic fuzzy transportation problem under an ambiguous environment, considering uncertainties and fuzziness inherent in real-world transportation scenarios. The paper also addresses the minimum spanning tree (MST) problem, which involves a graph with either trapezoidal or triangular fuzzy numbers assigned to each arc length. The graded mean integration representation of fuzzy numbers is used to solve these problems. The paper proposes an alternative undefined outranking method by extending the Elimination Et Choix Traduisant La Realite (ELECTRE 1) Method method to consider uncertain, imprecise, and linguistic assessments a group of decision-makers provides. The report addresses the gap in the Electre 1 literature for problems involving conflicting systems of criteria, uncertainty, and imprecise information. [ABSTRACT FROM AUTHOR]

In this research, we use the harmonic mean technique to present an interactive strategy for addressing neutrosophic multi-level multi-objective linear programming (NMMLP) problems. The coefficients of the objective functions of level decision makers and constraints are represented by neutrosophic numbers. By using the interval programming technique, the NMMLP problem is transformed into two crisp MMLP problems, one of these problems is an MMLP problem with all of its coefficients being upper approximations of neutrosophic numbers, while the other is an MMLP problem with all of its coefficients being lower approximations of neutrosophic numbers. The harmonic mean method is then used to combine the many objectives of each crisp problem into a single objective. Then, a preferred solution for NMMLP problems is obtained by solving the single-objective linear programming problem. An application of our research problem is how to determine the optimality the cost of multi-objective transportation problem with neutrosophic environment. To demonstrate the proposed strategies, numerical examples are solved. [ABSTRACT FROM AUTHOR]

Data envelopment analysis (DEA) is a linear programming approach used to determine the relative eficiencies of multiple decision-making units (DMUs). A transportation problem (TP) is a special type of linear programming problem (LPP) which is used to minimize the total transportation cost or maximize the total transportation profit of transporting a product from multiple sources to multiple destinations. Because of the connection between the multi-objective TP (MOTP) and DEA, DEA-based techniques are more often used to handle practical TPs. The objective of this work is to investigate the TP with Fermatean fuzzy costs in the presence of numerous conflicting objectives. In particular, a Fermatean fuzzy DEA (FFDEA) method is proposed to solve the Fermatean fuzzy MOTP (FFMOTP). In this regard, every arc in FFMOTP is considered a DMU. Additionally, those objective functions that should be maximized will be used to define the outputs of DMUs, while those that should be minimized will be used to define the inputs of DMUs. As a consequence, two different Fermatean fuzzy effciency scores (FFESs) will be obtained for every arc by solving the FFDEA models. Therefore, unique FFESs will be obtained for every arc by finding the mean of these FFESs. Finally, the FFMOTP will be transformed into a single objective Fermatean fuzzy TP (FFTP) that can be solved by applying standard algorithms. A numerical example is illustrated to support the proposed method, and the results obtained by using the proposed method are compared to those of existing techniques. Moreover, the advantages of the proposed method are also discussed. [ABSTRACT FROM AUTHOR]

To better deploy the landside rapid transit network for large airports, this study proposes a multi-objective transit network design model to maximize passenger demand coverage, reduce passenger travel time and minimize operational cost simultaneously. This model is formulated as an equivalent integer programming problem by predefining the transportation corridors and passengers' OD pairs. A branch-and-cut algorithm is proposed to find a non-inferior solution set. We also conduct trade-off analysis between efficiency, effectiveness and equity under each deployment strategy using the modified Gini coefficient method. The effectiveness of the proposed model and solution algorithm are tested with rapid transit network of the Beijing Capital International Airport. Results show that among the three common network topologies, including star, tree and finger, the passenger demand coverage and travel time reduction per unit cost under star topology outperform the other two topologies. As for finger topology, the performances of the passenger demand coverage and travel time reduction are the best among the three, but the cost is the poorest. In addition, the trade-off analysis shows that the solution whose objective is to maximize passenger demand coverage has a higher efficiency and a lower unit cost than the solution whose objective is to reduce travel time. However, the latter has a higher level of equity, especially for the medium and low-cost solutions. The proposed method in this study can help the decision makers to design effective landside rapid transit networks for large airports to improve the service level. [ABSTRACT FROM AUTHOR]

Purpose. To improve the distribution methods of freight flows on the railway network under conditions of capacity constraints. Methodology. Methods of railway operation theory and operations research were used. The problem of cargo flow distribution on the railway network was solved as a multi-product (interchangeable cargoes) transport linear programming problem with capacity constraints in the network form. The average cost of freight transportation is established by the methods of probability theory. Findings. In the course of the research the methods of cargo traffic calculation on the railway network are improved. The proposed approach to the formalisation of the task makes it possible to take into account the presence of different cargoes to be transported, capacity constraints of some railway network sections, as well as non-linear nature of dependence between the volume and cost of transportation. To meet the requirement of consignors’ equal access to public carrier services, the method for calculating the cost of transportation for an individual consignor is improved. Originality. Scientific novelty of the paper consists in improvement of methods of cargo traffic distribution on the railway network and tariffing of cargo transportation services in conditions of restricted supply capacity of separate sections. Practical value. The extractive industries have a steady flow of goods. The main logistic tasks in this case are to ensure transportation of the given volume of cargo and reduce the cost of transport services. Using the proposed mathematical methods of optimization allows you to get higher-quality solutions compared to the method of technical-economic comparison of options, which provides an overall cost reduction for cargo transportation. The improved method of tariffication of transportation can reasonably allocate the savings from reducing the cost of transportation among cargo consignors and thus reduce their logistics costs. [ABSTRACT FROM AUTHOR]

'GMmethod' is proposed to solve Solid Transportation Problem which uses the concept of modular arithmetic. In this method given problem with three constraints is solved by considering three different forms and minimal answer (maximal answer) from allanswers of possible forms is considered as best settlement solution of given minimization (maximization) STP. Proposed method is structured in an algorithm and illustrated by numerical examples. It is also coded in MATLAB for the user to use it with ease. [ABSTRACT FROM AUTHOR]

Optimization is very useful in the problems like transportation problems which is a special case of linear programming problems. It is an extremely handy tool for demand and supply chains to minimize time or cost and maximize profit. In this paper, we presented a new ranking method and a new algorithm to solve pentagonal FTP. We compared the solution with the proposed algorithm with the solution of existing methods. Here we transform FTP into a crisp problem and by using the proposed ranking technique we solved numerical examples to demonstrate the method. [ABSTRACT FROM AUTHOR]

In this research study, a new approach was introduced to determine Intuitionistic triangular fuzzy transportation problems with an objective function of the type of maximization which are used to reach the largest required profit. A utilization of this new approach was experimented in terms of the type of results obtained when it was used to solve many fuzzy transportation problems in life, and some of the illustrations have highlighted in this paper. After that, the solutions have compared with the proposed techniques like NWCM, LCM & VAM. [ABSTRACT FROM AUTHOR]

Pythagorean Transportation Problem (PTP) is applied on Capacity and Requirement of commodities taken from one source to the different destinations. In this paper Decagonal Pythagorean Fuzzy Numbers using Transportation problem by ranking method and Centroid Ranking Technique and Proposed Ranking Method.. The transportation cost can be minimized by using of Proposed Ranking Method under Score function Method. The procedure is illustrated with a numerical example. [ABSTRACT FROM AUTHOR]

We propose the Sign Distance Ranking technique of Hexagonal Intuitionistic Fuzzy Number in this paper. This technique is used for solving the Intuitionistic Fuzzy Transportation Problem (IFTP) with the Hexagonal Intuitionistic Fuzzy Number (HIFN) as the membership and non-membership functions. Here, The HIFN are transformed to crisp data by a Sign Distance Ranking technique. And from this ranking crisp data, the initial and the optimal solution of the IFTP are obtained. The efficiency of this technique is illustrated with two numerical examples. [ABSTRACT FROM AUTHOR]

This paper proposed a new approaches for project scheduling via Hesitancy Fuzzy network diagram. This study helps to planning, controlling and managing the project. It is an essential tool to estimate the project completion or cost. In this paper we introduce the concept of Hesitancy Fuzzy Network diagram with algorithm to analyze the optimization techniques such as PERT and Assignment problems with real life examples. Conclusions: The Project evaluation and review techniques plays a vital role in applied Mathematical modeling. It is useful to assign work to the and determination of the time schedule for the activities of a construction project. In this paper, we construct the Hesitancy Fuzzy networks to find out the project completion time and also useful to assign work to the relevant persons. This algorithm is used for the following situations like Minimal spanning tree, Shortest path problem, Maximal flow and Critical path problems. [ABSTRACT FROM AUTHOR]

The subject of assignment issues is fascinating, and it is constantly used to solve difficulties in engineering and management science. We suggested a novel ranking approach in trapezoidal fuzzy numbers to get the best answer in this research. The ranking system is entirely responsible for the best answer. Value costs are characterized by trapezoidal fuzzy numbers. When making decisions under uncertain environment, ranking of fuzzy numbers is extremely significant. This rating approach is the most dependable, easy to use, and applicable to all sorts of assignment difficulties. Our objective is to use a novel ranking algorithm to convert fuzzy data into crisp values. In assignment problem, we use crisp values. Our objective is to use a novel ranking algorithm to transform fuzzy data into crisp values. In the assignment issue, we use crisp values. The Fuzzy Hungarian Method is then used to find the best solution to the fuzzy assignment problem. It is clear from the numerical examples that the suggested ranking measure is simple to calculate and cost-effective for a fuzzy assignment issue, and it delivers much higher optimum value. [ABSTRACT FROM AUTHOR]

In many practical applications, transportation issues are crucial to Maintaining the supply from the source to the destination is the goal of this issue. The Transportation Problem is frequently utilized to take on a real-world problem. Due to some unanticipated circumstances, unpredictability and imprecision will always exist in the actual world. In this study I have, use robust ranking technique for Defuzzification process, to which resource have the lowest shipping cost. The study to investigate the least transportation cost of zero suffix method is less than the heuristic method. [ABSTRACT FROM AUTHOR]

Finding the optimal assignment of locomotives to fulfill freight train transportation schedule under time constraints is a complex problem, even on a linear section of the railway. In previous studies, a graph model was proposed that allows solving the assignment problem using a static graph algorithm. It was proved that finding the optimal assignment without constraints is equivalent to finding the minimal path cover of a specific acyclic graph. However, due to time constraints, the optimal solution may not be valid. This paper presents methods for modifying the found solution in order for it to satisfy the time constraints on locomotives. Two operations on path in the minimal path cover of a graph are introduced: crossover and changeover. They allow to rebuild the found solution without spoiling the admissible sequences of transportation, while the invalid ones are corrected. [ABSTRACT FROM AUTHOR]

The transportation problem is one of the special type and the applications of linear programming problems. The usual transportation problem is unspecifiedthat the decision maker is sure about the accurate values of transportation cost, supply and demand of the product. In some situations decision maker is not in the position to specify the objective precisely but rather than which can be specified in fuzzy concepts. We study fuzzy transportation problem (FTM) using Icosikaitetragonal fuzzy number and its membership function. We have defined the ranking to the Icosikaitetragonal fuzzy numbers to convert the fuzzy valued transportation to crisp valued transportation problem. To illustrate these approaches, a real life problem has been solved using the Least Cost Method. [ABSTRACT FROM AUTHOR]

In this article, we are developing a new approach for solving a transportation problem in fuzzy environment to find out the lease fuzzy transportation cost. Here, we are solving trapezoidal fuzzy transportation problem with the help of ranking technique, whose parameters are trapezoidal fuzzy numbers. This new approach is well defined procedure and it can be utilized for all types of fuzzy transportation problem whether maximize or minimize objective function. At the end, this method is illustrated with a numerical example. [ABSTRACT FROM AUTHOR]

Dual hesitation fuzzy sets are applied to handle inaccurate, preliminary or incomplete information and knowledge situations in actual operational investigation situations. This work presents a new method called Russell's Approximation Method (RAM) to solve the dual hesitant fuzzy transport problem. This procedure is illustrated using a numerical example, and the results achieved by this procedure are compared to the result obtained from North West corner method. [ABSTRACT FROM AUTHOR]

The two-echelon location-routing problem (LRP-2E) considers the first-level routes that serve from one depot a set of processing centres, which must be located and the second-level routes that serve customers from the opened processing centres. In this paper, we consider an extension of the LRP-2E, where the second-level routes include three constraints that have not been considered simultaneously in the location routing literature, namely multi-product, pickup and delivery, and the use of the processing centre as intermediate facility in the second-level routes. This new variant is named two-Echelon Multi-products Location-Routing problem with Pickup and Delivery (LRP-MPPD-2E). The objective of LRP-MPPD-2E is to minimise both the location and the routing costs, considering the new constraints. The first echelon deals with the selection of processing centres from a set of potential sites simultaneously with the construction of the first-level routes, such that each route starts from the main depot, visits the selected processing centres and returns to the main depot. The second echelon aims at assigning customers to the selected processing centres and defining the second-level routes. Each second-level route, starts at a processing centre, visits a set of customers, through one or several processing centres, and then returns to the first processing centre. We present a mixed-integer linear model for the problem and use a Cplex solver to solve small-scale instances. Furthermore, we propose non-trivial extensions of the nearest neighbour and insertion approaches. We also develop clustering-based approaches that have not been extensively investigated with regards to location routing. Computational experiments are conducted to evaluate and to compare the performances of the proposed approaches. The results confirm the effectiveness of clustering approaches. [ABSTRACT FROM PUBLISHER]

A transportation problem can be involving multiple objectives, multiple products, and multiple conveyances. These kinds of transportation problems are named multi-objective multi-attributes solid transportation problems (MMSTP). In this study, a solution based on goal programming has been proposed for MMSTP, in which the supply and demand are uncertain. Moreover, to handle uncertainty, different uncertainty parameters, which are between 0.6 and 0.9, have been used. Then, the results with obtained these parameters are compared by using cost function values. The results indicate that when the uncertainty parameter decreases, the cost increases. Finally, it is shown that an optimal solution can be found using this model through an example. [ABSTRACT FROM AUTHOR]

In the present paper, we focused on finding an initial basic feasible solution for transportation problems. The new method is compared to four different proposed mean methods namely, Proposed Arithmetic Mean (PAM), Proposed Harmonic Mean (PHM), Proposed Geometric Mean (PGM) and Proposed Quadratic Mean (PQM) methods along with existing traditional methods like North West Corner Method (NWCM), Least Cost Method (LCM) and Vogel Approximation Method (VAM). Also, the deviation percentage of the outcomes has been figured out in contrast to distinct methods. The approach thus developed, involves elementary arithmetic and statistics, which could be of keen interest even for beginners and is beneficial to decision makers dealing with the problem of supply chain as well as logistics. Suitable examples are given for examining optimality and to validate the results obtained. [ABSTRACT FROM AUTHOR]

Transportation problem (TP) is a popular branch of Linear Programming Problem in the field of Transportation engineering. Over the years, attempts have been made in finding improved approaches to solve the TPs. Recently, in Quddoos et al. (Int J Comput Sci Eng (IJCSE) 4(7): 1271–1274, 2012), an efficient approach, namely ASM, is proposed for solving crisp TPs. However, it is found that ASM fails to provide better optimal solution in some cases. Therefore, a new and efficient ASM appoach is proposed in this paper to enhance the inherent mechanism of the existing ASM method to solve both crisp TPs and Triangular Intuitionistic Fuzzy Transportation Problems (TIFTPs). A least-looping stepping-stone method has been employed as one of the key factors to improve the solution quality, which is an improved version of the existing stepping-stone method (Roy and Hossain in, Operation research Titus Publication, 2015). Unlike stepping stone method, least-looping stepping-stone method only deals with few selected non-basic cells under some prescribed conditions and hence minimizes the computational burden. Therefore, the framework of the proposed method (namely LS-ASM) is a combination of ASM (Quddoos et al. 2012) and least-looping stepping-stone approach. To validate the performance of LS-ASM, a set of six case studies and a real-world problem (those include both crisp TPs and TIFTPs) have been solved. The statistical results obtained by LS-ASM have been well compared with the existing popular modified distribution (MODI) method and the original ASM method, as well. The statistical results confirm the superiority of the LS-ASM over other compared algorithms with a less computationl effort. [ABSTRACT FROM AUTHOR]

The study concerns the location-routing problem with simultaneous pickup and delivery (LRPSPD) in which the pickup and delivery take place at the same time for each customer. The goal is to determine the facility locations and vehicle routes in order to minimise the total system cost as a sum of facility opening cost, vehicle fixed cost and vehicle travel cost. A simulated annealing (SA) heuristic is proposed for the problem and extensive computational experiments are conducted. The results show that the proposed SA effectively solves LRPSPD and outperforms existing exact approaches in terms of solution quality. [ABSTRACT FROM AUTHOR]

The basic transportation problem (TP) deals with the transportation of goods from a set of supply points to a set of demand points so as to minimise linear transportation costs. The multi-objective transportation problem (MOTP) extends TP to take into consideration multiple conflicting objectives such as transportation cost, average delivery time of the commodities, unfulfilled demand and so forth. We develop an interactive approach to determine the preferred compromise solution for the MOTP where the coefficients of the objective functions and the source and destination parameters have been expressed as interval values by the decision-maker to deal with the impreciseness in the parameters. The proposed method is applied to a real-world MOTP faced by a leading provider of complete broadband access solutions. Results of the case study indicate that the developed method is a practical technique for solving the MOTP with interval parameters. [ABSTRACT FROM PUBLISHER]

In this work, we analyse the transportation problem of a real-life situation by obtaining the optimal feasible solutions, thus carrying out the sensitivity analysis of the problem. The work utilises the data obtained from the Asejire and Ikeja plants of Coca-Cola company, aiming to aid decision- making regarding the best possible options to satisfy customers at the barest minimum cost of transportation. Rerunning the optimization of a problem is an expensive scheme for gathering and obtaining enough data required for a problem. Thus, to minimize the transportation cost, the sensitivity analysis of parameters is a good tool to determine the behaviour of some input parameters where the values of these parameters are varied arbitrarily such that optimal results are verified. Maple 18 Software is used to solve the problem and the result obtained is compared with the values evaluated from northwest corner method, least cost method and Vogel's approximation method. The study critically shows how a little change in a unit or more of any model parameter affects the expected results. [ABSTRACT FROM AUTHOR]

Multi-choice programming problems arise due to the diverse needs of people. In this paper, multichoice optimization has been applied to the bilevel transportation problem. This problem deals with transportation at both the levels, upper as well as lower. There are multiple choices for demand and supply parameters. The multi-choice parameters at the respective levels are converted into polynomials which transmute the defined problem into a mixed integer programming problem. The objective of the paper is to determine a solution methodology for the transformed problem. The significance of the formulated model is exhibited through an example by applying it to the hotel industry. The fuzzy programming approach is employed to obtain a satisfactory solution for the decision-makers at the two levels. A comparative analysis is presented in the paper by solving the bilevel multi-choice transportation problem with goal programming mode as well as by the linear transformation technique. The example is solved using computing software. [ABSTRACT FROM AUTHOR]

In this paper, a solid transportation problem has been considered in which the transportation is accomplished in two stages – firstly, from the origin(s) to the near by station(s) of the destination(s) and secondly, from the near by station(s) to the exact destination(s). Here, a fuzzy AUD (all unit discount) policy has been introduced based upon the amount of transportation along with a fuzzy fixed charge. In addition, a budget constraint has been incorporated taking fuzzy unit transportation cost. Then the proposed model has been converted into a single objective optimisation problem using interval arithmetic method. To solve the model, Genetic Algorithm (GA) has been used depending on roulette wheel selection, crossover and mutation. Finally, a numerical example has been illustrated to study the feasibility of the model. [ABSTRACT FROM AUTHOR]

A special case of the linear programming problem is the transportation theory. It also examines the case in which goods are transported from suppliers to activities. The primary aim is to minimize the overall cost of shipment while maintaining both the manufacturing limitation and the demand criterion. A new approach for solving piecewise quadratic fuzzy transportation problems for finding an optimal solution to a transport problem is included in this article. The most attractive aspect of this approach is that it requires very simple arithmetical and logical modeling. Therefore, it is very straightforward and easy to learn and use. [ABSTRACT FROM AUTHOR]

With the wide application of location theory in a variety of industries, the presence of barriers ‎merits the attention of managers and engineers.‎ In this paper, we assess the Weber location problem in the presence of a polyhedral barrier which probabilistically occurs on a given horizontal barrier route in the rectilinear space. A left triangular distribution function is used for the starting point of the barrier and therefore an expected rectilinear barrier distance function is formulated. In addition, a modification of the polyhedral barrier is presented which is equivalent to the original problem. Therefore, a mixed integer nonlinear programming model, which has a nonconvex solution space, is presented. Furthermore, by decomposing the feasible space into a finite number of convex solution spaces, an exact heuristic solution method is proposed. Then, a lower bound problem based on the forbidden region is applied. Some theorems and an example are reported. [ABSTRACT FROM PUBLISHER]

In this paper, a dual problem formulation is developed in order to solve a multi-objective, multi-period and multi-commodity production–distribution (re)planning problem for a multi-stage centralised upstream network with structure dynamics considerations. The original idea of this study is to use the real logic of decision-making in companies and exclude demand constraint from the linear programming (LP) model. This allows transit from the classical transportation problem, formulated as an LP model in order to improve service level at the strategic inventory holding point. The formulation as an LP model makes it possible to formulate the dual problem. The performed structural analysis revealed some interesting managerial insights into building robust distribution plans and interconnecting decisions on distribution network design, planning, and sourcing. [ABSTRACT FROM AUTHOR]

Several fuzzy approaches have been used for finding the compromise results in the context of “multi-objective transportation problem (MOTP)” with fuzzy parameters. In this work, we have examined a MOTP with “hexagonal fuzzy numbers (HFNs)” as its parameters, i.e., demand, supply and penalties of the problem are mold in HFNs with a new approach developed with the help of a genetic algorithm. Robust ranking is used for the defuzzified value of the hexagonal fuzzy parameters. We have found the BFS (basic feasible solution) of the problem by adopting the zero-point technique. Then the genetic algorithm is used for obtaining the compromising superlative solution by the set of feasible solutions obtained by the zero-point technique of the problem. An algorithm has been developed for the procedure. To figure out the adaptability of the proposed technique, a numerical example has been used. [ABSTRACT FROM AUTHOR]