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Transportation cost accounts for one to two-thirds of the logistics cost for many organizations. So, minimizing the transportation cost in a Transportation Problem (TP) would help the organization to maximize profit. Though there are various methods, such as linear programming approach, network approach, transportation method, etc., available for addressing TP, the transportation method - particularly any simple and efficient heuristic method (which is expected to give very near optimal solution to TP) - is widely used as this type of method could easily be coupled with any another logistics/supply chain decision-making methods/tools to have an integrated decision-making process. Due to this, many researchers are continuously proposing simple heuristic method(s) for solving TP to get near-optimal solutions. However, from the analysis of the literature, it is observed that there is no good comparative study with good computational experiments considering all heuristic methods, which are (a) claimed as relatively 'better heuristic method' and published in reputed journals during the year 2013-2022, (b) evaluated using a large number of tiny test data taken from the literature, and (c) evaluated with large scale test data - generated from popular experimental design available in the literature. To address this research gap, this study considers 10 'better heuristic methods' reported in the literature and proposed 4 heuristic methods. Further, from the detailed performance analyses carried out using 640 randomly generated problem instances, this study identified the 'best' heuristic method(s) and the same is reported with insights. [ABSTRACT FROM AUTHOR]

The global trend to combat climate change by maintaining the balance of climate-active gases has a significant impact on the economic, social, and environmental spheres around the world. One of the important aspects of its solution is the construction of economic models that encourage businesses to "green up". The publication considers an economic model for making calculations on obligations related to compensation of greenhouse gas emissions by companies, financial support for environmental services, sale of rights to additional emissions. Data on mutual obligations can be presented in a matrix, where indexes determine the enterprises between which obligations have arisen, and the element of the matrix is the value of the obligation. The information on mutual obligations of enterprises presented in the matrix allows you to calculate the values of the balance of the settlement participants. The problem of minimizing mutual obligations is a linear programming problem with a special structure of the constraint matrix. In the matrix of coefficients, we can distinguish a matrix with a structure characteristic of the transport problem of linear programming. To solve it, we have developed an algorithm. It allows you to find the optimal distribution of mutual debts in a finite number of steps and has the following main advantages: firstly, step-by-step compliance with the rules for conducting financial transactions; secondly, taking into account the features of filling with non-zero elements of the matrix containing information about obligations. [ABSTRACT FROM AUTHOR]

Transportation plays an important role in supply chain management. To meet customer demands and reduce transportation costs, vehicle needs to be allocated to the optimal route. Vehicle allotment and route optimization are the critical factors for transportation service providers while providing best possible services. In this proposed model, optimization algorithm is developed to address the pain points of transport service providers, which will aid in making critical decisions. The algorithm uses the transactional data of the organization to calculate the loads to be transferred between two hubs/locations. Maximum load to be transferred, available vehicle type and its capacity are used as factors to determine the vehicle allotment. Simultaneously the algorithm allocates the vehicle to a route in such a way that the assigned vehicle is completely utilized. The algorithm is designed to consider cases with load availability less than the full capacity of allocated vehicle between two hubs by assigning touch points on the route in order to maximize the capacity utilization of the vehicle. By using this hub-to-hub optimization model, load factor of vehicle has improved. Operation efficiency has improved through this optimum model. The results of model calculation show that after using this model cost saving of 8% is calculated. Thus, this hub-to-hub model gives the best vehicle placement for available load at each hub in vehicle allotment and route optimization for transportation services. [ABSTRACT FROM AUTHOR]

Transportation plays a vital role in logistics which is an inseparable part of today's supply chain management. An effective transportation network can optimize the supply chain to a great extent by reducing total cost, total time as well as maximizing profit. In this paper, we deal with one stage (supplier to manufacturer) multimodal fixed cost transportation problem (FCTP) of a local paper mill. Here we have formulated three different models which are road transportation model, rail transportation model and a combination of road and rail transportation models using linear programming to analyze and select the most optimized one for the case. For solving the case, we collected data for keeping the capacity constraints of each source and the demand constraints for each destination. We have used an excel solver to solve the models and the results show that the Rail route is the most cost-effective, but it leaves some of the demands unfulfilled. But the combination of both road and rail routes provide the most cost-effective solution satisfying the demands of the destinations. Henceforth, we compared the results by conducting cost analysis to select the most optimized one for the organization. [ABSTRACT FROM AUTHOR]

In this paper we used solid transportation problem to analyze the cost of raw materials which are used for road and bridge works in PWD, West Bengal. We all are aware of the classical Transportation Problem Which involves only two components - supply and demand where a homogenous product is transported from various sources to different destinations in such a way that total transportation cost is minimum. But in real life situation mode of transportation plays an important role on transportation cost. From the practical point of view, an increase in transportation cost may also increase the selling price of commodity. So, keeping this in mind we can give our effort to slash down total transportation cost which in turn may reduce the selling price. That is why the mode of transportations is taken into the account in transportation problem and this causes the emergence of concept of solid transportation. Solid transportation problem (STP) involves three components -- supply, demand and capacity of conveyance. Here the transportation cost is optimized by delivering a homogeneous commodity from various sources to different destinations in different conveyances. If there are m number of origins, n number of destinations and p number of conveyances, then for classical TP, no of feasible solutions is m+n-1, whereas for STP, number of feasible solutions is m+n+p-2. For making the problem generalized we have collected the data from PWD, Government of West Bengal. They published a Rate book which includes different types of rates for different material which are used for construction in West Bengal.Here we are taking data from the 'SCHEDULE OF RATES' for road and bridge works, published by The Superintending Engineer Building Planning Circle. [ABSTRACT FROM AUTHOR]

Optimization of financial and material flows requires the analysis of many factors and large amounts of information, which is impossible without the information technology use. The presence of counter financial flows is possible, both between economic entities, for example, budgetary institutions and unitary enterprises, non-state sector enterprises and state institutions of federal subordination. The current level of information technologies makes it possible to create a database containing information on the receivables and payables of budget institutions and their counterparties for a certain time point. Creation and maintenance of such a base in the current state of the information-analytical center of the region is necessary for optimizing financial flows. When collecting information for the database creation, it should be taken into account that the most important information is about the mutual debts within the considered group of subjects of economic relations. In the article, we consider the question of for which values of the coefficients the problem reduces to a transportation problem. The outlined approach to optimization of financial and commodity flows in integrated structures by solving the problem of counter flows repayment as a problem of linear programming of the transport class has a number of advantages. The next problem of the algorithm development for calculating the net result for solving practical problems is the large dimension of the mutual debts matrix. As the experience of works on repayment of non-payments in the Sverdlovsk region has shown, the matrix of mutual indebtedness is characterized by a large dimension and high discharge. To solve the problem of the return of mutual debts, we have developed an algorithm that, after a finite number of steps, solves the problem and leads to the state of minimally possible mutual debts, and, the higher the discharge of the matrix is, the less number of algorithm steps are required to get the optimal distribution of mutual debts. One of the advantages of the presented algorithm is that it is focused on a step-by-step compliance with the rules for conducting financial transactions. The algorithm for solving the problem of counter financial flows repayment allows us to find the optimal distribution of mutual indebtedness for a finite number of steps and has following main advantages: first, step-by-step compliance with the rules for conducting financial transactions; second, taking into account the specifics of the filling of non-zero elements of the matrix of mutual debts. [ABSTRACT FROM AUTHOR]

Finding an initial basic feasible solution is the prime requirement to obtain an optimal solution for the transportation problems. In this article, a new approach is proposed to find an initial basic feasible solution for the transportation problems. The method is also illustrated with numerical examples. Keywords: Transportation Problem, Transportation Cost, Initial Basic Feasible Solution, Optimal Solution [ABSTRACT FROM AUTHOR]

In the present paper some possibilities for construction and application of various modifications of the well-known transportation problem are proposed aiming the minimizing of the transportation costs for transferring the material flows between suppliers and consumers. The transportation costs are usually a significant part of the total logistical expenses and each logistic system has its own specifics and characteristics for transportation of materials, goods and products. This gives opportunities for applying different optimization models and methods which concern most of all the particular characteristics of each economic situation. In the well-known classical model of the transportation problem the optimal distribution of the transport is determined but not the timing of the delivery. In the present research paper the authors make an attempt to construct a three dimensional transportation problem with the third dimension is the moment of delivery and an optimal solution is determined for the transport between suppliers and consumers for a given period of time. Some modifications of the model are examined which differ in some characteristics of the problem with a reflection in the constraints. The methods of the linear optimization are used during the construction of the model of three dimensional transportation problem for minimizing the transportation costs. [ABSTRACT FROM AUTHOR]

Transportation problem is a special case of the linear programming problem. There are several methods of problems solving fuzzy transportation proposed by the researchers. In this paper, we present PMZ method for solving fuzzy transportation problems, by use information of Zimmermann method and Thorani ranking function. At the end, PMZ method is illustrated by numerical example. Keywords: Fuzzy Transportation, PMZ method, Zimmerman method, and Thorani rangking function. [ABSTRACT FROM AUTHOR]

In the field of transportation problems the most common optimization criterion is transportation costs minimization. However, there are situations where it is necessary to transport the materials quickly. This is especially in the case of transportation of perishable materials. In case the material is transported in time, i.e. before it expires, it may further be used which brings economic profit. Otherwise, there is degradation with all ensuing consequences. This paper seeks to find out how to minimize the time of transportation from collection points to places of processing. Emphasis was placed on minimizing the transportation time, because the transported material is a perishable fruit. Each of the transport points has its own daily limitations regarding the number of material sent and number of material received and also its total limitations per whole transport campaign. When the total limitation is met, the transport point does not participate in the process any more. For solving the problem it was not possible to use the known methods of transportation problems. Therefore, the author proposed a new method, leading to the optimal solution of the described problem. This method is expantiated in the study below. [ABSTRACT FROM AUTHOR]

This article considers bilevel linear programming problems where the coefficients of the objective functions in the problem are given as a possibilistic variable characterized by a quadratic membership function. An extended Stackelberg solution is defined by incorporating the notions of possibility theory into the original concept of Stackelberg solutions. The characteristic of the proposed model is that the corresponding Stackelberg problem is exactly solved by using nonlinear bilevel programming techniques. [ABSTRACT FROM AUTHOR]

A transportation problem basically deals with the problem, which aims to find the best way to fulfill the demand of n demand points using the capacities of m supply points. Here we studied a new method for solving transportation problems with mixed constraints, and described the algorithm to find an optimal more-for-less (MFL) solution. The optimal MFL solution procedure is illustrated with numerical examples and also by using computer programming. Though maximum transportation problems in real life have mixed constraints, these problems are not solved by using usual method. The proposed method builds on the initial solution of the transportation problem which is very simple, easy to understand and apply. [ABSTRACT FROM AUTHOR]

The right-hand side parameters of the transportation problem, such as supply or demand values, sometimes can be determined by managerial policy decisions, which evaluate the marginal values of changing the supply or the demand values. Parameters in the transportation problem are estimated in practice, herein, sensitivity analysis can provide the information to realize the perturbation range while a parameter changing, which might vary the shipping flows or the shipping patterns. The most well-known algorithm for solving the transportation problem is stepping stone method, which is performed in a transportation tableau. However, few papers investigate implementing sensitivity analysis by transportation tableau. This paper proposes two lemmas, and modifies the labeling procedures in a transportation tableau to obtain the larger perturbation range, considering the invariant changing rate of objective function value. Sensitivity analysis technique can be especially implemented under the circumstances that no more-for-less paradox and exists the multiple equivalence shadow prices of the transportation problem. Consequently, the results of sensitivity analysis can provide decision makers more practical information, and can reduce the computing efforts on obtaining the boarder perturbation ranges. [ABSTRACT FROM AUTHOR]

The effects of global warming are threatening the earth's ecosystem sustainability. Countries and companies need to get appropriate measures to maintain sustainability. One of the joint commitments made is about carbon emissions reductions. Practically, this commitment defines a different capacity of carbon limit for each country or company. Firms are expected to find the best solution to reduce the amount of carbon emissions while minimizing the total cost, including by optimizing transportation. This research is about modeling the combination of multimodal land transportation (truck and rail) from the origin (supplier) to the destination (manufacturer) with considering carbon emission emitted. Our objective is to find a tradeoff between transportation costs and emissions. We show how the parameters associated with carbon emissions affect transportation cost from the supplier to the manufacturer. The method used in this article is Mixed Integer Linear Programming. [ABSTRACT FROM AUTHOR]