scholarly journals An optimization of solid transportation problem with stochastic demand by Lagrangian function and KKT conditions

2020 ◽  
Author(s):  
Barun Das ◽  
Anjana Kuiri ◽  
Sanat Kumar Mahato
Keyword(s):  
Transportation Problem ◽  
Profit Maximization ◽  
Transportation Cost ◽  
Lagrangian Function ◽  
Kkt Conditions ◽  
Solid Transportation Problem ◽  
Objective Functions ◽  
Numerical Example ◽  
Primary Model ◽  
Demand Patterns

In this paper, a stochastic solid transportation problem (SSTP) is constructed where the demand of the item at the destinations are randomly distributed. Such SSTP is formulated with profit maximization form containing selling revenue, transportation cost and holding/shortage cost of the item. The proposed SSTP is framed as a nonlinear transportation problem which is optimized through Karush-Kuhn-Tucker (KKT) conditions of the Lagrangian function. The primary model is bifurcated into three different models for continuous and discrete demand patterns. The concavity of the objective functions is also presented here very carefully. Finally, a numerical example is illustrated to stabilize the models.

scholarly journals Application of fuzzy programming techniques to solve solid transportation problem with additional constraints

2020 ◽  
Vol 30 (1) ◽  
Author(s):  
Sharmistha Halder (Jana) ◽  
Biswapati Jana
Keyword(s):  
Transportation Problem ◽  
Real Life ◽  
Transportation Cost ◽  
Fuzzy Programming ◽  
Solid Transportation Problem ◽  
Generalized Gradient ◽  
Proposed Model ◽  
Programming Techniques ◽  
Total Transportation Cost ◽  
Additional Constraints

An innovative, real-life solid transportation problem is explained in a non-linear form. As in real life, the total transportation cost depends on the procurement process or type of the items and the distance of transportation. Besides, an impurity constraint is considered here. The proposed model is formed with fuzzy imprecise nature. Such an interesting model is optimised through two different fuzzy programming techniques and fractional programming methods, using LINGO-14.0 tools followed by the generalized gradient method. Finally, the model is discussed concerning these two different methods.

scholarly journals Profit Maximization Solid Transportation Problem with Gaussian Type-2 Fuzzy Environments

2018 ◽  
Vol 16 (2) ◽  
pp. 323-335
Author(s):  
Sharmistha Jana ◽  
◽  
Barun Das ◽  
Goutam Panigrahi ◽  
Manoranjan Maiti ◽  
...  
Keyword(s):  
Transportation Problem ◽  
Profit Maximization ◽  
Solid Transportation Problem ◽  
Gaussian Type

scholarly journals A Fuzzy Approach to Multi-Objective Solid Transportation Problem with Mixed Constraints Using Hyperbolic Membership Function

2021 ◽  
Vol 21 (4) ◽  
pp. 158-167
Author(s):  
Nurdan Kara ◽  
Hale Gonce Kocken
Keyword(s):  
Membership Function ◽  
Transportation Problem ◽  
Social Issues ◽  
Transportation Cost ◽  
Ease Of Use ◽  
Solid Transportation Problem ◽  
Fuzzy Approach ◽  
Safety Level ◽  
Multi Objective ◽  
Conflicting Objectives

Abstract Multi-objective Solid Transportation Problem (MSTP) is known as a special class of vector-minimization (or maximization) problems and has three parameters: source, destination, and conveyance. The objectives such as transportation cost, transportation time, transportation safety level, and objectives in terms of environmental and social issues are generally in conflict with each other. In this paper, we present a fuzzy approach to bring these conflicting objectives together as high as possible. Instead of using the linear membership function, which is frequently used in the literature for ease of use, we use the hyperbolic membership function in our approach. Also, while most of the papers in the literature deal with the standard equality constrained form of MSTP, the mixed constrained form is addressed in this paper. Finally, a numerical example from the literature is used to illustrate the construction of the hyperbolic membership function and how well it represents the objective functions’ degree of satisfaction.

Time minimizing solid transportation problem

Optimization ◽  
1976 ◽  
Vol 7 (3) ◽  
pp. 395-403
Author(s):  
H.L. Bhatia ◽  
Kanti Swarup ◽  
M.C. Puri
Keyword(s):  
Transportation Problem ◽  
Solid Transportation Problem

OPTIMAL FEASIBLE SOLUTIONS TO A ROAD FREIGHT TRANSPORTATION PROBLEM

2020 ◽  
Vol 5 (1) ◽  
pp. 456
Author(s):  
Tolulope Latunde ◽  
Joseph Oluwaseun Richard ◽  
Opeyemi Odunayo Esan ◽  
Damilola Deborah Dare
Keyword(s):  
Transportation Problem ◽  
Optimal Solution ◽  
Transportation Cost ◽  
North West ◽  
Life Problems ◽  
Basic Feasible Solutions ◽  
Feasible Solutions ◽  
Road Freight Transportation ◽  
The Cost ◽  
Cost Of Transportation

For twenty decades, there is a visible ever forward advancement in the technology of mobility, vehicles and transportation system in general. However, there is no "cure-all" remedy ideal enough to solve all life problems but mathematics has proven that if the problem can be determined, it is most likely solvable. New methods and applications will keep coming to making sure that life problems will be solved faster and easier. This study is to adopt a mathematical transportation problem in the Coca-Cola company aiming to help the logistics department manager of the Asejire and Ikeja plant to decide on how to distribute demand by the customers and at the same time, minimize the cost of transportation. Here, different algorithms are used and compared to generate an optimal solution, namely; North West Corner Method (NWC), Least Cost Method (LCM) and Vogel’s Approximation Method (VAM). The transportation model type in this work is the Linear Programming as the problems are represented in tables and results are compared with the result obtained on Maple 18 software. The study shows various ways in which the initial basic feasible solutions to the problem can be obtained where the best method that saves the highest percentage of transportation cost with for this problem is the NWC. The NWC produces the optimal transportation cost which is 517,040 units.

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