scholarly journals Linear programming problems with some multi-choice fuzzy parameters

2018 ◽  
Vol 28 (2) ◽  
pp. 249-264 ◽  
Author(s):  
Avik Pradhan ◽  
Biswal Prasad
Keyword(s):  
Linear Programming ◽  
Fuzzy Numbers ◽  
Programming Model ◽  
Real Life ◽  
Optimal Solution ◽  
Linear Programming Model ◽  
Mixed Integer ◽  
Non Linear Programming ◽  
A Value ◽  
Linear Programming Problems

In this paper, we consider some Multi-choice linear programming (MCLP) problems where the alternative values of the multi-choice parameters are fuzzy numbers. There are some real-life situations where we need to choose a value for a parameter from a set of different choices to optimize our objective, and those values of the parameters can be imprecise or fuzzy. We formulate these situations as a mathematical model by using some fuzzy numbers for the alternatives. A defuzzification method based on incentre point of a triangle has been used to find the defuzzified values of the fuzzy numbers. We determine an equivalent crisp multi-choice linear programming model. To tackle the multi-choice parameters, we use Lagranges interpolating polynomials. Then, we establish a transformed mixed integer nonlinear programming problem. By solving the transformed non-linear programming model, we obtain the optimal solution for the original problem. Finally, two numerical examples are presented to demonstrate the proposed model and methodology.

scholarly journals Near optimal minimal convex hulls of disks

2021 ◽  
Author(s):  
Josef Kallrath ◽  
Joonghyun Ryu ◽  
Chanyoung Song ◽  
Mokwon Lee ◽  
Deok-Soo Kim
Keyword(s):  
Linear Programming ◽  
Convex Hull ◽  
Programming Model ◽  
Linear Programming Model ◽  
Mixed Integer ◽  
Convex Hulls ◽  
Non Linear Programming ◽  
Minimal Convex ◽  
Non Linear ◽  
Problem Instances

AbstractThe minimal convex hulls of disks problem is to find such arrangements of circular disks in the plane that minimize the length of the convex hull boundary. The mixed-integer non-linear programming model, named [17], works only for small to moderate-sized problems. Here we propose a polylithic framework of the problem for big problem instances by combining the following algorithms and models: (i) A fast disk-packing algorithm based on Voronoi diagrams, non-linear programming (NLP) models for packing disks, and an NLP model for minimizing the discretized perimeter of convex hull; (ii) A fast convex-hull algorithm to compute the convex hulls of disk arrangements and their perimeter lengths; (iii) A mixed-integer NLP model taking the output of as its input. We present complete analytic solutions for small problems up to four disks and a semi-analytic mixed-integer linear programming model which yields exact solutions for strip packing problems with up to one thousand congruent disks. It turns out that the proposed polylithic approach works fine for large problem instances containing up to 1,000 disks. Monolithic and polylithic solutions using usually outperform other approaches. The polylithic approach yields better solutions than the results in [17] and provides a benchmark suite for further research.

scholarly journals Cross-docks scheduling with multiple doors using fuzzy approach

2020 ◽  
Vol 79 (ET.2020) ◽  
pp. 1-18
Author(s):  
Mitra Movassaghi
Keyword(s):  
Linear Programming ◽  
Objective Function ◽  
Programming Model ◽  
Linear Programming Model ◽  
Mixed Integer ◽  
Non Linear Programming ◽  
Cross Docking ◽  
Proposed Model ◽  
Delivery Routes ◽  
Programming Techniques

One of the most important practices in logistics is Cross-Docking which sets its goals as inventory reduction and customer satisfaction increase. Customers receive goods through docks. Docks are responsible to provide a place for goods before being delivered to the customers. Then, these materials are directly loaded into outbound trucks with little or no storage in between to send to customers in the shortest possible time. This paper is mainly aimed at introducing a mixed integer, non-linear programming model to solve scheduling several cross-docking problems. The proposed model is highly facilitated to allocate the most optimal destinations to storage doors and truck scheduling in docks while selecting the collection and delivery routes. Using optimization approaches at uncertainty conditions is also of great importance. Mathematical programming techniques vividly fail to solve transportation problems that include fuzzy objective function coefficients. A fuzzy multi-objective linear programming model is proposed to solve the transportation decision-making with fuzzy objective function coefficients.

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