scholarly journals Integer linear programming application in production results optimization using cutting plane method

2021 ◽  
Vol 4 (1) ◽  
pp. 57-66
Author(s):  
Fery Firmansah ◽  
Fitriana Wulandari
Keyword(s):  
Linear Programming ◽  
Integer Linear Programming ◽  
Raw Materials ◽  
Optimal Solution ◽  
Cutting Plane ◽  
Cutting Plane Method ◽  
Daily Production ◽  
Plane Method ◽  
Decision Variables ◽  
The Right

Integer Linear Programming is a special form of linear programming which the decision variables are in integer form. Berkah Rasa is a home industry business in the form of Jenang Ayu and Jenang Krasikan processed food.  The daily production that carried out by Berkah Rasa is based on the availability of raw materials and the number of requests. So far, Berkah Rasa has not had the right strategy in producing Jenang to get maximum profit. The purpose of this research is to apply integer linear programming to the optimization of Jenang Ayu and Jenang Krasikan production. The method used to solve this problem is the cutting plane method. The results of the research obtained is the optimal solution for Berkah Rasa, that is by producing 25 kg of Jenang Ayu and 22 kg of Jenang Krasikan every day. So that the benefits obtained by Berkah Rasa every day are IDR 727,000.00.

scholarly journals An Analytic Center Cutting Plane Method to Determine Complete Positivity of a Matrix

2021 ◽  
Author(s):  
Riley Badenbroek ◽  
Etienne de Klerk
Keyword(s):  
Optimization Problem ◽  
Optimization Problems ◽  
Optimal Solution ◽  
Cutting Plane ◽  
Mixed Integer ◽  
Cutting Plane Method ◽  
Analytic Center ◽  
Completely Positive ◽  
Plane Method ◽  
Copositive Cone

We propose an analytic center cutting plane method to determine whether a matrix is completely positive and return a cut that separates it from the completely positive cone if not. This was stated as an open (computational) problem by Berman et al. [Berman A, Dur M, Shaked-Monderer N (2015) Open problems in the theory of completely positive and copositive matrices. Electronic J. Linear Algebra 29(1):46–58]. Our method optimizes over the intersection of a ball and the copositive cone, where membership is determined by solving a mixed-integer linear program suggested by Xia et al. [Xia W, Vera JC, Zuluaga LF (2020) Globally solving nonconvex quadratic programs via linear integer programming techniques. INFORMS J. Comput. 32(1):40–56]. Thus, our algorithm can, more generally, be used to solve any copositive optimization problem, provided one knows the radius of a ball containing an optimal solution. Numerical experiments show that the number of oracle calls (matrix copositivity checks) for our implementation scales well with the matrix size, growing roughly like [Formula: see text] for d × d matrices. The method is implemented in Julia and available at https://github.com/rileybadenbroek/CopositiveAnalyticCenter.jl . Summary of Contribution: Completely positive matrices play an important role in operations research. They allow many NP-hard problems to be formulated as optimization problems over a proper cone, which enables them to benefit from the duality theory of convex programming. We propose an analytic center cutting plane method to determine whether a matrix is completely positive by solving an optimization problem over the copositive cone. In fact, we can use our method to solve any copositive optimization problem, provided we know the radius of a ball containing an optimal solution. We emphasize numerical performance and stability in developing this method. A software implementation in Julia is provided.

scholarly journals SUPPLIER SELECTION AND ORDER QUANTITY ALLOCATION OF RAW MATERIAL USING INTEGER LINEAR PROGRAMMING

JOURNAL ASRO ◽  
2018 ◽  
Vol 9 (1) ◽  
pp. 98
Author(s):  
Ika Deefi Anna ◽  
Putri Rani Fhiliantie
Keyword(s):  
Sensitivity Analysis ◽  
Linear Programming ◽  
Integer Linear Programming ◽  
Supplier Selection ◽  
Raw Materials ◽  
Raw Material ◽  
Delivery Time ◽  
Order Quantity ◽  
Holding Costs ◽  
The Right

ABSTRACT The production activities of a company are influenced by sufficient availability of raw materials. The availability of raw materials will be fulfilled if the supplier regularly sends raw materials in accordance with the planned delivery time. However, each supplier has different capabilities in terms of supply capacity, price, product quality, and delivery time. Determining the right supplier will help the company maintain its production process. This study aims to identify which suppliers are selected to fulfill the demand for each production period and determine allocation of raw material orders to each selected supplier. The model developed to determine selected suppliers have been an integer linear programming. The model has the objective function of minimizing the total cost which consists of purchasing, ordering and holding costs. The constraints include supplier capacity, order quantity allocation, demand, inventory balance, safety stock, timely delivery, non negative and binary. Calculation results in giving a numerical example shows that the developed model is able to select suppliers per period. The model is also able to determine the allocation of raw material orders to selected suppliers. Sensitivity analysis is done to find out which parameters are sensitive. The results of the sensitivity analysis indicate that the parameters of supplier capacity and demand are sensitive parameters.  Keywords: Supplier selection, order quantity allocation, integer linear programming

scholarly journals Solving fully fuzzy linear programming problems by controlling the variation range of variables

2021 ◽  
Vol 103 (3) ◽  
pp. 13-24
Author(s):  
S.M. Davoodi ◽  
◽  
N.A. Abdul Rahman ◽  
Keyword(s):  
Linear Programming ◽  
Optimal Solution ◽  
Fuzzy Linear Programming ◽  
Ranking Functions ◽  
Fuzzy Variables ◽  
Decision Variables ◽  
Proposed Model ◽  
Linear Programming Problems ◽  
Left And Right ◽  
The Right

This paper deals with a fully fuzzy linear programming problem (FFLP) in which the coefficients of decision variables, the right-hand coefficients and variables are characterized by fuzzy numbers. A method of obtaining optimal fuzzy solutions is proposed by controlling the left and right sides of the fuzzy variables according to the fuzzy parameters. By using fuzzy controlled solutions, we avoid unexpected answers. Finally, two numerical examples are solved to demonstrate how the proposed model can provide a better optimal solution than that of other methods using several ranking functions.

Multiple Cuts in the Analytic Center Cutting Plane Method

2000 ◽  
Vol 11 (1) ◽  
pp. 266-288 ◽  
Author(s):  
Jean-Louis Goffin ◽  
Jean-Philippe Vial
Keyword(s):  
Cutting Plane ◽  
Cutting Plane Method ◽  
Analytic Center ◽  
Plane Method

LEXICOGRAPHIC PROBLEMS OF CONVEX OPTIMIZATION: SOLVABILITY AND OPTIMALITY CONDITIONS, CUTTING PLANE METHOD

2021 ◽  
Vol 1 ◽  
pp. 30-40
Author(s):  
Natalia V. Semenova ◽  
◽  
Maria M. Lomaga ◽  
Viktor V. Semenov ◽  
◽  
...  
Keyword(s):  
System Optimization ◽  
Cutting Plane ◽  
Recession Cone ◽  
Cutting Plane Method ◽  
Optimal Solutions ◽  
Feasible Set ◽  
Plane Method ◽  
Multicriteria Problems ◽  
Lexicographic Optimization ◽  
Feasible Solutions

The lexicographic approach for solving multicriteria problems consists in the strict ordering of criteria concerning relative importance and allows to obtain optimization of more important criterion due to any losses of all another, to the criteria of less importance. Hence, a lot of problems including the ones of com­plex system optimization, of stochastic programming under risk, of dynamic character, etc. may be presented in the form of lexicographic problems of opti­mization. We have revealed conditions of existence and optimality of solutions of multicriteria problems of lexicographic optimization with an unbounded convex set of feasible solutions on the basis of applying properties of a recession cone of a convex feasible set, the cone which puts in order lexicographically a feasible set with respect to optimization criteria and local tent built at the boundary points of the feasible set. The properties of lexicographic optimal solutions are described. Received conditions and properties may be successfully used while developing algorithms for finding optimal solutions of mentioned problems of lexicographic optimization. A method of finding lexicographic of optimal solutions of convex lexicographic problems is built and grounded on the basis of ideas of method of linearization and Kelley cutting-plane method.

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