Inventory Model with Price-Dependent Demand Rate and No Shortages: An Interval-Valued Linear Fractional Programming Approach (original) (raw)
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The paper is developed to study interval-valued inventory optimization problem. We consider a constant demand inventory model without shortages the input data of which are not fixed, but vary in some real bounded intervals. The aim of this paper is to determine the optimal order quantity, maximizing the total profit and minimizing the holding cost subjecting to three constraints: budget constraint, space constraint, and budgetary constraint on ordering cost of each item. We apply interval-valued linear fractional programming (IVLFP) approach to solve the model. In this respect, we convert the IVLFP problem to an optimization problem with interval-valued objective function having its bounds as linear fractional functions. We solved three numerical examples to illustrate the proposed model in crisp case and interval-valued case.
A study on the solution of interval linear fractional programming problem
Bulletin of Electrical Engineering and Informatics
Interval linear fractional programming problem (ILFPP) approaches uncertainties in real-world systems such as business, manufacturing, finance, and economics. In this study, we propose solving the interval linear fractional programming (ILFP) problem using interval arithmetic. Further, to construct the problem, a suitable variable transformation is used to form an equivalent ILP problem, and a new algorithm is depicted to obtain the optimal solution without converting the problem into its conventional form. This paper compares the range, solutions, and approaches of ILFP with fuzzy linear fractional programming (FLFP) in solving real-world optimization problems. The illustrated numerical examples show a better range of interval solutions on practical applications of ILFPs and uncertain parameters. This is an open access article under the CC BY-SA license.
Solving the Interval-Valued Linear Fractional Programming Problem
American Journal of Computational Mathematics, 2012
This paper introduces an interval valued linear fractional programming problem (IVLFP). An IVLFP is a linear fractional programming problem with interval coefficients in the objective function. It is proved that we can convert an IVLFP to an optimization problem with interval valued objective function which its bounds are linear fractional functions. Also there is a discussion for the solutions of this kind of optimization problem.
Multisection Technique to Solve Interval-valued Purchasing Inventory Models without Shortages
Journal of Information …, 2010
This paper investigates an interval valued economic order quantity (EOQ) problem without shortage. Since it is almost impossible to find an analytic method to solve the proposed model, an optimization algorithm is designed. First, a brief survey of the existing works on comparing and ranking any two interval numbers on the real line is presented. Finally, the effectiveness of the designed algorithm is illustrated by a numerical example.
Solution of Interval-valued Manufacturing Inventory Models With Shortages
International Journal of Engineering …, 2010
A manufacturing inventory model with shortages with carrying cost, shortage cost, setup cost and demand quantity as imprecise numbers, instead of real numbers, namely interval number is considered here. First, a brief survey of the existing works on comparing and ranking any two interval numbers on the real line is presented. A common algorithm for the optimum production quantity (Economic lot-size) per cycle of a single product (so as to minimize the total average cost) is developed which works well on interval number optimization under consideration. Finally, the designed algorithm is illustrated with numerical example.
2016
Non linear programming is the most important optimizations. One of them is linear fractional programming problem. On some applications of linear programming problems, the coefficient on the model often can not be determined precisely. One method to solve this linear programming problem is to use an interval approach, where uncertain coefficients are transformed into the form of intervals. The linear fractional programming problem with interval coefficients in the objective function is solved by the variable transformation. The transformation was introduced by Charnes and Cooper. In this method a combination of the first and the last points of the intervals are used in place of the intervals. This research showed that optimization linear fractional programming problems with interval coefficient in objective function can be transformed with Charnes and Cooper’s transformation.
Interval linear fractional programming: optimal value range of the objective function
Computational and Applied Mathematics, 2020
In the real world, some problems can be modelled by linear fractional programming with uncertain data as an interval. Therefore, some methods have been proposed for solving interval linear fractional programming (ILFP) problems. In this research, we propose two new methods for solving ILFP problems. In each method, we use two sub-models to obtain the range of the objective function. In the first method, we introduce two sub-models in which the objective functions are non-linear and the two sub-models have the largest and smallest feasible regions; therefore, the optimal value range of the objective function has been obtained. In the second method, two sub-models have been proposed in which the objective functions are linear and the optimal value of the objective function lies in the range obtained from the first method. We use our approaches to maximize the ratio of the facilities optimal allocation to the non-return fund in a bank.
An algorithm for solving general fractional interval programming problems
Naval Research Logistics Quarterly, 1976
A Linear Fractional Interval Programming problem (FIP) is the problem of extremizing a linear fractional function subject to two-sided linear inequality constraints. In this paper we develop an algorithm for solving (FIP) problems. We first apply the Charnes and Cooper transformation on (FIP) and then, by exploiting the special structure of the pair of (LP) problems derived, the algorithm produces an optimal solution to (FIP) in a finite number of iterations. Max (crx + co)/(dTx + do) subject to k 6 Ax b+ We remark that for a suitable choice of the vectors band b+ the constraints set of (FIP) is sufficiently general to cover all bounded polyhedral sets. Problems with linear fractional objective function arise, e.g. in attrition games [14], Markovian replacement problems [ l l , 151, reduction of integer programs to knapsak problems [4], the cutting stock problem [13], in primal dual approaches to decomposition procedures [l, 161. The linear interval constraints arise in problems of capital budgeting, blending and mixing problems, production planning problems and more, see e.g. [3, 191. *This research was partially supported by NRC Grant number A-4024 and by ONR Contracts NOOOl4-67-A-0126-0008
Existence of X-optimal Solution of Fractional Programming Problem with Interval Parameters
Journal of Computer Science & Computational Mathematics, 2015
This paper solves a nonlinear fractional programming problem in which the coefficients of the objective function and constraints are interval parameters. Methodology is developed to transform the model into a general optimization problem, which is free from interval uncertainty. Relation between the original problem and the transformed problem is established. Finally, the proposed methodology is explained through a numerical example.