The noncooperative fixed charge transportation problem simone sagratella marcel schmidty nathan sudermannmerxz december 20, 2018 abstract we introduce the noncooperative xed charge transportation problem nfctp, which is a gametheoretic extension of the xed charge transportation problem. Pdf a new and strong convexified formulation of the fixed charge transportation problem is provided. The indefinite quadratic transportation problem was first studied by arora and khurana 45 in 2001. A fixed cost or charge in fctp is incurred for every rout that is opened or used to send the demands. Their test re sults on fixed charge transportation problems are the best published to date.
Suppose that x is feasible for the fixed charge problem. The singlesink fixed charge transportation problem is an important problem with applications in many areas. Varma and kumar 2015 have demonstrated how nonlinear transportation problem can be solved efficiently by minimizing time and cost. Since problems with fixed charge are us ually np hard problems 1, the computational time to obtain exact solutions increases in the.
Introduction a special version of the transportation problem tp is the fixed charge transportation problem fctp. Fixed charge transportation, fixed charge transportation, convergence, genetic algorithm, arti. Klingman and russel 16 considered solving constrained transportation problems. Due to nphardness of the problem, we utilize three types of electromagnetismlike algorithms em, genetic algorithm ga, and simulated annealing sa which are firstly being proposed and comprised in this research area. Solving the twostage fixedcharge transportation problem with a hybrid genetic algorithm petrica. Solving fixed charge transportation problem with truck load. Solving a simple transportation problem using lingo. Pop1, cosmin sabo1, benjamin biesinger2, bin hu2 and gunther. Here we study the structure of the projection polyhedron of this problem, in the space of 01 variables associated with fixed charges, and we develop several classes of valid inequalities and.
In this paper, we describe a new integer programming formulation with exponentially many variables. Here we study the structure of the projection polyhedron of this problem, in the space of 01 variables associated with fixed charges, and we. A new and strong convexified formulation of the fixed charge transportation problem is provided. The fixed charge transportation problem has two kinds of costs. The fuzzy fixed charge transportation problem in which both fixed and transportation cost are fuzzy numbers is considered in this paper. A set covering reformulation of the pure fixed charge. Addressing a fixed charge transportation problem with. The pure fixed charge transportation problem is reformulated into an equivalent set covering problem with, in general, a large number of constraints.
Solving fuzzy step fixed charge transportation problems. The fixed charge transportation problem generalizes the wellknown transportation problem where the cost of sending goods from a source to a sink is composed of a fixed cost and a continuous cost proportional to the amount of goods sent. Introduction to approximation algorithms k center problem duration. An approximation method for fuzzy fixedcharge transportation. Adaptive genetic algorithm for fixedcharge transportation. Anand jayakumar a et al 3 have optimized a fixed charge problem using python. Fixed charge problems suppose that there is a linear cost of production, after the process is set up. On modeling the step fixedcharge transportation problem. The noncooperative fixed charge transportation problem. Usually, anfctp is formulated and solved as a mixed integer network programming problem. While not being linear in each of the variables, the objective function has a fixed cost associated with each origin. The uncertain fixed charge transportation problem is. Received march, 1976 abstractthis investigation evaluates an approximate method of solution developed by m. In this paper, fctp is formulated using a mixed integer programming model, and transformed into a series of minimum cost maximum flow.
Fixedcharge transportation problem ger restriction on yij. The direct cost is the cost associated with each sourcedestination pair, and the fixed charge occurs when the transportation activity takes place in the corresponding sourcedestination pair. In many distribution problems, the transportation cost consists of a fixed cost, independent of the amount transported, and a variable cost, proportional to the amount shipped. Preferableinterval method for the multiplesink fixed.
Jun 25, 2012 mod08 lec32 location problems p median problem, fixed charge problem. On step fixedcharge transportation problem request pdf. The fixed charge transportation problem fctp is a generalization of the wellknown transportation problem, where the cost for sending goods from origins to destinations is composed of a xed cost and a continuous cost proportional to the amount of goods sent. One of its variations is the fixed charge transportation problem fctp where fixed cost. Fixedcharge transportation problem with fuzzy costs. Properties of optimal solutions to the singlesink fixedcharge transportation problem are investigated. The sfctp has received little attention in the transportation problem literature. Solving the twostage fixedcharge transportation problem. This gives an increased fixed charge which is proportional to the number of trips performed. The fixed charge facility location problem the fixed charge facility location problem is a classical location problem and forms the basis of many of the location models that have been used in supply chain design. On logarithmic fixedcharge transportation problem 533. Shiangtai liu 2003 developed a method to calculate the lower and upper bounds of the total transportation. A new optimization method for largescale fixed charge. Solution of the transportation model b3 to from a b c supply 68 10 1 150 711 11 2 175 45 12 3 275 demand 200 100 300 600 table b1 the transportation tableau transportation problems are solved manually within a tableau format.
Mod08 lec32 location problems p median problem, fixed charge problem nptelhrd. Solution approaches using preferable intervals are presented. The singlesink fixedcharge transportation problem is an important problem with applications in many areas. Here we study the structure of the projection polyhedron of this problem, in the space of 01 variables associated with fixed charges, and we develop several classes of valid inequalities and derive. Fixed charge transportation problem and its uncertain. Fixed charge transportation problem fctp is an extension of classical transportation problem in which a fixed cost is incurred, independent of the amount transported, along with a variable cost that is proportional to the amount shipped.
The indefinite quadratic transportation problem was first studied by. Fixed charge transportation fct problems addressed in literature assumed shipment between a source and a destination is fulfilled in a single lot. The fixed charge transportation problem fctp is a special case of the transportation problem where a fixed charge is associated with each route that can be opened, in addition to the variable transportation cost proportional to the amount of goods shipped. Modified method for fixed charge transportation problem. In order to make the transportation problem more practical, many research papers assume that a fixed cost is also incurred along with variable cost of each commodity. An improved lower bound on the fixed costs developed in the paper and. Fixed charge transportation problem with fuzzy costs. Bilevel capacitated fixed charge transportation problem ritu arora department of mathematics, keshav mahavidyalaya, university of delhi, delhi deepa thirwani department of mathematics, hans raj college, university of delhi, delhi abstract bilevel programming is a twostage optimization problem.
A fixed charge is any type of fixed expense that recurs on a regular basis. The fixed charge problem is a nonlinear programming problem of practical interest in business and industry. The pure fixed charge transportation problem pfctp is a variation of the fixed charge transportation problem fctp in which there are only fixed costs. Each cell in a transportation tableau is analogous to a decision variable that indicates the amount allocated from a. A study of the fixed charge transportation problem pinup roams and leon cooper school of engineering and applied science, southern methodist university, dallas, texas 75275, u. Fixedcharge transportation problem fctp deals with determining optimal quantities of goods to be shipped and the routes to be used to satisfy the customers demands at minimal total cost. Thestochasticmultistagefixedcharge transportationproblem. Integer programming formulations mit opencourseware. While not being linear in each of the variables, the objective function has a fixed cost associated with each variable. Pdf in the present paper the fixed charge transportation problem under uncertainty, particularly when parameters are given in interval forms. Exact approaches for the fixed charge transportation problem. There is a cost of setting up the production process. By using a technique developed by the authors to improve the approximation.
Properties of optimal solutions to the singlesink fixed charge transportation problem are investigated. In this paper we consider the wellknown fixedcharge transportation problem. Many practical transportation and distribution problems can be modeled as fixed charge transportation problems fctp. A branching method for the fixed charge transportation problem. Initial approximation solutions to the problem were mainly heuristic 5, 9, 24, 26, 28. P a g e 70 the optimum solution of this problem are tabulated in table 3. Two constraint generation procedures for its solution are suggested. Pdf solving fixed charge transportation problem with interval. An exact algorithm is developed for the model and implemented by using lingo ver6. Fixed charges can include insurance, salaries, utilities, vehicle payments, loan payments and mortgage. The fixed charge problem steinberg 1970 naval research.
Solving the twostage fixed charge transportation problem with a hybrid genetic algorithm petrica. In the present paper threedimensional fixed charge bicriterion indefinite quadratic transportation problem, giving the same priority to cost as well as. Such problem are called fixed charge transportation problem fctp. To the best of our knowledge, two heuristics proposed by kowalski and lev 20 altassan, et al. Fixed charge transportation problem with indicator constraints description this problem finds a least cost shipping schedule that meets requirements at markets and supplies at factories and has a fixed charge if something flows on an network arc.
Introduction the fixed charge transportation problem differs from the linear transportation problem only in the nonlinearity of the objective function. Anand jayakumar a and krishnaraj c 4 have created a mathematical model for pricing and revenue management of perishable assets. Pdf on logarithmic fixedcharge transportation problem. Example of transportation plan the fixed charge transportation problem can be formulated as follows. Another modification of the tp, in the cases that just fixed charge value is considered for the opened routes in the tp without considering the conveyances in the problem, is called fixed charge transportation problem. However, in reality the lot size may exceed the capacity of the carrier and hence the shipment needs to be executed by conducting more than one trip. In the fctp, each route is associated with a fixed cost and a transportation cost per unit shipped.
The total cost contains a fixed component which is incurred for every route that is part of the solution along with the variable cost that is. On the fixedcharge transportation problem sciencedirect. Introduction and background the xed charge transportation problem concluding comments. Tabulated results to a large number of test problems show the solutions obtained by the approximation to be only fair. This paper presents the computational experience obtained with an experimental branchand bound code for the fixedcharged transportation problem. Other wellknown heuristic approaches are the ones by cooper and drebes 6, the xedcharge transportation problem can be sta denzler 8, diaby 7 and kuhn and baumol 11, ted as a distribution problem in which there are m sup. Pdf fixedcharge transportation problem with fuzzy costs. Step fixed charge transportation problem sfctp is an extended version of the fctp and is introduced by kowalski and lev 20. In this paper, we accepted june 2014 consider the fixed charge transportation problem under uncertainty, particularly when available online 15. In this paper an exact algorithm is presented which is computationally feasible for large problems. Anand jayakumar a et al 2 have optimized a p median problem using python.
They assumed that the products are transferred in batches in a fixed charge transportation problem. In practical applications, the xed costs may represent toll charges on highways, land. If x, w is feasible for the ip, then x is feasible for the fixed charge problem, and the ip cost is the same as the cost in the fixed charge problem. Balinski presented a technique which provides an approximate solution for any given fixed charge transportation problem 1. The fixedcharge transportation problem can be stated as a distribution problem in which there are m suppliers warehouses or factories and n customers destinations or demand points.
Also, the fuzzy values are applied according to the parameters value. Each of the m suppliers can ship to any of the n customers at a shipping cost per unit c ij unit cost for shipping from supplier i to customer j plus a fixed. The process is not set up unless there is production. In this paper, we propose an efficient algorithm for solving the fixed charged transportation problem, based on murtys extreme point ranking scheme. In this paper, a new concept of preferable interval is introduced. To send any flow from source s i to destination t j, we incur a unit variable shipping cost of c ij and a fixed cost f ij. A study of the fixed charge transportation problem. The pure fixed charge transportation problem wiley online library. A special version of the transportation problem tp is the fixed charge transportation problem fctp. Fixed charge problems arise in a large number of production and transportation systems. In this paper we consider the wellknown fixed charge transportation problem.
A strong formulation based on lagrangian decomposition and column generation. Solving the fixed charge transportation problem by new. The fctp differs from the linear tp only in the nonlinearity of the objective function. The fixed charge transportation problem can be stated as a distribution problem in which there are m suppliers warehouses or factories and n customers destinations or demand points. Yet, until now no computationally feasible exact method of solution for large problems had been developed. Mod08 lec33 location allocation problems in supply chain. D 1 d 2 d 3 d 4 a i o 1 5 9 9 9 19 5 8 5 1 o 2 4 10 6 2 6 10 o 3 2 1 1 2 11 11 b j 1 j. Received march, 1976 abaraetthis investigation evaluates an approximate method of solution developed by m. Thirwani 17 considered fixed charge bicriterion transportation problem with enhanced flow. Introduction and background the xed charge transportation problem concluding comments fixed charge transportation problem fctp for each arc i. Bilevel capacitated fixed charge transportation problem ritu arora department of mathematics, keshav mahavidyalaya, university of delhi, delhi deepa thirwani department of mathematics, hans raj college, university of delhi, delhi abstract bilevel programming is a twostage optimization problem where the.
Mod08 lec32 location problems p median problem, fixed. The method is based on the computation of a lower bound and an upper bound. Kennington used this code in 31 to study the effects on problem. Pdf fixedcharge transportation problem with fuzzy costs ali. An improved lower bound on the fixed costs developed in the. Pdf on the fixedcharge transportation problem krzysztof.
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