Linear programming formulation of the set partitioning problem
نویسنده
چکیده
In this paper, we present a linear programming (LP) model of the set partitioning problem (SPP). The number of variables and the number of constraints of the proposed model are bounded by (third-degree) polynomial functions of the number of non-zero entries of the SPP input matrix, respectively. Hence, the model provides a new affirmative resolution to the all-important ‘P vs. NP’ question. We use a transportation problem-based reformulation that we develop, and a path-based modelling approach similar to that used in Diaby (2007) to formulate the proposed LP model. The approach is illustrated with a numerical example.
منابع مشابه
FGP approach to multi objective quadratic fractional programming problem
Multi objective quadratic fractional programming (MOQFP) problem involves optimization of several objective functions in the form of a ratio of numerator and denominator functions which involve both contains linear and quadratic forms with the assumption that the set of feasible solutions is a convex polyhedral with a nite number of extreme points and the denominator part of each of the objecti...
متن کاملA mixed integer linear programming formulation for a multi-stage, multi-Product, multi-vehicle aggregate production-distribution planning problem
In today’s competitive market place, companies seek an efficient structure of supply chain so as to provide customers with highest value and achieve competitive advantage. This requires a broader perspective than just the borders of an individual company during a supply chain. This paper investigates an aggregate production planning problem integrated with distribution issues in a supply chain ...
متن کاملA Branch-Cut-and-Price Algorithm for the Energy Minimization Vehicle Routing Problem
We study a variant of the capacitated vehicle routing problem where the cost over each arc is defined as the product of the arc length and the weight of the vehicle when it traverses that arc. We propose two new mixed integer linear programming formulations for the problem: an arc-load formulation and a set partitioning formulation based on q-routes with additional constraints. A family of cycl...
متن کاملA Single Machine Capacitated Production Planning Problem Under Uncertainty: A Grey Linear Programming Approach
The production planning is an important problem in most of manufacturing systems in practice. Unlike many researches existing in literature, this problem encounters with great uncertainties in parameters and input data. In this paper, a single machine capacitated production planning problem is considered and a linear programming formulation is presented. The production costs are assumed to be u...
متن کاملSolving Parallel Machine Scheduling Problems by Column Generation
We consider a class of problems of scheduling n jobs on m identical, uniform, or unrelated parallel machines with an objective of minimizing an additive criterion. We propose a decomposition approach for solving these problems exactly. The decomposition approach rst formulates these problems as an integer program, and then reformulates the integer program, using Dantzig-Wolfe decomposition, as ...
متن کامل