A Faster Algorithm for Two-Variable Integer Programming
نویسندگان
چکیده
We show that a 2-variable integer program, defined by m constraints involving coefficients with at most φ bits can be solved with O(m+ φ) arithmetic operations on rational numbers of size O(φ). This result closes the gap between the running time of two-variable integer programming with the sum of the running times of the Euclidean algorithm on φ-bit integers and the problem of checking feasibility of an integer point for m constraints.
منابع مشابه
OPTIMIZATION OF A PRODUCTION LOT SIZING PROBLEM WITH QUANTITY DISCOUNT
Dynamic lot sizing problem is one of the significant problem in industrial units and it has been considered by many researchers. Considering the quantity discount in purchasing cost is one of the important and practical assumptions in the field of inventory control models and it has been less focused in terms of stochastic version of dynamic lot sizing problem. In this paper, stochastic dyn...
متن کاملA generalized implicit enumeration algorithm for a class of integer nonlinear programming problems
Presented here is a generalization of the implicit enumeration algorithm that can be applied when the objec-tive function is being maximized and can be rewritten as the difference of two non-decreasing functions. Also developed is a computational algorithm, named linear speedup, to use whatever explicit linear constraints are present to speedup the search for a solution. The method is easy to u...
متن کاملA Non-linear Integer Bi-level Programming Model for Competitive Facility Location of Distribution Centers
The facility location problem is a strategic decision-making for a supply chain, which determines the profitability and sustainability of its components. This paper deals with a scenario where two supply chains, consisting of a producer, a number of distribution centers and several retailers provided with similar products, compete to maintain their market shares by opening new distribution cent...
متن کاملA Combined Stochastic Programming and Robust Optimization Approach for Location-Routing Problem and Solving it via Variable Neighborhood Search algorithm
The location-routing problem is one of the combined problems in the area of supply chain management that simultaneously make decisions related to location of depots and routing of the vehicles. In this paper, the single-depot capacitated location-routing problem under uncertainty is presented. The problem aims to find the optimal location of a single depot and the routing of vehicles to serve th...
متن کاملModeling and scheduling no-idle hybrid flow shop problems
Although several papers have studied no-idle scheduling problems, they all focus on flow shops, assuming one processor at each working stage. But, companies commonly extend to hybrid flow shops by duplicating machines in parallel in stages. This paper considers the problem of scheduling no-idle hybrid flow shops. A mixed integer linear programming model is first developed to mathematically form...
متن کامل