The problem with integer programming

On the integer max-linear programming problem

For a generic class of matrices we show that integer solutions to two-sided max-linear systems and programs can be found in polynomial time. For general matrices we adapt the existing methods for finding real solutions to obtain algorithms for finding integer solutions.

A Mixed Integer Programming Formulation for the Heterogeneous Fixed Fleet Open Vehicle Routing Problem

The heterogeneous fixed fleet open vehicle routing problem (HFFOVRP) is one of the most significant extension problems of the open vehicle routing problem (OVRP). The HFFOVRP is the problem of designing collection routes to a number of predefined nodes by a fixed fleet number of vehicles with various capacities and related costs. In this problem, the vehicle doesn’t return to the depot after se...

Comparing Mixed-Integer and Constraint Programming for the No-Wait Flow Shop Problem with Due Date Constraints

The impetus for this research was examining a flow shop problem in which tasks were expected to be successively carried out with no time interval (i.e., no wait time) between them. For this reason, they should be completed by specific dates or deadlines. In this regard, the efficiency of the models was evaluated based on makespan. To solve the NP-Hard problem, we developed two mathematical mode...

Mixed integer bilinear programming with applications to the pooling problem

An Imperialist Competitive Algorithm and a Mixed Integer Programming Formulation for the Capacitated Vehicle Routing Problem

The Vehicle Routing Problem (VRP), a famous problem of operation research, holds a central place in combinatorial optimization problems. In this problem, a fleet vehicles with Q capacity start to move from depot and return after servicing to customers in which visit only ones each customer and load more than its capacity not at all. The objective is to minimize the number of used vehicles and t...