this paper uses the l1−norm and the concept of the non-dominated vector, topropose a method to find a well-dispersed subset of non-dominated (wdsnd) vectorsof a multi-objective mixed integer linear programming (momilp) problem.the proposed method generalizes the proposed approach by tohidi and razavyan[tohidi g., s. razavyan (2014), determining a well-dispersed subset of non-dominatedvectors of...

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...

a considerable problem in competitive trade world is choosing the best supply chain. as a result in much more serious circumstances of competitions looking for the best supplier for manufacturing, for preparing raw material, is very significant. meantime suppliers have different scenarios to be fulfilled, such as changing selection variables like lead-time, transportation cost and transportatio...

network location models comprise one of the main categories of location models. these models have various applications in regional and urban planning as well as in transportation, distribution, and energy management. in a network location problem, nodes represent demand points and candidate locations to locate the facilities. if the links network is unchangeably determined, the problem will be ...

This paper uses the weighted L$_1-$norm to propose an algorithm for finding a well-dispersed subset of non-dominated solutions of multiple objective mixed integer linear programming problem. When all variables are integer it finds the whole set of efficient solutions. In each iteration of the proposed method only a mixed integer linear programming problem is solved and its optimal solutions gen...

We consider the mixed integer version of bipartite vertex cover. This is equivalent to the mixed integer network dual model, recently introduced in [2], that generalizes several mixed integer sets arising in production planning. We derive properties of inequalities that are valid for the convex hull of the mixed integer bipartite covers by projecting an extended formulation onto the space of th...

We present a version of GMI (Gomory mixed-integer) cuts in a way so that they are derived with respect to a “dual form” mixed-integer optimization problem and applied on the standard-form primal side as columns, using the primal simplex algorithm. This follows the general scheme of He and Lee, who did the case of Gomory pure-integer cuts. Our input mixed-integer problem is not in standard form,...