We present a generic branch-and-bound algorithm for finding all the Pareto solutions of biobjective mixed-integer linear program. The main contributions are new algorithms obtaining dual bounds at node, checking node fathoming, presolve, and duality gap measurement. Our is predominantly decision space search method because branching performed on variables, akin to single objective problems, alt...

in this paper, for the first time, blood inventory-routing problem (irp) is defined and a mixed integer linear programming formulation is presented. to do so, the concepts of assigned inventory, transfusion to crossmatch ratio, crossmatch release period, older-first policy and order-up-to level inventory policy along with perishability considerations are incorporated into the latest inventory-r...

this paper presents an application of benders decomposition to deal with the complexities in the simultaneous generation expansion planning (gep) and transmission expansion planning (tep). unlike the power system operation fields of study, the power system planning methods are not expected to be fast. however, it is always preferable to speed up computations to provide more analysis options for...

this paper proposes a new mathematical model for designing and planning postal parcels carriage and postal networks. the objective of postal network designing is to determine the location, size and connection between the postal stations in a city, province or country. in this paper, a kind of multiple locations-allocations hub problem with limited capacity in collecting, distributing and broadc...

the capacitated location-routing problem (clrp) is a new research area in logistics and distribution management. this problem combines two difficult problems: the facility location problem (flp) and vehicle routing problem (vrp). the goal of the clrp is to open a subset of depots, assign the customers into open facilities, and then design vehicle tours in order to minimize the total cost. the t...

A Nonlinear Mixed Integer Programming approach is presented to select the number of membrane modules required in the extraction and stripping sectors of a Non Dispersive Solvent Extraction Plant for effluent treatment and metal recovery. The differential equations that model each membrane module are discretized using orthogonal collocation on finite elements leading to an algebraic system of eq...

The aim of this work is to propose a mathematical programming model for the Economic Lot Scheduling Problem (ELSP) with performance decay. The main difficulties related to this model are the nonlinearities and/or nonconvexities associated with the dynamic behavior of the system with time. Firstly, the problem is formulated as a Mixed Integer Non Linear Program (MINLP), which is found to be nonc...

an interactive heuristic approach can offer a practical solution to the problem of linear integer programming (lip) by combining an optimization technique with the decision maker’s (dm) judgment and technical supervision. this is made possible using the concept of bicriterion linear programming (blp) problem in an integer environment. this model proposes two bicriterion linear programs for iden...