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...

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...

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...

Water is a basic part of our daily lives, as such effective water supply paramount importance. Thus, result the rise in population size and shortage there need for proper, suitable optimal utilization resources to efficiently be distributed among populace. The proper allocation distribution field network planning modelled through mathematical parameters objective system. This approach requires ...