In this paper, we introduce the Steiner Bi-objective Shortest Path Problem. This problem is defined on a directed graph G=(V,A), with subset T?V of terminals. Arcs are labeled travel time and cost. The goal to find complete set efficient paths between every pair nodes in T. motivation behind stems from data preprocessing for vehicle routing problems. We propose solution method based labeling ap...

In this paper, the strategic planning of a supply chain under a static chain-to-chain competition on the plane is addressed. It is assumed that each retailer has a coverage area called the radius of influence. The demand of each demand zone is divided equally between the retailers which can cover that market. However, the demand of distant customers who are not in the retailers’ radius of influ...

Flow shop scheduling deals with the determination of optimal sequence jobs processing on machines in a fixed order main objective consisting minimizing completion time all (makespan). This type problem appears many industrial and production planning applications. study proposes new bi-objective mixed-integer programming model for solving synchronous flow problems time. The functions are total m...