We consider a continuous multi-facility location problem where the demanding entities are regions in the plane instead of points. Each region may consist of a finite or an infinite number of points. The service point of a station can be anywhere in the region that is assigned to it. We do not allow fractional assignments, that is, each region is assigned to exactly one facility. The problem we consider can be stated as follows: given m demand regions in the plane, find the locations of q facilities and allocate regions to the facilities so as to minimize the sum of squares of the maximum Euclidean distances of the demand regions to the facility locations they are assigned to. We assume that the regions are closed polygons as any region can be approximated within any desired accuracy with a polygon.We first propose mathematical programming formulations of single and multiple facility location problems. The single facility location problem is formulated as a second order cone program (SOCP) which can be solved in polynomial time. The multiple facility location problem is formulated as a mixed integer SOCP. This formulation is weak and does not even solve medium-size problems. We therefore propose heuristics to solve larger instances of the problem. We develop three heuristics that work when the regions are polygons. When the demand regions are rectangles with sides parallel to coordinate axes, a special heuristic is developed. We compare our heuristics in terms of both solution quality and computational time.
PurposeThis study aims to create a reliable, collaborative and sustainable business environment with suppliers of a company for providing high-quality and low-cost products on time. A supplier management system that sustains existing suppliers by sharing work based on systematic performance evaluation while developing the supplier base with potential suppliers is proposed.Design/methodology/approachBuilt on quantitative approaches, supplier management functions are integrated in the designed system. A quantitative strengths, weaknesses, opportunities and threats (SWOT) analysis is adapted for evaluating potential suppliers. A multi-objective integer linear programming (ILP) model is developed for the distribution of orders among selected potential and existing suppliers. A performance evaluation scheme based on an exponentially weighted moving average (EWMA) is proposed to evaluate and monitor suppliers' performance over time.FindingsProposed system develops a supplier base by methodically selecting and approving new suppliers, and a sustainable relationship with both new and existing suppliers is established based on performance over time. Decisions on retaining or removing suppliers from the base are objectively made by quantitative evaluations. Orders are fairly distributed among suppliers under the constraints imposed by the management. Dependence on a certain set of suppliers and its associated risks are reduced while agility in offering goods is enabled.Originality/valueBusiness processes for selecting new suppliers, distributing orders among all suppliers, evaluating and monitoring performance over time are quantitatively integrated to add value in operational decision-making. The proposed system is original in the holistic approach for managing and sustaining multiple suppliers of a company based on performance.
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