In some cases, the waste generated by the production of material at a facility must be disposed of at special waste disposal locations. We need to identify.

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Presentation transcript:

In some cases, the waste generated by the production of material at a facility must be disposed of at special waste disposal locations. We need to identify which waste facilities to open, given a capacity for each waste unit and per-unit transportation costs for shipping waste from a plant facility to a waste facility. We can model this problem by extending our facility location models. Suppose we have the network shown on the next slide and let K={4, 9, 10} be possible locations for our waste disposal facilities. At each plant j  J, the amount of waste material produced is proportional (with proportionality constant 0<  j <1) to the amount of goods produced; for example, if plant 5 produces 500 units, then it also produces 500  units of waste. These proportionality constants are The one-time fixed cost associated with opening a waste disposal facility at k  K is and their capacities are The cost of shipping one unit of waste from plant j  J to waste disposal unit k  K is $10d jk, where d jk is the shortest distance from j to k, while the cost of shipping one unit of demand from plant j to customer i is $20d ij. Assuming that a customer can receive its demand from multiple plants and that the waste from a plant can be shipped to multiple disposal locations, determine how to satisfy customer demands and waste removal requirements at minimum cost. Where are the plants and waste disposal units?

Fixed-Charge Location Problem

Solution Optimal cost is $42, Optimal solution opens plants in all possible locations. Plant 3 services customer 3, plant 5 serves customers 2 and 5, plant 6 serves customers 1, 6, and 9, plant 7 serves customer 7, and plant 8 serves customers 4, 8, and 10. Optimal solution opens waste disposal facilities at locations 4 and 10, with location 4 handling waste from plants 3, 5, and 7, and location 10 handling waste from plants 6 and 8.