lect23

# lect23 - Transportation Management Vehicle Routing Chris...

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Chris Caplice ESD.260/15.770/1.260 Logistics Systems Nov 2006 Transportation Management Vehicle Routing

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© Chris Caplice, MIT 2 MIT Center for Transportation & Logistics – ESD.260 Local Routing Large Number of Network Problems – we will look at four ± Shortest Path Problem ² Given: One origin, one destination ² Find: Shortest path from single origin to single destination ± Transportation Problem ² Given: Many origins, many destinations, constrained supply ² Find: Flow from origins to destinations ± Traveling Salesman Problem ² Given: One origin, many destinations, sequential stops, one vehicle ² Find: Shortest path connecting each stop once and only once ± Vehicle routing Problem ² Given: One origin, many destinations, many capacitated vehicles ² Find: Lowest cost tours of vehicles to destinations
© Chris Caplice, MIT 3 MIT Center for Transportation & Logistics – ESD.260 Shortest Path Problem Find the shortest path in a network between two nodes – or from one node to all others Result is used as base for other analysis Connects physical to operational network Issues ± What route in practice is used? Shortest? Fastest? Un- restricted? ± Frequency of updating the network ± Using time versus distance (triangle inequality) ± Impact of real-time changes in congestion ± Speed of calculating versus look-up

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© Chris Caplice, MIT 4 MIT Center for Transportation & Logistics – ESD.260 Shortest Path Network ± Arc/Link & Nodes ± Cost is on nodes, c ij Think of a string model Basic SP Algorithm (s to t) 1. Start at origin node, s=i 2. Label each adjacent nodes, j, L’ j =L i +c ij iff L’ j <L j 3. Pick node with lowest label, set it to i, go to step 2 4. Stop when you hit node t Building Shortest Path Tree Many, many variations on this algorithm, ± Label Setting ± Label Correcting i \ j 1 234. . . n 1 d 12 d 13 d 14 d 1n 2 d 23 d 24 d 2n 3 d 34 d 3n 4 d 4n . . . n s t Shortest Path Matrix
© Chris Caplice, MIT 5 MIT Center for Transportation & Logistics – ESD.260 Transportation Problem Find minimum cost routes for between multiple origins and destinations Flow is fungible – same products ± Cost on arcs, c ij , ± Flow on arcs, x ij Many solution approaches ± Balanced problem – Supply=Demand ± Unbalanced – ± Transhipment Problem – neutral nodes DC1 DC2 Cust A Cust B Cust C Supply 1 Supply 2 Demand A Demand B Demand C 1 1 .. 0 ij ij ij N n ij i j n ij j i ij Min c x st x Supply i x Demand j xi j = = =∀ = ≥∀

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© Chris Caplice, MIT 6 MIT Center for Transportation & Logistics – ESD.260 Traveling Salesman Problem Starting from an origin, find the minimum distance required to visit each destination once and only once and return to origin. m-TSP: best tour for msalesmen Very old problem ~1832 ± For history, see: http://www.tsp.gatech.edu/index.html 1 10 100 1,000 10,000 100,000 1,000,000 10,000,000 100,000,000 1,000,000,000 10,000,000,000 100,000,000,000 1 2 3 4 5 6 7 8 9 1 01 11 21 31 41 5 Number of tours with n cities
© Chris Caplice, MIT 7 MIT Center for Transportation & Logistics – ESD.260 TSP Solution Approaches Heuristics ± Construction ² Nearest neighbor ²

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## This note was uploaded on 12/06/2011 for the course ESD 1.260j taught by Professor Chriscapliceesd during the Fall '06 term at MIT.

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lect23 - Transportation Management Vehicle Routing Chris...

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