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Vehicle Routing Part 2

Vehicle Routing Part 2. John H. Vande Vate Fall, 2002. Minimize Transportation Cost (Distance) Traveling Salesman Problem Respect the capacity of the Vehicle Multiple Traveling Salesmen Consider Inventory Costs Estimate the Transportation Cost Estimate the Inventory Cost

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Vehicle Routing Part 2

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  1. Vehicle RoutingPart 2 John H. Vande Vate Fall, 2002 1

  2. Minimize Transportation Cost (Distance) Traveling Salesman Problem Respect the capacity of the Vehicle Multiple Traveling Salesmen Consider Inventory Costs Estimate the Transportation Cost Estimate the Inventory Cost Trade off these two costs. Our Approach 2

  3. If Ford owned the dealerships... More frequent deliveries Reduce inventory Increase transportation How often should Ford deliver? High level approach Estimate Transportation Cost as function of frequency of delivery Estimate Inventory cost as function of frequency of delivery Trade off the two Idea 3

  4. Transportation costs are T now What will they be if we deliver twice as frequently? 2T The Simple Story   • Duh     4

  5. Inventory Carrying Costs are C now What will they be if we deliver twice as frequently? C/2 Q/2 Simple Story Continued Q 5

  6. n = Number of times to dispatch per year Total Cost = nT+C/n How often to dispatch? n = C/T Look Familiar? 6

  7. We don’t know the transportation cost How to estimate it? Assume we have estimates of cm = $/mile (may include $/hr figures) cs = $/stop (may include $/hr figures) ci = $/item …. System Design 7

  8. Stops Number of customers Number of deliveries Items Customer demand Miles? What might we be important to know? The Easy Stuff 8

  9. Is this rural North Dakota or Downtown Manhattan? Might estimate it from Census information Marketing information GIS Customer Density  customers per sq. mile Customer Distribution 9

  10.  = 9 customers per sq. mile       1/3 mile    How Far between Customers?       1 mile    10 1 mile

  11. Customer density about  customers per sq. mile leads to average distance between customers of about 1/ miles What does this mean for transportation costs? Conclusion 11

  12. N is the number of customers C is the number of customers per vehicle If there are “few” routes, e.g, No. of routes much less than customers/route N/C << C or N << C2 If there are “many” routes, e.g, No. of routes much more than customers/route N/C >> C or N >> C2 Extreme Cases 12

  13. Avoid “line hauls” x x x x x x x x x x x x x x x x Few Routes 13

  14. Customer density about the same in each zone. Each zone visits C customers Each zone travels about kC1/ Total Travel about kN1/ k is a constant that depends on the metric x x x x x x x x x x x x x x x x Total Distance 14

  15. If there are “many” routes, e.g, No. of routes much more than customers/route N/C >> C or N >> C2 Can’t fit them all around the DC Approach more like the strip heuristic Many Routes 15

  16. Partition the Customers x x x x x x x x x x x x x x x x 16

  17. Each partition Is k’/ wide Is C/k’ long Area is C/ C customers on average Effect on Travel? x x k’/ C/k’ The Partition 17

  18. Length of the route  2r + Ck1/ With N/C routes… Transportation Costs  2E(r)N/C + NkE(1/) x x The Line Haul x r 18

  19. Greater Atlanta (Hypothetical) 280,000 households 300 sq miles (17 miles x 17 miles) 5% market share 14,000 deliveries per week 2,000 per day 1,000 per shift Example: WebVan 19

  20. Delivery Density (on shift basis) 300 sq miles 1,000 per shift 3.3 customers per sq. mile 0.55 miles between customers WebVan Hypothetical 20

  21. Customers per route? Determined by driver schedule 7 hour shift 15 miles/hr avg. speed 0.55 miles between customers (2.2 minutes) 2 minutes per stop (4-5 minutes per customer) 12-15 customers/hr 84-105 customers per route 10-12 routes per shift Using Few Routes 21

  22. C  80+ Customers per route N  1000 Customers Middle ground Neither N >> C2 Nor N << C2 Consistent? 22

  23. What’s r roughly? Total Area 300 sq miles 17 miles by 17 miles 2r < 17 miles Line haul speed  30-35 miles/hr r costs  30 min. out of each 7 hr shift. (7%) x x Using Many Routes x r 23

  24. Delivery Density (on shift basis) 300 sq miles 1,000 per shift ==> 2,000 per shift 3.3 ==> 7 customers per sq. mile 0.55 ==> 0.38 miles between customers 2.2 ==> 1.5 minutes drive 4-5 ==> 3-4 minutes per customer 12-15 ==> 15-20 customers/hr 84-105 ==>100-140 customers per route Double Market Share 24

  25. What’s the impact of peak and off-peak times? What’s the impact of Scheduled deliveries? How might we estimate the average distance per customer? Realities 25

  26. Suppose Ford operated the delivery fleet What to do? Deliver to all the Dealerships at once? Stagger deliveries? What’s the trade-off? Proposals? Ford vs WebVan 26

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