This document summarizes key aspects of vehicle routing problems (VRP). It discusses the traveling salesman problem (TSP) as a special case of VRP where a single vehicle must visit multiple locations. It also describes more complex VRP formulations that involve multiple vehicles with capacity constraints serving multiple customers. Heuristics for constructing initial feasible routes and improving routes are described. Finally, an example employee pickup VRP problem in Bangalore, India is presented to illustrate a real-world application of VRP.

9. 1998 CLM DEFINITION OF LOGISTICS … .is that part of the supply chain process that plans, implements, and controls the efficient, effective flow and storage of goods, services, and related information from the point-of-origin to the point-of-consumption in order to meet customers' requirements. Council of Logistics Management, 1998; www.CLM1.org

10. Five Business Systems - Tightly Interconnected Within The Organization Copyright 2000 - All Rights Reserved Measurement Decisions Management Systems Reward Decisions Strategic Decisions Transportation Decisions Sourcing Decisions Inventory Decisions Logistics Systems { Price Decisions Promotion Decisions Marketing Systems Product Decisions Place (How, where, how much) } Production Scheduling Decisions Production Capacity Decisions Shop Floor Decisions Manufacturing Systems } Product Design Decisions Process Design Decisions Engineering Systems }

14. The Logistics (Strategic) Planning Triangle Which mode? Which carrier? Which route? Shipment size and frequency? Where?, How many? What size? Allocation? Strategy/Control system? How much? Where?

16. Routes of Goods Goods at shippers let us guess Freight forwarder warehouse Air terminal plane air Freight forwarder warehouse Goods at consignees Container terminal vessel sea May change transpor-tation modes truck land railway land barge mid-stream pier bulk goods sea

27. Illustration of VRP (Outlier) Depot 50 76 39 112 88 29 123 44 58 90 77 89 57 115 124 59 176 65 98 125 Truck Capacity = 250 What is the minimum # of trucks we would need? Maximum?

33. The VRP is applicable in many practical situations directly related to  the physical delivery of goods such as  distribution of petroleum products,  distribution of industrial gases,  newspaper deliveries,  delivery of goods to retail store,  garbage collection and disposal,  package pick-up and delivery,  milk pick-up and delivery, etc.  the non-movement of goods such as  picking up of students by school buses,  routing of salesmen,  reading of electric meters,  preventive maintenance inspection tours,  employee pick-up and drop-off , etc. APPLICATIONS OF VRP

34.  A DSS  Employee Bus Routing  Commodity Distribution  In COVERS  Efficient Heuristic Procedures  NNH  MNNH  MSCWH  Simulation Features  Manipulate the System Generated Routes  Completely User Generated Routes  COVERS Handles  Multi-Depot VRP  Heterogeneous VRP COVERS - C OMPUTERIZED VE HICLE R OUTING S YSTEM

35. E MPLOYEE P ICKUP V E HICLE R OUTING P ROBLEM (EPVRP) – BANGALORE, KARNATAKA, INDIA  Indian Telephone Industries [ITI] Limited  Bharat Electronics Limited [BEL]  Hindustan Machine Tools [HMT]  Hindustan Aeronautics Limited [HAL]  Indian Space Research Organization [ISRO]  National Aeronautical Laboratory [NAL]  Central Machine Tools of India [CMTI]  ………

36. AS A PROBLEM IN OR, A SIMPLIFIED EPVRP CAN BE DESCRIBED AS FOLLOWS: GIVEN  A set (fixed number) of pick-up or delivery points,  The demand at every pick-up or delivery points (deterministic),  A set (fixed number) of vehicles (homogeneous) and  All relevant distance information across pick-up points. IT IS REQUIRED TO FIND AN EFFECTIVE/EFFICIENT SOLUTION FOR  Assigning pick-up points to vehicles and  Sequencing pick-up points on the route of each vehicle SO AS TO ACHIEVE THE OBJECTIVE OF  Minimizing the total distance traveled by the vehicles and/or the number of vehicles used. UNDER THE CONSTRAINTS THAT  Every route originates and terminates at the depot  The capacity of vehicle is restricted  The maximum distance (time) allowed for a vehicle on any route is within a pre- specified limit  Each pick-up point is visited once only  Etc.,

37. AN ILP FORMULATION - EPVRP Source : WATERS (1998)  ASSUMPTIONS  Vehicle capacity is known and constant (homogenous)  The number of vehicles available is known (at least the minimum number of vehicles required is known)  The demand at every pick-up point is known (deterministic)  Maximum distance to be traveled by each vehicle is known and constant for all vehicles  Demand at every pick-up point is less than or equal to vehicle capacity  Every pick-up point is served by only one vehicle Further, keeping in line with Water’s formulation, the model formulation is oriented towards routing during drop-back rather than pick-up. It is assumed that the reverse logic holds good for pick-up.  Expanding the Scope of Linear Programming Solutions for Vehicle Scheduling Problems. OMEGA, 16(6), 577-583

38. COMPUTATIONAL COMPLEXITY - OPTIMAL SOLUTION Sutcliffe and Board (1990)  estimated that a simple extrapolation of Waters’ (1988) ILP approach using the SCICONIC software might take nearly 1,20,000 years of CPU time on a VAX 8600 machine to solve a VRP with 38 pick-up points !  Optimal Solution of VRP: Transporting Mentally Handicapped Adults to an Adult Training Center. JORS, 41(1), 61-67. 270 225 187 147 114 85 60 # Constraints 47.8 37.4 31.0 31.0 28.6 26.4 13.2 Optimal Distance (Km.) 3 2 2 2 2 2 1 # Routes 4963340 43021 70724 2780 353 330 45 # Iterations (LINDO) 3 25 75 71 5 2 16 48 61 4 23 49 147 106 7 6 36 108 79 6 667 (11 Mts) 81 243 132 9 80 64 192 117 8 100800 (28 Hrs.) 100 300 137 10 CPU Time (AT 486) # (0, 1) Variables # Variables Including (0, 1) Variables Tot Quantities (Units) # PUP

39.  N earest I nsertion H euristic ( NIH )  C heapest I nsertion H euristic ( CIH )  P arallel V ersion of C larke & W right H euristic ( PCWH )  S equential V ersion of C larke & W right H euristic ( SCWH )  C onvex H ull H euristic ( CHH )  N earest N eighbour H euristic ( NHH )  M odified NNH ( MNNH )  M odified SCWH 1 ( MSCWH-1 )  M odified SCWH 2 ( MSCWH-2 ) HEURISTIC ALGORITHMS

40. CASE STUDY : DETAILS OF ROUTES, DISTANCES & SEAT UTILIZATION  Ignored in our study  Each Bus Route (Trip) Repeated; Two Trips a day, Once for Pick-up and once for Drop-off .  Distinct Pick-up Points 213+ (426) ---- 30 53 66 64 # Routes 7005.0  (14010) ---- 1056.7 1808.3 2163.0 1977.0 Total Distance per Trip (Km.) ---- ---- 54.0 90.0 94.3 89.0 Seat Utilization (%) 313 3999 07.30 – 04.15 PM FG 303 3659 06.15 – 02.15 PM A 242 975 02.15 – 10.15 PM B 286 3042 08.45 – 05.30 PM AG 410  11715 Total ---- 40 10.15 – 06.15 AM C  # Pickup Points # Commuters Timings Shift

41. COMPARATIVE PERFORMANCE (CASE STUDY) – TOTAL DISTANCE (Figures in Table represent travel distance in Km. For Pick-up only) 1 7.81 6458.1 858.9 1740.7 2040.8 1817.7 MNNH 2 7.78 6460.3 910.2 1687.5 2066.4 1796.2 MSCWH-1 1 7.29 6494.1 900.0 1708.0 2063.2 1822.9 NNH 1688.5 1749.2 1889.2 1761.1 1914.2 1734.1 1808.3 Shift – 3 AG 908.5 964.7 1014.5 1080.9 1020.7 890.3 1056.7 Shift – 4 B 6443.4 6665.4 7349.5 6671.6 7412.4 6547.9 7005.0 Total Distance (Km.) 8.02 4.85 - 4.9 4.76 - 5.8 6.5 ----- Savings (in %) 12 2047.7 1875.8 NIH ---- 2163.0 1977.0 Existing Practice (Manual) 19 2026.1 1803.5 PCWH 52 2322.3 2155.2 CIH 55 2047.7 1903.8 CHH 18 2306.6 2139.2 SCWH 2 2047.0 1799.4 MSCWH-2 CPU Time PC/AT – 486 @ 33 MHz (Minutes) Shift – 2 FG Shift – 1 A Procedures

42. COMPARATIVE PERFORMANCE (CASE STUDY) – TOTAL NUMBER ROUTES Figures in Table represent number of trips for Pick-up only 8.92 194 23 51 63 57 MNNH 8.45 195 24 49 63 58 MSCWH-1 8.45 195 24 50 64 57 NNH 49 51 55 56 52 51 53 Shift – 3 AG 24 25 28 36 27 23 30 Shift – 4 B 194 198 218 223 213 197 213 Total Routes 8.92 7.04 - 2.3 - 4.7 0 7.51 ----- Reduction in Trips (%) 63 60 NIH 66 64 Existing Practice (Manual) 68 63 PCWH 69 65 CIH 62 60 CHH 70 65 SCWH 63 58 MSCWH-2 Shift – 2 FG Shift – 1 A Procedures

43.  N earest N eighbour H euristic ( NHH )  M odified NNH ( MNNH )  M odified SCWH-2 ( MSCWH-2 ) HEURISTIC ALGORITHMS - DSS IMPLEMENTATION

44. A Schematic Diagram of COVERS DATA MANAGEMENT MODULE  General file  Depot Data File  Vehicle Data File  Pickup point Demand Data File  Inter-Stop Distance Data File MODEL MANAGEMENT MODULE  Heuristic Procedures  Simulation Model REPORT MANAGEMENT MODULE  Details of Route Sequence  Summary of Routes  Overall Summary of Routes  Depot wise Route Allocation  Vehicle Type wise Route Allocation CONTROL MODULE COMPUTER SYSTEM USER

45. ThankYou