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10Vehicle Scheduling2009

# 10Vehicle Scheduling2009 - Prof Dr Fsun lengin Fsun lengin...

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Prof. Dr. Füsun Ülengin 1 Füsun Ülengin, 2009

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The “Savings” Method for VRP Depot Depot (a) Initial routing Route distance = d 0,A +d A,0 +d 0,B + d B,0 (b) Combining two stops on a route Route distance = d 0,A +d A,B +d B,0 A B d A,0 d 0,A d 0,B d B,0 A B d B,0 d 0,A d A,B Stop Stop 0 0 “Savings” is better than “Sweep” method has lower average error 2 Füsun Ülengin, 2009
Savings Method Observation The points that offer the greatest savings when combined on the same route are those that are farthest from the depot and that are closest to each other. This is a good principle for constructing multiple-stop routes 3 Füsun Ülengin, 2009

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Vehicle Scheduling :Clarke-Wright savings approach 1 . Initially, assume that enough vehicles are available and allocate one to a customer. For our example we will assume that we have 3 trucks of 5,000- gallon capacity, 4 trucks of 6,000-gallon capacity and an unlimited supply of 4,000- gallon capacity. One truck of the smallest capacity is initially allocated to each customer and provides an initial feasible solution of the problem 2 . For hand computation, set up a matrix (see the distributed sheet) 4 Füsun Ülengin, 2009
Clarke-Wright Savings Approach(cnt.) The load to be delivered to each customer P i is listed in column q. The right-hand value in each cell is the distance dy,z between Py and Pz, where y and z are specific customers. The left-hand value represents the savings Sy,z in distance associated with Py and Pz when Py enters the tour. The value in the middle of the cell ty,z indicates whether the customer combinations Py and Pz are in the tour. The dsignatorhas the following values: t y,z = 1 is two customers are linked on a truck route t y,z = 0 if the customers are not linked on a truck route t y,z = 2 if the customer is served exclusively by a single truck For ease of computation, the matrix is ordered from left to right on the basis of increasing savings S y,z 5 Füsun Ülengin, 2009

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Clarke-Wright Savings approach(cnt.) 3 . Search the matrix for the largest savings subject to the following conditions for any cell (y,z,) A) t y,0 and t z,o are >0 B) P y and P z are not already on the same truck run C) By this allocation you do not exceed the capacity of the trucks available 4. Make the necessary changes in the t values of the combined tours See the distributed sheet 6 Füsun Ülengin, 2009
Clarke-Wright Savings Approach :Example 2 (Web van Case) One morning the DC manager at Webvan has orders from 13 different customers that are to be delivered Four trucks, each truck is capable of carrying up to 200 units The location of the DC, each customer on a grid , and the order size a j from each customer i are shown in table below: 7 Füsun Ülengin, 2009

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8 Füsun Ülengin, 2009
Webvan Example (continues) Identify the distance matrix Identify the savings matrix Assign customers to vehicles or routes Sequence customers within routes The optimum solution is : 1-3-4 2-9 6-7-8-11 5-10-12-13 9 Füsun Ülengin, 2009

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