This preview shows pages 1–10. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: Prof. Dr. Füsun Ülengin 1 Füsun Ülengin, 2009 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 “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 multiplestop routes 3 Füsun Ülengin, 2009 Vehicle Scheduling :ClarkeWright 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 6,000gallon 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 ClarkeWright Savings Approach(cnt.) The load to be delivered to each customer P i is listed in column q. The righthand value in each cell is the distance dy,z between Py and Pz, where y and z are specific customers. The lefthand 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 ClarkeWright 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 ClarkeWright 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 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 : 134 29 67811 5101213 9 Füsun Ülengin, 2009 Improvements:...
View
Full
Document
This note was uploaded on 11/10/2009 for the course LOGISTICS 20091 taught by Professor Fusunulengin during the Spring '09 term at Istanbul Technical University.
 Spring '09
 FUSUNULENGIN

Click to edit the document details