Computation Section
Subunit Inventory Analysis
 Systems - Pull Tree




An example worksheet with the pull tree structure shown is below. The example has the same structure as at the left. The operations have been assigned the letters A, B, C, D and E, corresponding to the indices 1, 2, 3, 4 and 5. As described for the Line example, the data defining the operations and their parameters are in rows 1 through 11. The lot size variables are in rows 12 through 14. We have entered data to represent a possible manufacturing system. The batch process, operation C, has a high setup cost, so we are using a large processing lot size for that operation. The Delay operation does not use all the parameters as suggested by the x in some cells.

Rows 21 through 26 define the tree structure and compute the operation flows. Line 21 assigns indices to the operations and line 22 repeats their names. The values of the flows pulled from the operations are in line 23. In addition to the flow of 100 pulled from operation E, we pull an additional 50 units from operation C. Row 24 shows the precedence ordering defining the tree. Each operation has a unique following operation, specified by the index in row 24. Operation E has the index 0 indicating that it has no follower. Row 25 holds the proportions transferred from each operation to its following operation. For the pull tree this proportion is relative to the flow passing through the following operation. For the example, operation C receives 70% of its input from A and 30% from B. Operation 5 receives one unit from each of operations C and D for every unit produced. This information is placed in row 25. Row 26 holds the computed flows through each operation. This information is transferred to row 4 for analysis purposes.


The yellow cells in the output lot size row, row 14, indicate that the output lot size of an operation is automatically set equal to the input lot size of its unique following operation. An exception is the output lot size at operation E, the lot size that flows to the customers.

Rows 15 through 19 show the results for each operation. The queue operation requires 4 servers to handle the flow.

The system results in column G have one important change from the Line structure case. As before, the System WIP is the sum of the operation WIP's. The cycle time for the system is not the sum of the cycle times for the operations. Rather it is the system WIP divided by the total output flow that appears in G23, 150. We cannot the sum of operation cycle times because flow varies between the operations.

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tree roots

Operations Management / Industrial Engineering
by Paul A. Jensen
Copyright 2004 - All rights reserved