Determining Production Lot Sizes Four products are routed through a machining center that is notorious for its delays. Each product has had stable demand for some time, so that average weekly demand is predictable over a 3-6 month time frame. However, in the short run, demand fluctuates a great deal, and the load at the machining center varies considerably. The production control system dictates the lot size for each of the products. These quantities are shown, along with other relevant information, in the following table.
|
Product no.
|
Demand
(weekly)
|
Setup
(hours)
|
Run time
(hours/1003)
|
Lot
size
|
|
I
|
100
|
3
|
30
|
100
|
|
2
|
500
|
IS
|
45
|
500
|
|
3
|
50
|
6
|
75
|
100
|
|
4
|
250
|
24
|
150
|
1500
|
With the current lot sizes, the machining center is running at a utilization of about 76%, but long lead times, sometimes over 2 weeks, have discouraged production planners from increasing its load. (A week contains 120 productive hours.) In the past, lead times spiraled out of control when utilization grew to around 80%.
A lead time model for this problem has been constructed on a spreadsheet.2 The model permits the user to select lot sizes and thereby influence the average lead time through the bottleneck work center. The lead time prediction is based on advanced modeling techniques, but the details of the model are not of primary importance.
What is the shortest possible lead time, and what lot sizes achieve this value?