The Experiment

After examining the demand for each item, we designate the Top 7 products as A-type items and the remaining items as B/C-type items. The aggregate demand for the A-type items is shown in Figure 21 and the aggregate demand for the B/C-type items is shown in Figure 22.

A-type Items Historical Demand

0 1000 2000 3000 4000 5000 6000 7000

10/1/98 10/15/98 10/29/98 11/12/98 11/26/98 12/10/98 12/24/98 1/7/99 1/21/99 2/4/99 2/18/99 3/4/99 3/18/99 4/1/99 4/15/99 4/29/99 5/13/99 5/27/99 6/10/99 6/24/99 7/8/99 7/22/99 8/5/99 8/19/99 9/2/99 9/16/99 9/30/99

Date

Units Demanded

Capacity

Figure 21. Aggregate demand for Top 7 (A-type) items.

B/C-type Items Historical Demand

0 1000 2000 3000 4000 5000 6000

10/1/98 10/15/98 10/29/98 11/12/98 11/26/98 12/10/98 12/24/98 1/7/99 1/21/99 2/4/99 2/18/99 3/4/99 3/18/99 4/1/99 4/15/99 4/29/99 5/13/99 5/27/99 6/10/99 6/24/99 7/8/99 7/22/99 8/5/99 8/19/99 9/2/99 9/16/99 9/30/99

Date

Units Demanded

Capacity

Figure 22. Aggregate demand for B/C-type items.

Observe that while the demand for the A-type items often exceeded the daily production capacity, the demand for B/C-type items only exceeded the daily production capacity on two days over the course of one year. Usually the production facility has sufficient capacity to produce all of the requirements for the B/C-type items, which will receive production priority on a daily basis. Any remaining production capacity will be used to produce the A-type items.

The data used in this experiment for the 30 items are summarized in Figure 23. Based on selling margins and discussions with management, backorder costs were estimated at 25 times their respective unit holding costs. We will use the same target system inventory level of 7,039 units. For the three operating policies of interest, item-level target inventory levels are shown.

Product Holding

Figure 23. Data for the industrial experiment.

We simulated the three operating polices with the various inventory allocations and obtained the results in Figure 24. The simulation of the current policy resulted in a fill rate of 78% and 1,518 units in imbalance on average, or 22% of the total inventory. We attribute the difference in the simulated fill rate of 78% and the actual reported fill rate of 87% to the use of overtime and other changes to the system, such as outsourcing and negotiating with customers.

The 78% fill rate serves as a benchmark to which we may compare the other operating policies.

Simulating the No B/C policy using the newsvendor function for inventory allocation decisions resulted in an improved fill rate of 89%. Notice, however, that 15% of the inventory, or roughly 1,061 units each day were imbalanced. This is due to the way in which the newsvendor function determined the item-level allocations, shown in Figure 23. Notice that 3,372 units were held in item 5. The newsvendor function made this decision because item 5 has the lowest unit holding cost.

Simulating the No B/C policy using the Q-function for the item-level allocation decisions resulted in a fill rate of 95% and only 2.2%, or 153 units on average were in imbalance. Instead of holding 3,372 units in item 5, the Q-function selected 4,190 units of item 1 because of its higher probability of being demanded.

Operating Policy

Number of Stocked

Items

System Inventory

Level (T)

Allocation Used Among Items

Fill Rate Achieved

Average Number of

Units in Imbalance

Percent of Total Units

in Imbalance

Current Policy 30 7,039 ^* Newsvendor 77.96% 1,517.8 21.6%

No B/C Policy using Newsvendor

7 7,039 Newsvendor 89.26% 1,061.4 15.1%

No B/C Policy using Q-function

7 7,039 Q-function 94.73% 152.7 2.2%

* the current item-level target inventory levels were used.

Figure 24. Results of applying the No B/C Policy to an industrial environment.

8 Conclusion

In this paper, we develop a computationally efficient approach for setting base stock levels in a capacitated manufacturing environment in which forecasts for the majority of items are not available. We quantify the value of obtaining advanced demand information for decision-making. The value of this information, while consistently valuable, diminishes as the capacity utilization increases. We illustrate the implications operating the environment without explicit consideration of the finite capacity. We demonstrate the obtaining advanced demand information combined with inadequate capacity planning can result in substantial deviations from optimality.

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Acknowledgements

This research was partially funded by the National Science Foundation (Grant DMI0075627) and by Aspen Technology.