Ski Jacket Production
Executive Summary
The problem is to determine the optimal production level of the Egress new designed jacket given the uncertainty in the forecasted demand. As oppose to determining a single profit value in the deterministic approach, the probabilistic method will incorporate the uncertainty in estimated demand and provide insights of the range of profit outcomes and its associated risk (deviation from mean). The key issue is to understand impact of demand uncertainty and production level to the profit range and its distribution. In this case, we will determine the optimal decision variables (jacket production quantity) that will maximize our objective (average profit).
The given information from management
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Values | Q=7,800 | Q=12,000 | | Average Profit | 44,478 | 48,970 | | Min Profit | (446,084) | (656,084) | | Max Profit | 56,000 | 140,000 | | Std. Deviation | 49,696 | 136,722 | |
Even though demand is normally distributed, profit is not normally distributed. The average profits in these two cases are pretty close in the range of $44,000-$49,000. However, the standard deviation of producing 12,000 jackets is 3 times higher than 8,000 jackets. Therefore, management has to consider both average profit and its deviation. In this case, we would recommend producing at 7,800 jackets rather than 12,000 jackets to reduce the chance of loss from the larger standard deviation. The detailed simulation model can be found in Exhibit 1 and 2.
Answer (3): To maximize profit, Egress should produce 10,174 ski jackets. The average profit would be $61,849 with standard deviation of $94,136.
There are two approaches to find the optimal jacket production quantity that will maximize the profit. First approach is using EXCEL-SOLVER to find the Q produce (changing parameter) that will maximize the average profit (target). The solver solution for optimal Q is at 10,174 jackets. Second approach is using DATA TABLE to find the profit at each predetermined Q production.
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