Problem Diagnosis
The main issue that is being faced by Lorex is the case of unfilled bottles due to which the company is experiencing clogged storage. The main contributing factor for this problem is the standard deviation of one which has been allowed by the management of the company above 10 ounces which is the required amount. Therefore, the management now wants to find out the fill rate at which the company could achieve a tradeoff between the costs and the revenues of the whole process. A fill rate of 10.2 ounces is the only fill rate that has been experienced by the management of the company. This fill rate was chosen randomly however, now the target fill rate is to be determined by Mr. Blakely.
Analysis of Decision Alternatives
In order to find the optimal fill rate a range of fill rates could be chose above and below 10.2 ounce fill rate that had been chosen by the management. Based on these fill rates, the bottles that could be completely filled and that would be left half or unfilled, the total revenues and costs could be calculated and ultimately the contribution per case could be calculated. The calculation has been performed in this way as shown in the appendix attached to the end of the solution.
The data has been provided for the filling line test and the range of the fill rates that has been chosen ranges from 10 ounces to 10.5 ounces. In order to arrive the correct contribution per case, first of all the relevant costs need to be identified which in this case would include the rework cost per case, active ingredient cost per case and the packaging cost per case. All these variables were calculated with regard to their relative impact upon the decision variable with respect to the different fill rates. As the fill rate increased, the active ingredient cost increased but the rework cost decreased. Packaging cost was not considered because the amount that was required for packaging was same.
The amount of the bottles that would be filled completely for each fill rate has been then determined. Two prices had been provided. One for full bottles and the other for unfilled bottles is provided. These prices were$ 186 per case and $ 148.8 respectively. Revenue was directly related to the increases in the fill rates. The total cost per case for medication included the labor and active ingredients cost which on a per ounce basis was calculated to be $0.40 per case. Since, the cost of rework was 8.5 per hour for 12 cases per hour then the rework cost per case was calculated to be $0.70 per case.
Recommendation
Finally, the contribution has been calculated. If we see at the fill rate of 10.4 ounce, then we could see that it is the fill rate at which a balance between the revenues and the costs has been achieved. Although, the highest revenue is generated at a fill rate of 10.5 ounce per bottle fill rate, but the resulting increase in the costs is much larger. Therefore, the most recommended fill rate for the management to use is 10.4 ounce per bottle fill rate. In the short run, the costs under this fill rate might also appear to be higher due to increased active ingredients cost but in the long run the savings achieved due to small costs of rework would prove to be more profitable and beneficial for the company and generate the highest contribution per case.
Lorex Pharmaceuticals Case Solution
Appendix
Statistics |
|
Mean |
10.198205 |
Standard Error |
0.0135498 |
Median |
10.190144 |
Mode |
#N/A |
Standard Deviation |
0.1625975 |
Sample Variance |
0.0264379 |
Kurtosis |
0.7714275 |
Skewness |
0.2453597 |
Range |
0.9973631 |
Minimum |
9.7583702 |
Maximum |
10.755733 |
Sum |
1468.5415 |
Count |
144 |
DATA |
|||
Bottles filled for more than 10 ounce get sold for |
186.000 |
||
Bottles under filled get sold at 20% discount |
148.800 |
||
Active ingredient cost |
0.403 |
per ounce | |
Each worker can repackage |
12.000 |
@ |
8.500 |
cases per hour | per hour | ||
Rework cost per case |
0.708 |
Oz |
Z-VALUE |
Probability of Correct Fill | Revenue Per Case | Active ingredient cost per case | Rework cost per case | Contribution per case |
10.000 |
0.000 |
0.500 |
167.400 |
48.326 |
0.354 |
118.720 |
10.100 |
-0.623 |
0.735 |
176.142 |
48.809 |
0.188 |
127.145 |
10.160 |
-0.997 |
0.850 |
180.420 |
49.099 |
0.106 |
131.215 |
10.200 |
-1.246 |
0.894 |
182.057 |
49.292 |
0.075 |
132.690 |
10.300 |
-1.870 |
0.969 |
184.847 |
49.775 |
0.022 |
135.049 |
10.400 |
-2.493 |
0.994 |
185.777 |
50.259 |
0.004 |
135.514 |
10.500 |
-3.116 |
0.999 |
185.963 |
50.742 |
0.001 |
135.220 |
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