# Lorex Pharmaceuticals Harvard Case Solution & Analysis

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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