Quiz 15: Risk-Pooling Strategies to Reduce and Hedge Uncertainty

Business

The variances of two or more independent random variables can be added up to get the overall variance. So, if there are n number of independent demand centres, the variance of a replacement consolidated centre will be the sum of variances of these independent centres. The standard deviation of the consolidated centre can off-course be found by taking the square root of its variance. a. Note that the standard deviation of the weekly demand in each of the single warehouses is 30. So, the variance is img . img So, the standard deviation of the consolidated warehouse img b. Compute the pipeline inventory as follows: img So, there will be a pipeline inventory of img

The coefficient of variation (CV) of two independent random variables can be computed by knowing their individual coefficient of variation and the correlation between them. The following formula can be used. img Where, img are the total CV, individual CV, and correlation coefficient respectively. Note the given information: img Compute the coefficient of variation for total demand as follows: img So, the coefficient of variation of total demand is img

In a base stocking policy, the ordering is done is a fixed interval. The order-up-to level is decided based on the average demand during the lead time plus review period, its standard deviation, and the required service level percentage. The expected ending inventory at the end of the period can be computed using the following formula: img Where img stand for the replenishment lead time and review period respectively. a. Note the given data: Average weekly demand, d = 1.25 Review period, p = 1 week Delivery lead time, img days Compute the total average ending inventory using the following method: The in-stock probability is 0.95. From the Poisson table, F (11) = 0.975 and F (10) = 0.946. So, the appropriate order-up-to level, img Form the Poisson distribution table, for L (11) = 0.0467. This is the expected backorder level. img For 200 SKUs, the total inventory level is img b. Note the given data: Average weekly demand, d = 50 Standard deviation of weekly demand, img Review period, p = 1 week Delivery lead time, img days Compute the total average ending inventory using the following method: The required in-stock probability is 95%. The corresponding value of img The corresponding value of loss function is img So, the expected back-order level img img img For 5 SKUs, the total inventory level is img c. Compare the inventory holding cost before and after the improvement in fill rate as follows: For the in-stock probability of 98%, the corresponding value of img The corresponding value of loss function is img So, the expected back-order level img img img For 5 SKUs, the total inventory level is img The holding cost becomes equal to img The holding cost with initial condition was img So, the change in store's holding cost to the original situation is img . So, the change in store's holding cost to the original situation is img

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