1. General Mills faces annual demand for its Wheat Chex and Corn Chex cereals of 480,000 and 840,000 boxes respectively. Each box contains 18 ounces of cereal, and 50% of the weight of the cereal comes from its grain (wheat or corn). General Mills has computed its ordering cost as $60 per order. They pay their supplier 15 cents per pound (there are 16 ounces in a pound) of wheat and 10 cents per pound of corn. The annual holding cost of either grain is 20% of the value of the grain.
a. What are the optimum order sizes for wheat and corn when purchased separately?
b. If you combine orders for each grain into one monthly order, it will still only cost $60 for the combined order. If an order is placed every month, what is the difference in the total annual procurement related cost between this new policy and the policy calculated above (part a).
2. At a distributor of spare auto parts,the weekly demand for part XYZ is estimated to be normally distributed with mean 30 and standard deviation 5. The delivery lead time from the manufacturer of the part is six weeks. The distributor is following a (Q, R) inventory management policy to manage this part.
Assuming there are 52 weeks in a year, please answer the following questions.
a. Under the (Q, R) policy assume that the reorder point for the part is 210. Under this policy,what percentage of the order cycles will the distributor stock out of this part?
b. Assume that the distributor is willing to stock out during no more than 5% of the order cycles, and will set their reorder point accordingly. If they purchase the part from the supplier with the 6-week lead time, the unit cost of the part is $50. However they can also purchase the part from a local supplier with a lead time of one week, and the unit cost is only $0.50 more (i.e. $50.50). Assuming that the fixed cost of an order is $50 (regardless of supplier used) andthe annual holding cost rate is 20%, please determine which supplier they should choose. (Note: You can ignore the cost of purchasing the items to be held in safety stock since this would represent a one-time cost.)
3. Alex Tuber, store manager of Edgeway Grocery Store in Washingtown, is worried about allocating enough shelf space to a new breakfast cereal, Rice Krimpies. The cereal will be restocked from the distributor once a week, at noon on each Thursday. At that time, the delivery person will arrive with ample stock to fill the shelf area that is reserved for Rice Krimpies, thereby replenishing the packages that were sold during the previous week rather than some set amount ordered in advance. As the week progresses, and the stock of Rice Krimpies drops, the space reserved can not be used for any other product.
Each package of Rice Krimpies costs Alex $2 to purchase. Alex sells a package of Rice Krimpies for $4. The opportunity cost of the shelf space that Alex must reserve for Rice Krimpies is $2.50 per week per foot of shelf space. Ten packages of Rice Krimpies can be stored and displayed per foot of shelf space. (Assume any shelf length in feet is viable and that the number of Rice Krimpies boxes is ten times this length.) Other carrying costs (i.e., other than shelf space) of the Rice Krimpies are so small that they can be safely neglected in this problem.
Based on his past experience, Alex estimates that the weekly demand for cereal will be normally distributed with a mean of 140 packages and a standard deviation of 40 packages. Alex also figures that if his store runs out of the new cereal during the week, customers will go elsewhere to buy the cereal that week, but will hold no permanent grudges against the Edgeway store. In particular, the stockout will have no effect on sales of other products in the store or on sales of the cereal in the future.
How many feet of shelf space should Alex reserve for Rice Krimpies?