A wholesale bottler and distributor of both imported and domestic alcoholic drinks purchases half its spirits in barrets, which it then blends and bottles (approximately 60 different types of spirit in up to 5 different bottle sizes). The most time-consuming activity is the changeover of the bottling line for a different bottle size. This takes one full day. Therefore, products that have the same bottle size are bottled one batch after another, saving the bottle-size changeover time (however, there is a smaller setup time for spirit, bottle, and label changeover). ROP of the I-litre (L) bottles is set to one month of demand because they' are usually bottled once a month. Each time, approximately 10 different spirits are run one after another. The actual bottling time is negligible (only 2 days for all 10 spirits). Management wants bottling run length (batch size) of each spirit is equal to its EOQ. Note that because production rate is so much faster than the demand rate, we can use the EOQ formula instead of the EPQ formula.
Suppose now is the beginning of June, and there is going to be a changeover to the 1-L bottles tomorrow. The on-hand inventory' of the I - L bottles of vodka is only 144 cases, whereas the demand forecast this SKU in June is 312 cases. Assume that the demand has no trends or seasonality. The setup cost per bottle run for vodka is $73.23. The cost per case of vodka is $29.31. The carrying cost rate is 15 percent of unit cost per year.
a. Calculate tire optimal batch size (i.e., EOQ) for vodka
b. After talking to the supervisor, it became clear that he does not use the EOQ to determine the batch size. Instead he produces enough I-L bottles of a spirit so that this quantity plus any on-hand inventory is expected to last until the next production run for I-L bottles, which is one month later. However, for items with uncertain demand such as vodka, he produces a quantity that, together with any on-hand inventory', is expected to meet two months of demand. Assuming that the standard deviation of monthly demand for vodka is 98 cases, what service level is the supervisor implicitly using?