A retail store (such as Kmart) stocks black toner cartridges. The following data are available:
Average demand: 180 units per month.
Ordering cost: $38/order
Purchase cost of the toner cartridge: $50
Rate charged for inventory holding cost: 17% per year
a) i)What is the Economic Order Quantity? Round your answer to the nearest integer. (SHOW YOUR CALCULATION)
II) What is the total annual cost of cycle stock and ordering costs? (SHOW YOUR CALCULATION)
b) The purchasing manager believes that the ordering cost for this item could be reduced to $19/order he ties his ordering system into his inventory system so orders could be made automatically. Establishing this would require an initial investment so the manager is interested in the savings per year the store could expect once the automation was established. Compute these savings.
c) Suppose the purchasing manager misestimates the cost reduction due to the automation. Suppose the actual cost is $24 but he bases his quantity on his estimate of $19. What does this error cost on an annual basis? To do this suppose QKQK is the correct quantity for ordering cost of K and TCK(Q)TCK(Q) is the cost of holding and setup (but not purchasing), of using Q when K is the ordering cost.
Compare TC24(Q24)TC24(Q24) to TC24(Q19)TC24(Q19). The error in the cost estimate is 21%. What is the percentage error in the annual costs? Express your answer as a positive percent, e.g., 5% is entered as 5, 0.3% as 0.3. Be sure to always round off every EOQ you compute to the nearest integer before using it in a total cost formula.
d) Now return to the data given at the beginning of the problem, and thus your answer to (a) is the correct EOQ. Further assume this data is accurate and correct. Suppose for reasons specific to shipping phones the vendor wants to ship in multiples of 60, e.g., 60, 120, 180, etc. Of these choices which is the one with the least total annual cost of holding cycle stock and ordering costs? Give the order quantity.
e) What is the percentage change in Q from the optimal you found in (a)? Express your answer as a positive percent, e.g., 5% is entered as 5.
f) What is the percentage change in cost from that found in (a)? Express your answer as a positive percent, e.g., 5% is entered as 5.