KC Engineering Works (KCEW) sells compressors for air conditioning units to several HVAC dealers in the Midwest region. The annual demand for the compressors is 65,000 units. For the reasons of simplicity assume that the demand is uniform throughout the year. Each compressor unit weighs 10 lbs. KCEW buys the compressors at $130 a piece directly from the manufacturer based in Louisville, KY, in batch sizes that minimize its overall cost. They maintain a safety stock that is 25% of the demand during the lead-time and that the holding cost is 18% of the cost per compressor per year. They have received the following transportation proposals from different providers. Assume 260 days per year. (1 cwt = 100 lbs)
Carrier Name
Minimum Shipment
(cwt)
Rate
($/cwt)
Lead
Time (days)
BNSF Railway
300+
8.50
12
C.H. Robinson
50+
14.00
8
UPS Supply Chain Solutions
100-200
12.00
9
200-400
8.50
9
400+
6.50
9
a) What is KCEW’s annual holding cost for pipeline stock if KCEW uses C.H. Robinson as the transportation provider?
b) What is the average safety stock at KCEW (in units of product) if KCEW uses BNSF Railway as the transportation provider?
c) Ignoring the annual purchasing cost of the compressors (which is $130×65,000 = $8.45M), what is the total annual cost of KCEW if it buys compressors in batch sizes of 2,600 units (i.e., follows a fixed order quantity inventory policy) and uses UPS Supply Chain Solutions as the transportation provider?
d) Should KCEW increase its batch size to 4,000 units from 2,600 units while following a fixed order policy and using UPS Supply Chain Solutions as the transportation provider? Justify your answer numerically.
Question 2
S&T is a retailer of home goods. They receive inventory from their supplier with a 2-week lead time. Assume they order weekly, and they use the order-up-to model for managing inventories. A peppermint soap sells on average one box every 5 weeks. Suppose demand distribution for this peppermint soap is Poisson.
a) How many boxes of the peppermint soap do they order on average each week?
b) Suppose S&T chooses an order-up-to level of 1 for the peppermint soap. What is their average on-hand inventory (in boxes)?
c) S&T estimates that their annual holding cost per box of peppermint soap is 20% of the price per box. The supplier charges $120 per box peppermint soap and S&T sells it for $160 per box. If S&T chooses an order-up-to level of 1 for the peppermint soap, what is their average weekly holding cost for this peppermint soap? Assume there are 48 weeks per year.
d) Suppose due to recent global supply chain disruptions, S&T’s supplier increases the lead time to three weeks. Given the additional risks posed by global supply chain disruptions, S&T decides to increase its order-up-to level to 2 boxes. What is their stockout probability?
e) Given the new lead time (i.e., three weeks), suppose S&T wants to minimize inventory while achieving at least a 0.9875 in-stock probability for the peppermint soap. What order-up-to level (in boxes) should they use?
f) Given the new lead time (i.e., three weeks), suppose S&T uses an order-up-to level of 3 boxes. What is the expected on-order inventory?
Question 3
EShack sells a model of Creative Labs blue-tooth adapter for $35 and expect to sell it for foreseeable future. Given their clout with the manufacturer, they are able to procure it at a price of $7.50. EShack estimates its daily demand to be normally distributed with mean 200 and standard deviation of 28 units. It reviews the inventory of the blue-tooth adapter once every day and places an order with the supplier using e-procurement software. The supplier lead-time for replenishment is 10 days including all manufacturing, transportation etc.
a) If EShack decides on an order up-to level of 2150 units, what is its expected on-hand inventory of Creative Labs blue-tooth adapter?
b) If EShack decides to provide 99% in-stock probability, what would the order up-to inventory level for the blue-tooth adapter be?
c) Assume that it costs EShack $0.55 per day to keep a blue-tooth adapter in inventory, while a backorder is estimated to cost 10% of the gross margin that EShack earns for each sale of Creative Labs blue-tooth adapter. What order-up-to level should Eshack choose for this blue-tooth adapter if their goal is to minimize holding and backorder costs?