Question

Bruno Fruscalzo decided to start a small production facility in Sydney to sell gelato to the local restaurants. His local milk supplier charges $0.5 per kg of milk plus a $25 delivery fee (that is independent of the amount ordered). Bruno’s holding cost is $0.03 per kg per month. He needs 9750 kgs of milk per month. a. Suppose Bruno orders 9750 kgs each time. What is his average inventory (kgs)? kgs (Round your answer to 1 decimal place.) b. Suppose Bruno orders 6750 kgs each time. How many orders does he place with his supplier each year? orders c. How many kgs should Bruno order from his supplier with each order to minimize the sum of ordering and holding costs? kgs (Do not round intermediate calculations. Round your answer to 2 decimal places.) d. If Bruno’s storage vessel can hold only 4000 kgs of milk, what would be Bruno’s annual ordering and holding costs? (Do not round intermediate calculations. Round your answer to 2 decimal places.) e. If Bruno’s storage vessel can hold only 6500 kgs of milk, what would be Bruno’s annual ordering and holding costs? (Do not round intermediate calculations. Round your answer to 2 decimal places.) f. Bruno’s supplier’s truck can carry 20,000 kgs of milk. The supplier does not want to deliver to more than 3 customers with each truck. Thus, the supplier requires a minimum order quantity of 6,500 kgs. If Bruno orders the minimum amount, what would be the sum of his annual ordering and holding costs? Assume he has a storage vessel large enough to hold 6,500 kgs. (Round your answer to 3 decimal places.) g. Bruno’s supplier offers a 3% discount when a customer orders a full truck, which is 20,000 kgs. Assume Bruno can store that quantity and the product will not spoil. If Bruno orders a full truck, what would be the inventory holding and ordering cost incurred per kg of milk? Assume the discount also applies to the holding cost.

Answer 1

Answer a: Average inventory= ordered quantity/ 2= 9750/2= 4875 kgs

Answer b: As the monthly demand is 9750 kgs, yearly demand= 9750*12= 117,000 kgs

If he orders 6750 kgs, then total no. of orders= 117000/6750= 17.33 orders (18 orders if answer is required in whole number)

Answer c: EOQ must be applied in order to minimize the holding and ordering cost.

S = Setup costs (delivery fee per order) = $ 25
D = Demand (quantity demand per year) = 117000 kgs

H = Holding costs = $0.03*12 months= $ 0.36 per year

EOQ = √(2SD / H) = 2850.44 kgs

Bruno should order 2850.44 kgs

Answer d: if Bruno’s storage vessel has a capacity of 4000 kgs then Bruno should order according to EOQ, that is 2850.44 kgs

Total no. of orders= total demand/EOQ=117000/2850.44 = 41.046

total order cost= no. of orders *order cost= 41.046*25= $1026.157

In EOQ, total ordering cost= total holding cost

• Therefore, total cost= 2*total order cost= 2*1026.157= $ 2052.31