Question

Chocolate City is a specialty candy shop located on the boardwalk area in Myrtle Beach, South Carolina. One of the shop’s best-selling items is an 8oz bag of chocolate-covered espresso beans, with demand averaging 1,200 bags per year. The shop purchases the beans from a distributor located in Nashville, TN. The distributor charges a flat $25 order processing and shipping fee regardless of the size of the order. Chocolate City’s manager estimates that each order costs the store an additional $10 due to the time required to assess the current inventory level and place the order with the distributor. The distributor charges $6 per bag, and the shop sells them for $10 each. Chocolate City uses a holding cost rate of 20% to make its inventory decisions.

a. Determine Chocolate City’s optimal order quantity and the annual profit that it can expect to earn from the beans.

b. Suppose that the manager sets a policy that the shop can only order half of a month’s supply of the beans at one time (i.e., two orders per month) due to the fact that the quality of the beans degrades if they are stored in inventory at the shop any longer than two weeks. Determine the annual profit earned under this policy.

Answer 1

Annual demand, D = 1200 bags

Order cost, S = $ 25+10 = $ 35

Unit cost, C = $ 6

Holding cost, H = 6*20% = $ 1.2

a) Optimal order quantity, Q = SQRT(2DS/H)

= SQRT(2*1200*35/1.2)

= 265 bags

Total annual cost = Ordering cost + Holding cost + Purchase Cost of beans

= (D/Q)*S + (Q/2)*H + D*C

= (1200/265)*35 + (265/2)*1.2 + 1200*6

= $ 7517.5

Annual revenue = 1200*10 = $ 12000

Annual profit = Annual revenue - Annual cost

= 12000 - 7517.5

= $ 4482.5

b) Under the new policy, Order size Q = 1200/(12*2) = 50 bags

Total annual cost = (1200/50)*35 + (50/2)*1.2 + 1200*6

= $ 8070

Annual profit = 12000 - 8070

= $ 3930