Question

There is a two-stage make-to-order (MTO) supply chain that involves a bakery product retailer in Holland and a Hong Kong mooncake manufacturer. The retailer purchases locally made mooncakes from the Hong Kong manufacturer at the cost of $180 per box and sells the mooncakes to customers at the price of $300 per box during the festival. The manufacturer has set the purchase lot size as 500 boxes. The retailer can sell all unsold mooncakes to a discount store at $40 per box after the festival. The retailer has forecasted the product demand for the upcoming festival (see the table below).

Demand (boxes)	1,500	2,000	2,500
Probability (%)	25	30	45

For the mooncake manufacturer, the fixed production cost is $100,000 and variable production cost is $70 per box. The retailer has determined that its expected profit equals to $180,000 if order quantity is 1,500 boxes and $207,500 if order quantity is 2,000 boxes. Show the units and steps of calculation when you answer the following questions.                                                                                          (Total: 27 marks)

1. Determine the expected profit for the retailer if order quantity is 2,500 boxes, and the optimal order quantity that will maximize the retailer’s profit.                                                                                               

2. If the retailer adopts the optimal order quantity of Q4A, determine the manufacturer’s profit.                                                                      

To encourage the retailer to place a larger order, the manufacturer now plans to offer the retailer a buy-back contract. The manufacturer offers to buy unsold mooncakes from the retailer at $90 per box, although the retailer still pays the same wholesale price of $180 per box. Manufacturer can sell these unsold mooncakes to a discount store at $40 per box. There is no need for the retailer to salvage these mooncakes. For the manufacturer, the fixed and variable production costs remain unchanged. The retailer has determined that with this buy-back contract its expected profit equals to $180,000 if order quantity is 1,500 boxes and $213,750 if order quantity is 2,000 boxes.

3. Based on the buy-back contract, determine the expected profit for the retailer if order quantity is 2,500 boxes, and the optimal order quantity that will maximize the retailer’s profit.                                                          

4. If the retailer adopts the optimal order quantity of Q4C, determine the manufacturer’s expected profit.                                                                       

                                                                                                                      

5. Describe TWO drawbacks of using the buy-back contract in this case.      

6. Explain with TWO factors that support transport of mooncakes from Hong Kong to Holland by air. And explain with TWO factors that support transport of mooncakes from Hong Kong to Holland by sea.                        

Answer 1

1)

Profit on sold boxes = 300 - 180 = 120 per box

Loss on unsold = 180 - 40 = 140 per box

Expected Profit based on order:

1500 ordered : 0.25 x 1500 x 120 + 0.3 x (1500 x 120 ) + 0.45 x (1500 x 120) = 180000

2000 ordered : 0.25 x (1500 x 120 - 500 x 140 ) + 0.3 x196000 ( 2000 x 120 ) + 0.45 x ( 2000 x 120 )= 207500

2500 ordered :0.25 x (1500 x 120 - 1000 x 140) + 0.3 x ( 2000 x 120 - 500 x 140 ) + 0.45 x ( 2500 x 120) =  10000 + 51000 + 135000 = 196000

Profit at 2500 = 196000

Optimal Quantity = 2000

2) Manufacturer Profit at 2000 = 2000 x 180 - 2000 x 70 - 100000 = 120000

3) Buy-back scheme applied:

Expected Profit of retailer based on order:

1500 ordered : 0.25 x 1500 x 120 + 0.3 x (1500 x 120 ) + 0.45 x (1500 x 120) = 180000

2000 ordered : 0.25 x (1500 x 120 - 500 x 90 ) + 0.3 x196000 ( 2000 x 120 ) + 0.45 x ( 2000 x 120 )= 213750

2500 ordered :0.25 x (1500 x 120 - 1000 x 90) + 0.3 x ( 2000 x 120 - 500 x 90 ) + 0.45 x ( 2500 x 120) =  10000 + 51000 + 135000 = 216000

Thus expected profit at 2500 = 216000

Optimal quantity = 2500

4) Manufacturer's loss on unsold = 90 - 40 = 50 per box

Manufacturer's profit = 2500 x 180 - 2500 x 70 - 100000 - 2500 x 50 = 50000

5) Two drawbacks :

i) Reduces profit for Manufacturer and doesn't add much increased profit to retailer.

ii) Selling mooncakes back to manufacturer adds one more node in the supply chain. Thus come in logistics issues as well.

6)

By air : i) Faster delivery

ii) Less probability of spoilage and reduction in quality.

By ship :

i) Less expensive

ii)Specialised vessels such as refrigerated cargo and container ships