A brand of men’s wallets are sold for $20 per unit by a retailer. The retailer buys the wallets from a manufacturer for $11 per unit. The manufacturing cost for the manufacturer is $4 per unit. The average monthly demand is 1500 units and the standard deviation is 300. The demand is assumed to be normally distributed.
If the retailer and the manufacturer are operating as independent organizations, what is the order size that maximizes the retailer’s profit?
In above scenario, what is the expected profit for retailer?
If the actual order quantity should be rounded to the closest 100 units, what is the total supply chain expected profit?
Consider that the retailer acquired the manufacture. What is the order size for the vertically integrated supply chain?
What is the expected profit for the vertically integrated supply chain?
[10 points] Consider the above (Q6) problem.
The manufacturer offers to buy back any unsold items at a price of $2 per unit. What is the optimal order size for retailer? What is the total supply chain profit in this scenario? Compared to the Q6.a. scenario, has the profit of manufacturer or the retailer increased or decreased?
Instead of buy back, the manufacturer offers another alternative: revenue sharing. The manufacturer will sell to the retailer at their production cost ($4 per unit) if the retailer agrees to share 40% of the retailer’s revenue. If the retailer agrees to this alternative, what is the expected profit for retailer? What is the expected profit for the manufacturer?
[Extra credit: 10 points] Is above (Q7.b.) scenario increases profit for both manufacturer and retailer compared to the initial (Q6.a.) scenario? If not, what revenue sharing fraction would you suggest to increase profit for both parties?
[20 points] FTW Engineering is an aftermarket automobile parts manufacturer. One popular component they manufacture is a Cold Air Intake (CAI). The summary of sales from 2018 October to 2019 December for the CAIs is given in the table below. You are hired to determine the best technique for forecasting the CAI demand based on the given data.
Calculate a forecast for 2020 using simple three-month moving average.
Calculate a forecast for 2020 using three-period weighted moving average. Use weights of 0.6, 0.3, and 0.1 for the most recent period, the second most recent period, and the third most recent period, respectively.
Calculate a forecast for 2020 using the exponential smoothing method. Assume the forecast for period 1 is the average demand for all the data. Use alpha = 0.3.
The actual sales for 2020 is given in the table below. Determine the forecast error for each of the above three methods using cumulative forecast error and mean square error methods.
Which method produced the best forecast? Why? What forecast error did you use to arrive at above conclusion? How could you improve upon this forecast?
Sample Solution