Individual Assignment 4

Due Date: 11:59 pm, December 9th, 2024

Total Points: 125

1. A company has been selling a new product for 4 months and wants to forecast the demand for the 5th month. The company is considering different forecasting methods.

(a) The first forecasting method in consideration is simple moving average with n = 3. Please fill in the following table. (5 points)

(b) The second forecasting method in consideration is exponential smoothing with α = 0.5. Please fill in the following table. (5 points)

(c) The third forecasting method in consideration is double exponential smoothing with α = 0.5 and δ = 0.5. Please fill in the following table. (5 points)

(d) Which method do you recommend? Explain within two sentences. (5 points)

2. A San Diego company produces fertilizer. The following data on the amount of Nitrogen for one bag of fertilizer are collected when the process is in control.

(a) Calculate control limits for an R-chart and anX(̅)-Chart. Please use three-standard-deviation limits, and the standard deviation is calculated with  (5 points)

(b) After these data are collected, some new employees are hired. A new sample obtained is as follows: 625, 692, 612, and 635. Is the process still in control? (5 points)

3. Pioneer Chicken advertises “lite” chicken with 30 percent fewer calories. The process mean for “lite” chicken breasts is 420 calories, with a standard deviation of 25 calories. The product design calls for the  average chicken breast to contain 400 ± 100 calories. Calculate the  process capability index and the  modified process capability index. Use three standard deviations. (5 points)

4. A company produces plastic powder in lots of 2000 pounds at the beginning of each week. The company uses the powder in an injection molding process at the steady rate of 50 pounds per hour, for an eight- hour day, five days a week. The manager has indicated that the cost of placing an order is $100, but “we really have not determined what the holding cost is” .

(a) What weekly holding cost rate does the lot size imply, assuming the lot size 2000 is optimal? (5 points)

(b) Suppose the figure you compute for weekly holding cost rate has been shown to the manager, and the manager says that it is not that high. Would that mean the lot size 2000 is too large or too small? Explain in at most two sentences. (5 points)

5. A company is using the re-order point model to manage the inventory of a certain kind of product. Currently, the inventory system uses an economic order quantity of 600 units. Consider the following situations:

(a) Suppose the company is able to get much cheaper transportation such that the setup cost is reduced  from  $90  per  order  to  $10  per  order.  Everything  else  remains  unchanged.  Do  you  have  sufficient  information to determine the new economic order quantity? If not, explain why; if yes, what is it? (5 points)

(b) Suppose the company is able to negotiate a lower wholesale price from its supplier, from $14.4 per unit to $10 per unit. Everything else remains unchanged. Do you have sufficient information to determine the new economic order quantity? If not, explain why; if yes, what is it? (5 points)

(c) Suppose the optimal order quantity obtained from the basic EOQ formula is 600 units per order. In addition, the total inventory holding cost for one whole year is $600. Do you have sufficient information to determine the company’s inventory holding cost per unit per year for this product? If not, explain why; if yes, what is it? (5 points)

6. ABC Farm is a cranberry grower. It is now April 1st  and ABC is about to enter into a contract to sell all its cranberries to the Ocean Place Company. ABC’s cranberry crop will be harvested and processed in the fall. The quantity of cranberries produced by ABC is uncertain and follows a normal distribution. ABC estimates that the yield (the quantity of berries) available in the fall has a mean of 10,000 barrels and a standard deviation of 1,500 barrels.

For the current contract, ABC must specify now how many barrels it promises to sell to Ocean Place in the fall. The selling price is $500 per barrel, and under the contract, ABC is prohibited from selling cranberries to anyone but Ocean Place. ABC will pay a penalty of $200 for each barrel that is short of what it promises to deliver. For example, if ABC promises to deliver 5,000 barrels but can only deliver 4,500 barrels, Ocean Place would pay ABC a total of 500×4,500−200×(5,000−4,500).   If ABC can deliver all the 5,000 barrels as promised, Ocean Place would pay ABC a total of 500×5,000.

On September 1st  ABC will knowhow many berries are available. If the number of barrels is less than the number they have promised to deliver, ABC will process and deliver all of the berries that are available. If the  number of barrels available is greater than the  number they  have  promised to deliver, they will process and deliver only the number that has been promised. For each barrel delivered to Ocean Place, ABC also needs to incura cost of $100 for processing.

(a) How much should ABC promise to sell and deliver to Ocean Place? (5 points)

(b) With your answer to (a), what is the probability that ABC can NOT deliver the full amount it promises? (5 points)

(c) Suppose when ABC cannot harvest and process up to the amount they promise to deliver, they can makeup for the shortfall by buying from another grower at a price of $600. No processing cost is charged for this amount. How much should ABC promise to sell and deliver? (5 points)

(d) Suppose there is another identical grower, DEF. The quantity of cranberries available to DEF in the fall has a normal distribution with a mean of 10,000 barrels and a standard deviation of 1,500 barrels, and the cost to DEF to process and deliver is $100 per barrel. Assume that buying from another grower to make up for the shortfall is not possible. Suppose DEF can make an agreement with Ocean Place with exactly the same terms as stated above. Therefore, both ABC and DEF would promise to sell and deliver the same amounts of cranberry as your answer to (a). Now suppose ABC merges with DEF. Assume the amounts of cranberry available in the fall to these two growers are independent.  How  much should the  merged company promise to sell and deliver? (5 points)

7. A firm is managing its inventory system using order-up-to policy, and orders everyday. For the first 100 days, truck transportation is used and the lead time is 2 days. The corresponding order-up-to level is 150. On the 96th  day, the firm orders 45; on the 97th  day, the firm orders 50.

(a) Consider a case that the manager thinks that truck transportation is too expensive. Thus, starting from the order of the 101st  day, train transportation is used and the lead time becomes 3. Correspondingly, the order-up-to level is changed to 200. Fill in the following form. (5 points)

(b) Consider a case that the manager thinks that truck transportation is too slow. Thus, starting from the order of the 101st day, air transportation is used and the lead time becomes 1. Correspondingly, the order- up-to level is changed to 110. Fill in the following form. (5 points)

(c) Suppose that the demand for each day follows a normal distribution with mean 45 and standard deviation 3. What is the service level for the first 100 days? What is the service level after the 101st  day for (a)? What is the service level after the 101st  day for (b)? (5 points)

8. The Innat Penn hotel has 300 rooms with standard queen-size beds and two rates: a full price of $400 and a discount price of $240. To receive the discount price,a customer must purchase the room at least two weeks in advance (this helps to distinguish between leisure travelers, who tend to book early, and business travelers, who value the flexibility of booking late). For a particular Tuesday night, the hotel estimates that the demand from  leisure travelers could fill the whole  hotel  while the  demand from business travelers is distributed normally with a mean of 140 rooms and a standard deviation of 60.

(a) Suppose 100 rooms are protected for full-price rooms. What is the booking limit for the discount rooms? (5 points)

(b) Find the optimal protection level for full-price rooms (the number of rooms to be protected from sale at a discount price). (5 points)

(c) The Sheraton located nearby declared a price war by setting business travelers’ price to $300. The Inn at Penn has to match that price to keep demand at the same level. Does the optimal protection level increase, decrease, or remain the same? Explain your answer. (5 points)

9. In a Tom & Jerry supply chain, Tom is the manufacturer and Jerry is the retailer. The supply chain is going  to  offer  a  new  T-shirt  for  the  next  summer  selling  season.  The  following  events  take  place sequentially:

(i) Tom offers Jerry a wholesale price of $4.

(ii) Jerry decideshow much to order,Q, from Tom.

(iii) Tom produces Q units of the T-shirt at a unit production cost of $2 and deliver them to Jerry.

(iv) The selling season starts and Jerry sellsT-shirts at a retailer price of $10. Suppose the demand follows a normal distribution with mean 100 and standard deviation 20.

(v) The selling season ends and all the leftover T-shirts, if any, are thrown away. Answer the following questions:

(a) How much should Jerry order to maximize his own profit? How much should Jerry order to maximize the overall profit of the supply chain? (5 points)

(b) Now Tom considers offering Jerry a buyback price r, which means that he will  buy all the leftover inventory from Jerry at the end of the selling season. Tom’s purpose is that, when Jerry maximizes his own profit, he is also maximizing the overall profit of the supply chain. What should the value of r be? (5 points)

(c) Tom has another plan. He can promise to Jerry that, for any quantity of T-shirts sold beyond 100 units, a unit sales rebate of A will be awarded. What should the value of A be to achieve the same purpose? (5 points)

10. So, any final comments for the course before it ends? (optional)