1. Given the next 6 months aggregated demand forecast and other related information in the following tables.
2. 
   
3. MonthProject Demand (unit) Operation Cost (unit)Capacity/Month
4. (unit)
5. Jan200Regular$100200
6. Feb200Overtime$11540
7. Mar300Subcontract$130100
8. Apr400 another cost (unit)
9. May500Inventory/month$10
10. Jun200Backorder/month$40
11. Total1800
12.  Inventory (unit)
13. Beginning50
14. End of each month (Desired)100
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16. a)develop a Feasible Aggregate Plan that meets the requirements
17. b)given the aggregate plan you developed in part a), discuss how can you make improvement on it.
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19. Problem 2. (Resource Planning. Total 20 pts,)
20. The following Table provides the Master Production Schedule of a product for the next 8 weeks and the Customer Orders you have Committed so far.
21. 
    
22. Product A        
23. Begin InventoryWeeks
24. 12345678
25. MPS30201010155151010
26. Committed Orders 25 15 20 10
27. ATP:D        
28. Inventory30       
29. 
    
30. Answer the following questions
31. a)The Weekly Inventories of the eight weeks;
32. b)The Available-to-Promise-discrete (ATP.D) quantities of the eight weeks.
33. c)Briefly explain the Differences between the ATP and Inventory.
34. d)Briefly explain the meaning of the 2nd Non-zero ATP.D number you have calculated in a-ii) above.
35. e)Use the result obtained in a. to answer the following questions. Assume that you have just committed a New Customer Order of 10 units to be delivered in week 3. Can the manager delivery this order on time without changing the current MPS?
36. f)Can you relate the Concept of Time Fence System here? For example, what does it mean by, say, the Firmed Segment of the time fence system is set to be 4 weeks?
37. 
    
38.  
39. Problem 3. (Deterministic Inventory Model. Total 15 pts.)
40. David's Delicatessen sells a special Hebrew sausage. The owner, David Gold, estimates that the demand for the sausage is steady at 5000 kilograms a month. The special sausage cost Gold $5.00 a kilogram. The cost of ordering and shipping from the supplier is $150 each order. Gold's accountant, Irving Wu, estimated an annual holding cost of the sausage is 25% of the sausage purchase cost.
41. a)How many kilograms of the special sausage should Gold order each time to minimize the annual costs on holding and ordering? Calculate the annual total costs of holding, ordering, and purchasing the sausage.
42. b)What is the maximal inventory level, average inventory level? How many times will Mr. Gold order each year?
43. c)At what inventory level should Mr. Gold’s Reorder assuming that it will take half of a month to receive an order?
44. 
    
45. d)Recently, Mr. Gold received the following offer from his supplier: If Gold can change his order quantity to order once a month, his shipping cost will be reduced by $50. Should Gold accept the offer?
46. 
    
47. Problem 4. (Probabilistic Inventory Model. Total 15pts.)
48. The smart auto is a car dealer that sells new cars. Customer Demands and Order Delivery Time from the car manufacturer may vary randomly from time to time. Assume that historical data shows that the Demand During Delivery Lead-time can be summarized in the following table.
49. Demand During Leadtime (# of Cars)05101520
50. Probability0.050.200.350.250.15
51. 
    
52. Assume that SmartAuto can sell on average 1000 cars a year, and the manager currently orders 200 cars each time from the manufacturer whenever its inventory drops to 12.
53. a.Calculate
54. i.The Safety stock kept =
55. 
    
56. ii.the Chance of Stockout, and the Service level,
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58. iii.the Expected number of shortages that may incur within Each Ordering Cycle.
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60. b.Assume that it will cost the firm $200 to hold a car in inventory for a year; and will cost the firm an additional $150 on service for each car that has to be back ordered due to shortage. Find the optimal Reorder Point (or Safety Stock) such that the Total Costs in keeping Safety Stock and on Shortage are minimized.
61. (hint: use Excel spreadsheet since it can help to save calculation time significantly)
62. 
    
63.  Problem 5. (Probabilistic Inventory Model. Total 15pts.)
64. The Sweet Cream Dairy sells walnut fudge ice cream. Assume that historical accounting data shows that the daily Demand for ice cream can be approximated by a normal distribution with a mean of 10 gallons and a standard deviation of 6 gallons. The order delivery lead-time for restocking is 2 days.
65. a)Find the inventory level at which the manager should reorder if the Sweet Cream Dairy manager desires a 92% service level.
66. 
    
67. b)Assume that the store manager ordered 50 gallons ice cream yesterday morning by using the reorder point you obtained in a). (if you can’t determine a reorder point in a), use 30 as the Reorder Point ) so that you can continue on part b)). This morning, he received a phone call from the supplier that the order he made yesterday will be delayed by 2 day (the order will arrive in 3 days) due to an unexpected situation in the supplier’s factory. After the phone call, the manager checked inventory and found 6 gallons ice cream was sold on yesterday. Calculate the shortage probability at the time the order placed finally arrives. 
68. Problem 6. (Six Sigma. Total 15 pts.).
69. Blake, the owner of Blackstar’s Speedy Pizza, a home delivery pizza operation, keeps track of customer complaints. For each pizza delivery, there are three possible causes of complaints: a late delivery, a cold pizza or an incorrect pizza. Each week, Blake calculates the rate of delivery “defects” of pizza deliveries and then uses this information to determine his company’s Six Sigma quality level. During the past week, his company delivered 500 pizzas. His drivers received 15 late delivery complaints, 10 cold pizza complaints, and 6 incorrect pizza complaints.
70. a). Find the DPMO. And What is the corresponding Six Sigma operating level?
71. b). Can the value of DPMO you calculated in part a) be interpreted as the Number of Defective Pizzas in One Million Pizzas that Blackstar sold? Explain why?