[23] Problem 1 Material Requirements Planning

The product structure tree of product A is given below. The lead times and available inventories of each item are found in the following table.

[3]        (a)    Given the available inventories, how many additional units of E must be ordered if a total of 2,000 units of A are required? Show your work. (Hint: You do not need to develop an MRP plan; also, do not specify when the units of E must be ordered: we only want the total number of E to order).

[6]        (b)    Given the available inventories, how many additional units of C must be ordered if a total of 2,000 units of A are required? Show your work. (Hint: You do not need to develop an MRP plan; also, do not specify when the units of C must be ordered: we only want the total number of C to order).

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[6]        (d)    Given the available inventories and assembly lead times, complete the following table.

[2]        (e)   Given the available inventories and assembly lead times, how many weeks would be needed to meet a gross requirement of 1,200 units ofA? At the earliest, at the beginning of what week could an order of 1,200 units ofA be delivered? Justify and be precise.

[7] Problem 2 Inventory Management: Deterministic Demand

QUESTION (a) AND (b) ARE INDEPENDENTS

[3]        (a)    The Dine Corporation is both a producer and a user of brass couplings. The firm operates 220 days per year and uses the couplings at a steady rate of 50 per day. Couplings can be produced at a rate of 200 per  day. Assume  storage  costs  are  $1 per  coupling per year,  and machine  setup  costs  (or

ordering costs) are $35.

What is the optimal production order quantity of brass couplings?

[4]        (b)   Burger Prince orders paper cups from a supplier, and uses the basic Economic Order Quantity model to determine the order quantity. The ordering cost is constant and fixed irrespective of the order quantity, while the holding cost is determined as a certain percentage of the purchase cost of paper cups. Burger Prince was told that the cost of paper cups would increase by 10%.

[2]   i) Should the order quantity change and if so, Should Burger Prince order more or less than before? Briefly Justify.

[2]   ii) By what percentage the order quantity will increase or decrease following the increase of 10% in the cost of paper cups?  show your calculations.

[17] Problem 3 Inventory Management: Probabilistic Demand

Weekly demand of a product is stationary and has been forecasted using exponential smoothing. The expected demand is 196 units per week and the standard deviation of weekly demand is 25. The item is purchased from a vendor at a cost of $10 per unit: the ordering cost is $50 with a lead time of one (1) week; The holding  cost  is  $6 per unit per year. Assume there  are exactly  52 weeks per year. The following questions are all based on these data, but are independent.

[4]        (a)    Assume the manager decided to adopt a fixed-order-quantity model, but decided not to carry any safety stock (e.g. the size of the safety stock is 0). Calculate the probability of stocking out during the lead time, and the expected demand units lost during the lead time. Show your work and give sufficient details.

[2] Probability of stocking out during lead time:

[2] Expected demand units lost during the lead time:

[4]        (b)   Assume the manager decided to adopt a fixed-order-quantity model, and wishes to maintain a 90% service level. Calculate the optimal order quantity and the reorder point. Show your work and give sufficient details. (Reminder: this question is independent of question (a) ).

[2] Optimal Order Quantity:

[2] Reorder Point:

[5]        (c)   Assume now the manager decided to adopt a fixed-time-period model with T = 4 weeks as review period (i.e. time between orders). Assume the beginning inventory is 300 units. What should the order quantity be so that 98% of the demand will be satisfied? Show your work and give sufficient details.

[4]        (d)    The  production  manager  wishes  to  set  up  a  fixed-time-period  inventory  system  so  that  the probability of stockout is at most 2.5%. However, given storage space constraints, the size of the safety stock must be at most equal to the expected demand over one week which is 196 units. What is the maximum time between orders (e.g. T is the time between two orders) that would meet these criteria? Show all your work.

[9] Problem 4 Just-in-Time Philosophy

To  illustrate  the  process  of "continuous  improvement"  and  "elimination  of waste",  a  "Just-in-Time Production Game" was played in class: an inefficient production system was simulated, the inefficiencies were analyzed and a discussion  followed,  during which possible changes were proposed that would facilitate the transition of the production system to a "Just-in-Time" system.

State three of the seven JIT success factors which were implemented and briefly explain how they were used to eliminate inefficiencies . In each case, refer specifically to something that was done in the game.

JIT success factor number 1: ___________________________________________________________

Change to the system and resulting elimination of inefficiencies (please refer to the game):

JIT success factor number

2:___________________________________________________________

Change to the system and resulting elimination of inefficiencies (please refer to the game):

JIT success factor number

3:___________________________________________________________

Change to the system and resulting elimination of inefficiencies (please refer to the game):

[10] Problem 5 Quality Control: Control Charts

Forty-eight  (48)  samples  of  100  units  each  were  taken  on  the  production  of  an  assembly  line manufacturing microchips. The system operates around the clock, and there are two 12-hour shifts: the day shift begins work at 7:00 and the night shift begins work at 19:00. One sample was taken at the end of each production hour for a period of two consecutive days. The sample results are summarized in the Table below (samples taken between 8:00 and 19:00 inclusive were taken on the production of the day shift):