PRODUCTION AND Operations Analysis
IEOR 3402: Midterm Examination 2
生产和运营分析代考 You are allowed to use the textbook. You are allowed to use a simple non-scientific calculator. For any step of the work that cannot be directly
- You are allowed to use the textbook.
- You are allowed to use a simple non-scientific calculator. For any step of the work that cannot be directly calculated with anon-scientific calculator you should show your work.
- No other aid, including classnotes, are allowed.
- Duration: 75 minutes. 8:40am EST till 9:55am EST.
Copy the following Honor Pledge on the first page of your submission and sign it. Without the Honor Pledge your exam will not be graded.
2.(22 points) 生产和运营分析代考
A puzzle store, Dorogi’s Wizard Wheezes, has different variety of brainteasers and jigsaw puzzles. One particular puzzle, Impossible, sells for $25 each, and it costs $15 to purchase it from a designer. There is a $50 replenishment cost per order. A backorder results in the loss-of-goodwill with estimated cost $40 per puzzle. You can assume the unmet demand is backlogged. There is a 2-month lead time and an inventory carrying charge of 15 % annual interest rate. The monthly demand for Impossible puzzle follows a normal distribution with mean 300 and standard deviation 65. 生产和运营分析代考
(a) (4 points) What is the value of Q0, if Q0 is estimated using the EOQ model?
(b) (4 points) What is the value of R0?
(c) (4 points) What are the values of Q1 and R1?
(d) (10 points) Currently Dorogi’s uses the reorder point of 20 units and the lot size of 100 units. A manager from the new generation of puzzle masters, Natalia, plans to increase the lot size from 100 units to 120 units. Then, does the probability of not stocking out during the lead time increase or decrease? How about the proportion of demand that is met from on-hand stock? Explain your reasoning clearly either with math or in words.
3.(28 points) 生产和运营分析代考
During lunch time customers arrive at the Leaky Cauldron and order the world famous Liu cheesecake and do not leave without a treat. Arrivals are assumed to be Poisson in nature. The average time to choose a flavor of the cheesecake and place the order is 2 minutes. The service times vary greatly depending on the specific order as master Zhenyuan needs to prepare the special ingredient for each cake personally, so the process of serving the customer follows an exponential distribution.
(a) (4 points) What are the arrival and service rates in minutes if an arrival rate is 4 customers every 5 min and there is one server? Can the queue reach a steady state? Why or why not?
4.(20 points) 生产和运营分析代考
Suppose we are given the following demand requirement of Chen Wands (previously known as Olivanders) in Diagon Alley for the following 4 months:
| Month j | 6 | 7 | 8 | 9 |
| Demand dj | 200 | 180 | 70 | 40 |
We are currently at month 4 and the lead time is 2 months. There are 120 units planned to arrive at the beginning of month 6. The setup cost of production is $100, and the holding cost is $1 per unit per month.
(a) (8 points) Compute the planned order releases using the Least Unit Cost (LUC) heuristic which Mr. Olivander used since the time of Peverell brothers.
(b) (12 points) Caroline, the new proprietor is equipped with the muggle knowledge of Operations Research and is determined to do better. Help Caroline by calculating the optimal order releases in each month using the Wagner-Whitin method.
