ISDS 514 Third Exam

Dr. Zvi Drezner Fall, 2011

Answer any three of the following four questions. Prepare one file with separate sheets for different questions properly labeled. Email back the answer file to me at .

Question #0

The following is quarterly data of sales:

t / Xt
1 / 76
2 / 23
3 / 34
4 / 56
5 / 82
6 / 29
7 / 35
8 / 60
9 / 87
10 / 30
11 / 42
12 / 65
13 / 90
  1. Find the forecast for the next three quarters by using dummy variables.
  2. Find the forecast for the next three quarters by using index numbers and exponential smoothing using α=0.5, β=0.3.

Question #1

Ships arrive at the port around the clock 24 hours a day at a rate of 18 ships per day. There are 6 docks available for loading and unloading and it takes about 7 hours, on the average, from the moment a ship docks until the next ship can use the same dock. Assume Poisson arrival and exponential service time.

a. What is the probability a ship does not have to wait in line?

b. How many hours does it take from the moment a ship arrives at the port until it is done and leaves?

c. It costs the shipping company $6,000 per hour for a ship waiting in line. It considers investing in building additional docks at a daily operating cost (and amortized building cost) of $100,000 per additional dock. How many docks should the company add and what is the savings per ship it will enjoy?

Question #2

Workers are paid according to the service time they provide customers. Average service time ranges between 3 and 5 minutes (analyze it in increments of 0.1 minutes). A worker whose service time is 5 minutes is paid $15 per hour and for every improvement in service time by 0.1 minutes salary increases by $0.30 per hour so that a worker whose service time is 3 minutes is paid $21 per hour. The standard deviation of service time is about 40% of the average service time. Assume Poisson arrival. You have 6 customers arriving per hour. These customers work for you as well and they earn $30 per hour and the waiting time they spend in the service system is lost by the company (during the service itself they work). Find the hourly cost for the company for service times 3.0, 3.1, 3.2 ,…, 5.0 minutes. What is the best service time you should hire? Use Data Tables for solving this problem.

Question #3

Daily demand of widgets is normally distributed with a mean of 70 widgets and a standard deviation of 12 widgets. Annual holding cost of a widget is $80 and ordering cost is $400. Assume 363 business days per year. A shipment of widgets arrives 5 business days after an order is placed. Use 99% reliability.

a.  What is the expected total annual inventory cost?

b.  What is the average total inventory cost per widget?

c.  You pay $20 per widget and sell it for $25. What is your expected annual profit?

d.  Create a table of the expected cost per widget, expected annual cost, and expected annual profit for ordering cost between $300 and $500 in increments of $10.

Question #4

There are two stages in a production process. The first machine produces 1400 parts in a 12 hour day. These parts are assembled by 8 other machines (in parallel) that work continuously during those 12 hours and each machine assembles10 parts per hour. Holding parts in inventory cost you $2 per hour and start up cost of the first machine is $80.

a, What is the daily inventory cost?

b. What is the daily inventory cost per assembled product?

c. how many hours does the first machine produce parts before it is stopped?

d. What is the required assembly per hour by the other machines so that inventory cost per item is $1?