IE 423 HW#3 page 1 of 1

IE 423 Engineering OR II
Homework #3
Due Thursday, March 3, 2016

Part I: (s,S) Inventory without Backorder: Consider a reorder-point/order-up-to type of
inventory control system, sometimes referred to as ( s , S ) Inventory control system.
Suppose that the inventory is counted at the end of the week (Saturday evening), and if s is 2 or
fewer items remain, enough is ordered to bring the level up to S = 8 before the business reopens
on Monday morning. That is, it is assumed that an order may be placed and is instantaneously
received. The probability distribution of demand is the same each day:
P{D=0}= 0.15 P{D=1}= 0.25 P{D=2}=0.1 P{D=3}= 0.5
(a) Construct a one-step transition probability matrix using the following state of the system
which is defined according to the stock-on-hand (SOH) at the end of the week (Saturday
evening) before replenishment occurs (3 points).
Xn = 1 2 3 4 5 6 7 8 9
SOH = 0 1 2 3 4 5 6 7 8
(b) Over a long period of time, what is the percent of the weeks in which you would expect there
to be a stockout (zero inventory)? (2 points)
Part II: (s,S) Inventory with Backorder:
At the beginning of each day, a company observes its inventory level. Then an order maybe
placed (and is instantaneously received). The probability distribution of demand is the same
each day:
P{D=1}= 0.3 P{D=2}= 0.2 P{D=3}=0.15 P{D=4}= 0.35
If the on-hand inventory is 1 unit or less, enough is ordered to bring the on-hand inventory level
up to 5.
(a) Construct a one-step transition probability matrix using the following state of the system
which is defined according to the stock-on-hand (SOH) at the beginning of each day before
replenishment occurs (3 points).
State = 1 2 3 4 5 6 7
SOH = -2 -1 0 1 2 3 4
(b) Over a long period of time, what is the percent of the days in which backorders occur?
(2 points)

STATISTICS

Purpose of your research:
Your research is to determine if the value of Qatar’s import of food from other GCC countries (KSA, UAE, Bahrain, Kuwait, and Oman) depends on Qatar’s GDP, the GDP of the trading partners, and the distance between Qatar and each of the trading partners. In summary, you will estimate a Gravity Model of Trade for Qatar’s food trade with other GCC countries.

Tasks:
1. Use the United Nation’s Comtrade database (http://comtrade.un.org/) to download Qatar’s annual food imports from GCC member countries from 2000 to 2014. Use the BEC classification and select option 1 for “food and beverages”.

2. You will be able to download GDP values for all countries from the World Bank (http://data.worldbank.org/).

3. You will collect data on road distance between Qatar (Doha) and capital cities in GCC member countries from the web. Useful sources include http://geobytes.com/CityDistanceTool/.

4. You will estimate a multiple regression equation, with value of food imports as dependent variable, and (i) GDP of Qatar, (ii) GDP of other GCC member countries and (iii) distance between Qatar and other GCC countries as independent variables.

5. ?a. Present your original output as is.
?b. Reorganize and present your parameter estimates in a Table format.
?c. Explain your results in not more than one (1) page.
?d. Attach your data to your report.

STATISTICS

Purpose of your research:
Your research is to determine if the value of Qatar’s import of food from other GCC countries (KSA, UAE, Bahrain, Kuwait, and Oman) depends on Qatar’s GDP, the GDP of the trading partners, and the distance between Qatar and each of the trading partners. In summary, you will estimate a Gravity Model of Trade for Qatar’s food trade with other GCC countries.

Tasks:
1. Use the United Nation’s Comtrade database (http://comtrade.un.org/) to download Qatar’s annual food imports from GCC member countries from 2000 to 2014. Use the BEC classification and select option 1 for “food and beverages”.

2. You will be able to download GDP values for all countries from the World Bank (http://data.worldbank.org/).

3. You will collect data on road distance between Qatar (Doha) and capital cities in GCC member countries from the web. Useful sources include http://geobytes.com/CityDistanceTool/.

4. You will estimate a multiple regression equation, with value of food imports as dependent variable, and (i) GDP of Qatar, (ii) GDP of other GCC member countries and (iii) distance between Qatar and other GCC countries as independent variables.

5. ?a. Present your original output as is.
?b. Reorganize and present your parameter estimates in a Table format.
?c. Explain your results in not more than one (1) page.
?d. Attach your data to your report.