MGT 3730 (11353-FMWA)

Analysis of Management Processes

Benedetto C. Valenti

Fall 2015

Assignment 1

Due Wednesday, November 11 in class or by email.

This is an individual assignment. You may discuss it with others, but never in front

of a piece of paper, board, or screen. No spreadsheet is needed to be submitted. Each

Roman letter holds one twentieth of the full score.

1. The soy milk of Assignment 1 is now bottled and flows out of the production plant

at a constant rate of 150lb/hr. The bottles each contain 0.5lbs soy equivalent of milk and

all flow into a packaging facility annexed to the plant where they are shipped to clients

around the country. With a unit holding cost of $1 per week and per bottle, a fixed

shipping cost of $1000, and a shipping size of 3600 bottles, please (i) draw the inventory

level diagram and (ii) compute the average total cost per week. Also, compute (iii) the

economic shipping quantity Q*

, and (iv) the yearly savings that would be achieved when

using Q*

instead of 3600 for every order. Suppose that a shipping size cannot exceed

4,000 bottles, (v) what would be its optimal value? (vi) What if the shipping size cannot

exceed 8,000 bottles?

Suppose now that only two clients exist. 5,000 bottles are shipped every Monday night

at midnight to the first, and 7,600 bottles are shipped every Sunday night at midnight

to the second, all year round. Please, (vii) draw the inventory diagram of the facility.

(viii) What is the average inventory in the system? Can you use the Little’s law?

(ix) What would be the yearly average cost with the same holding and fixed shipping

costs? Finally, if the next Monday’s shipping needs to be suddenly anticipated because

inclement weather will increase its delivery lead time, (x) how many hours earlier can we

send out the entire order?

2. A company’s main expense is its workforce, and for it at the end of each month the

company has to pay $300,000 worth of salaries. The money comes from a payroll account

that is empty at the beginning of the year and receives a variable inflow from the sales

revenues net of the other operating costs. On a daily basis, $10,000 flow into the account

on average, normally distributed with a variance of 100,000 $2

. If at the end of each

month there is not enough money to pay all the employees, the account balance will go

negative, and some will be paid late. (xi) What is the distribution and the parameters

of the monthly inflow? (xii) What is the probability that at the end of each month all

employees are paid on time? (xiii) What is the initial (safety) capital that we need to

borrow from other accounts to raise this probability to 99%? (xiv) How would this probability

change if the $10,000 mean increases and the 100,000 $2 variance decreases? (xv)

What the probability that at the end of the year the account has zero balance?

3. For its most sold product, a department store estimates a stable mean demand

rate of 200 units per week and a weekly variance of 1,000 units2

, for the whole year.

If the store is able to place and receive orders almost immediately and whenever it desires,

(xvi) what would be the service level with zero safety inventory? (xvii) What would be

the safety inventory for a service level of 80%? If the lead time is now one week, (xviii)

what woud be the safety inventory for a service level of 80%? If the store places one

order every two weeks, (xix) what would be the safety inventory for a service level of

80%? If the lead time is one week and the store places one order every two weeks, (xx)

what would the safety inventory be for a service level of 80%?

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