# Today is the start of day 4 and john smith is ready to start

1)  (18 points)

Today is the start of Day 4 and John Smith is ready to start scheduling the following jobs.  Jobs are assigned a letter of the alphabet, starting with the letter A, based on their arrival.

 Job Processing Time (in days) Due Date (End of Day) A 3 10 B 10 12 C 2 25 D 4 8 E 5 15 F 8 18 G 7 20

a)  Sequence these jobs based on the following scheduling rules:  FCFS and critical ratio (CR) (time to due date/processing time).

b)  Based on average flow time measured from today (start of Day 4), which of the sequencing rules is preferred?

Based on the average flow time measured from today (start of Day 4), the preferred sequence is

c)  Based on the average lateness with no credit given for jobs completed early, which of the sequencing rules is preferred?

d)  Based on the average early time with zero days early if the job is completed late, which of the sequencing rules is preferred?

2).  (23 points)

The information technology department of Bellevue University buys paper for its copier machine frequently.  The office manager would like to determine the best quantity to order each time an order is placed.  She has estimated that the ordering cost is \$12 each time an order is placed.  The monthly demand for paper is 135 reams (500 sheets to a ream).  The cost of paper is \$6.50 per ream, and the carrying cost is 25 percent of the paper cost per month.  Base your answers to the following questions on the economics that are provided and using the traditional inventory models we have studied.

a)      How many reams should be ordered at a time?

b)  Suppose the information technology department of the university only has space to hold 35 reams of paper at any time.  How many reams should be ordered at a time?  Why?

c) There are 350 working days per year and the lead time is 3 days.  What are the reorder point and the inventory position immediately after placing the order?

d) If the university were to order at least 60 reams of paper every time it places an order, the paper company will lower the price of the paper by \$0.33 for all reams of paper.  The university can now acquire all of the storage space that it needs.  However, it will cost the university an additional \$1.00 per ream per month for storage.  What is the difference in the annual inventory cost between this policy and the policy found in a)?  Consider all relevant costs.

3).  (20 points)

You are to plan production for a four-month period:  February through May.  For February and March, you should produce to the exact demand forecast.  During February and March, you will follow a matching strategy and hire and layoff the works as required.  For April and May, you should use overtime and inventory with a stable workforce.  Stable means that the number of workers needed for March will be held constant through May.  However, government constraints put a maximum of 5,000 hours of overtime labor per month in April and May.  There is no overtime allowed in February and March.  If demand exceeds supply, then backorders occur.  If there is excess capacity in May, the workers are paid but there is no work performed hence there are no extra units produced in May.  There are 100 workers on January 31.  You are given the following demand forecast

February          –           80,000

March             –           64,000

April                –           100,000

May                 –           40,000

Productivity is four units per worker hour.  Each worker works eight hours per day, 20 days per month.  Assume zero inventory on February 1.  There is to be no inventory at the end of May.   Hiring costs are \$50 per worker, while layoff costs are \$70 per worker.  The inventory holding cost is \$10 per unit per month based on the number of units in inventory at the end of the month.  Straight time labor is \$10 per hour and overtime is 150% of the straight time labor rate.  Backorder costs are \$20 per unit per month.

Find the total cost of this plan.

4).  (22 points)

Below is the computer solution to a linear programming problem linear programming:

Note:  The Reduced Cost is often referred to as the Coefficient Sensitivity.

a)  Write the objective function in equation form and write the constraints as equalities or inequalities.

b)  What are the values of the variables at optimality and what is the value of the objective function at optimality?

c)  If there was an opportunity to purchase additional units of each resource (as expressed by the constraints), based on the sensitivity analysis which resource(s) would you consider for purchase?  Why?  Identify all of the resources that you would consider.  If you did not consider a resource for purchase, why did you exclude it?  Remember that Constraint 1 is equivalent to Resource 1, Constraint 2 is Resource 2, and Constraint 3 is Resource 3.

c)      Suppose the contribution of variable X2 in the objective function increases by 10.  What are the values of the variables at optimality now and what is the value of the objective function at optimality with this change?  Use the above sensitivity analysis in answering this question and provide the sensitivity analysis information you used.

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