Must show work and explain answers!

Mac-in-the-Box sells computer equipment by mail and telephone order.  Mac sells 2,400 flat-bed scanners per year.  Ordering cost is $300 and the annual holding cost is 25 percent of the item’s price.  There are 300 working days in the year and the lead time is 3 days.  The scanner manufacturer offers the following price structure to Mac-in-the Box:

• Given the above information and basing your decision on the economics, what order quantity do you recommend that Mac order from the scanner manufacturer?  Why?
• What is the low cost for each of the three Price per Unit options?
• For the optimal order quantity, what is the inventory position immediately after an order is placed?

The Austin, Texas plant of Computer Products produces disk units for personal and small business computers.  Gerald Knox, the plant’s production planning director, is looking over next year’s sales forecast for these products and will be developing an aggregate capacity plan for the plant based on this forecast.  The quarterly sales forecasts for the disk units are as follows:

Ample machine capacity exists to produce the forecast.  Each disk unit takes an average of 20 labor-hours.  In addition, you have collected the following information:

1. Inventory holding or carrying cost is $100 per disk unit per quarter. The holding cost is based on the inventory at the end of each quarter.
2. The plant works the same number of days in each quarter, 12 five-day weeks, 6 hours per day.
3. Beginning inventory is zero disk units.
4. In a backlog situation, the customer will wait for his order to be filled but will expect a price reduction each quarter he waits. The price reduction is $300 per disk for the first quarter the customer waits, $700 for the second quarter the customer waits, and $900 for the third quarter the customer waits.  In filling orders, backlogged items will always be filled before current quarter items,
5. The cost of hiring a worker is $800 while the cost of laying off a worker is $950.
6. The straight time labor rate is $20 per hour for the first quarter and increases to $22 per hour starting in the second quarter.
7. Overtime work is paid at time and a half (150%) of the straight time work.
8. Outsourcing (contract work) is paid at the rate of $475 per disk unit for the labor and you provide the material
9. Demand during the fourth quarter of the prior year was 1,980 units.
10. Because there is a scheduled plant shut-down at the beginning of next year, the company wants to have the beginning inventory for next year at 360 units. This can be considered as additional fourth quarter demand.  There will be no holding cost associated with these 360 units.
11. Assume that workers hired in any quarter will not need any training to reach full production in that quarter.

Compare the following three sales and operations plans.

1. i) Computer Products is considering a modified “matching” demand planning model for meeting the disk production. The company will hire and layoff workers to match the demand requirements each quarter as long as the capacity of the resulting workforce does not exceed 2,250 units per quarter. If it cannot meet the demand in a quarter because of this restriction, it will backlog the shortage until the next quarter.  Ignoring the material cost, what is the total cost to produce the disks for the year?  All workers will be fully utilized each quarter, in other words, there is no under utilization.

1. ii) As an alternative, the company will maintain a workforce capable of producing the demand during the fourth quarter of last year. If there are more workers in a quarter than required to produce the demand for that quarter, only the units required will be produced in that quarter and there will be underutilization. If demand is greater in a quarter than can be produced by the available workforce using straight time, the excess units will be outsourced.  What is the total cost of this option, excluding the material cost?

You are scheduling production of your popular Rustic Coffee table.  The demand for these coffee tables is 1536 tables.  The components of the table are a top and a base assembly.  The base assembly is composed of 4 legs, 2 short braces and 2 long braces.  There is a brass cap that goes on the bottom of each leg.

Additional information is the following:

Provide the additional number of all items, including the table itself, that are required to meet the total demand shown for the tables.  The On hand includes the Safety Stock. Ignore the timing of these requirements.

4.

Harkin Electronics is planning its production for the next quarter for its two product lines, relays and capacitors.  The profit contribution is $250 for a case of relays and $200 for a case of capacitors.  Three resources limit how much of each product the company can produce:  labor, stamping capacity, and testing capacity.  Next quarter 80,000 labor hours will be available; a case of relays requires 200 labor hours and a case of capacitors requires 150.  The stamping machine will be available for 1,200 hours next quarter and a case of relays requires 4 hours on the stamping machine and a case of capacitors requires 2 hours.  Relays require 3 hours of testing per case and capacitors require 5.  The testing machine will be available for 2,000 hours next quarter.  For every case of capacitors, the company can produce no more than two cases of relays.  At a minimum the company must produce at least 150 cases of relays.

You must submit your linear programming formulations and show the linear programming  solution that you obtained via POM or Solver.  If you solved this using another linear programming approach, you may submit that instead of the software solution.   

1. a) To maximize total profit next quarter, how many cases of relays and capacitors should Harkin Electronics produce during that period? If your answer is in fractional units of cases that is acceptable – do not round to whole number of cases.

1. b) How much profit will result? As a reminder, provide your linear programming formulation and the software solution to receive any credit for this problem.

1. c) Using your sensitivity analysis output, answer the following questions. You must indicate the source of your answers from the sensitivity analysis output.

• For which resources would it make sense to add additional capacity based on the company’s objective?  Why?
• If you excluded a resource, why did you exclude it?
• For those resources for which you would consider adding additional units, what is the range on the right-hand side values for the shadow prices to remain valid?
• How much would you need to change the price of the capacitor so that its value in the optimal solution changes from the current value or in other words when the current optimal solution is no longer valid?  Explain.

1. d) Now suppose that there is a requirement that of the total labor hours used by Harkins, at least 60% must be hours used for producing capacitors. Write the constraint for this requirement. However, you do not need to resolve the problem

5. 5.

Levy Furniture, a furniture manufacturer is planning a factory expansion project.  The activities required, their immediate predecessors, and the optimistic, most likely, and pessimistic estimates of their times (in days) are provided below.  The project network is also provided.

1. a) Construct the project network.

1. b) Identify the critical path and provide the project completion time.

1. c) Calculate the slack time for each activity and for each path (relative to the critical path).

1. d) Looking at only the critical path, find the probability that the store will take more than 23 working days to open.

1. e) What is the probability of completing path AGH in time for the store to open within 23 working days?

The Oxford Copy Shop and Typing Pool is a local copy shop that produces course packets.  Professors take copies of handout and other course-related materials to the Copy Shop, which duplicates them and sells them to students.  The jobs are due at the end of the day on the Due Dates that are provided.  It is now the beginning of Day 6 and the store has the following jobs on hand:

You are asked to schedule and evaluate several sequencing rules.   You are ready to schedule these six jobs.  They are all ready to be processed.

1. a) Determine the sequence of jobs using the following rules:

• Critical ratio rule (CR) – using the definition of the critical ratio rule that we used on our assignment
• Slack – using the definition of slack that we used in our assignment

1. b) Prioritize the rules used in a) based on average flow time measured from now.

1. c) Prioritize the rules used in a) based on average lateness with no credit for completing any test early (in other words, the late time would be set at zero if a job is early).

1. d) Prioritize the rules used in a) based on average early time with no penalty for completing any test late (in other words, the early time would be set at zero if a job is late).

The Peace Care Hospital uses 3,500 boxes of sterile bandages per month.  The annual holding cost rate per year is 20% of the acquisition price.  A typical box of sterile bandages costs $14.50 to purchase.  The ordering cost is $25 each time an order is placed, regardless of the order quantity.  There is storage space for at most 750 boxes of bandages at any time.  The hospital operates 365 days per year.  Peace Care Hospital would like to use the EOQ model.

1. a) How many boxes of sterile bandages should be ordered each time an order is placed if they want to minimize the annual inventory cost?

1. b) How many orders per years should be expected?

1. c) What is the expected total inventory (holding and ordering) cost per year?

1. d) How many days should one order last on average?

The manager of Cheryl’s hospital is determining how often to perform preventive maintenance.  When the testing machine fails, it costs the company $15,000 in lost production.  However, the cost of preventive maintenance is somewhat expensive.  The cost of performing preventive maintenance is $3,000.

1. a) Which interval (weeks between preventive maintenance) do you recommend for performing preventive maintenance? Base this recommendation on the economics as presented.

1. b) Suppose that the company has outsourced the preventive maintenance work. The cost of the preventive maintenance work is negotiable.  With everything else being the same as provided above, what is the preventive maintenance cost that makes the manager indifferent between a one week and a two week preventive maintenance strategy?  Assume that the preventive maintenance costs the same regardless of the weeks between preventive maintenance.

ABC Construction has developed the following set of activities for its budgeting process.

1. a) Using the Normal Times, what is the critical path and project completion time for the budgeting process? Also, what is the cost to complete the project based on the Normal Times?

1. b) If we want to reduce the project completion time to the minimum possible time by crashing activities, what is the new project completion time and what is the new total project cost?

1. c) Modify the problem as follows. There is now an indirect cost of $75 per day, which is in addition to the cost identified above. There is also a penalty cost of $200 per day for any project completion time over 11 days.  What is the minimum cost schedule for the project and what is the total cost for this schedule?  Identify what are the time and the path of this minimum cost schedule.

1. d) Suppose that the company wants to crash the project a total of 4 days. Based on the information provided in the table and in part c) and the results from part c), what would the minimum penalty cost have to be for this 4 day reduction to be justified using the minimum cost schedule approach?  Assume that the indirect cost remains at $75 per day.