BMGT 583: Exam 1 Review

Questions

1. List and briefly describe five differences between services and manufacturing. Provide examples. 2. Identify a large employer in your hometown. Describe this organization's inputs, processes, and outputs. 3. Name the two competitive priorities for quality, and give an example of each. 4. Name the three competitive priorities for time, and give an example of each. 5. List and explain the three service strategies. 6. List and explain the three manufacturing strategies. 7. Under what conditions can decision trees be useful? 8. Under what conditions can break-even analysis be useful? 9. List and briefly define five basic process types. 10. What is the difference between fixed automation and flexible (or programmable) automation? 11. What is the difference between a flow diagram and process chart?

Problems (Review all assigned problems)

1. Mabel's Ceramics spent $3000 on a new kiln last year, in the belief that it would cut energy usage 25% over the old kiln. This kiln is an oven that turns "greenware" into finished pottery. Mabel is concerned that the new kiln requires extra labor hours for its operation. Mabel wants to check the energy savings of the new oven, and also to look over other measures of their productivity to see if the change really was beneficial. Mabel has the following data to work with:

| |Last Year |This Year |
|Production (finished units) |4000 |4000 |
|Greenware (pounds) |5000 |5000 |
|Labor (hrs) |350 |375 |
|Capital ($) |15000 |18000 |
|Energy (kWh) |3000 |2600 |

Also, suppose that the average labor cost is $12 per hour and cost of energy is $0.40 per kwh. a) Were the modifications beneficial? (Compute labor, energy, and capital productivity for the two years and compare.) b) Compute the improvement in multi-factor productivity.

2. An Appliance Service company made house calls and repaired 10 lawn-movers, 2 refrigerators, and 3 washers in an 8-hour day with his standard crew of 3 workers. The average wage for the workers is $12 per hour. The materials cost for a day was $200 while the overhead cost was $50. a) What is the company’s labor productivity, if the retail price for each respective service is $50, $200, and $120? b) What is the multifactor productivity, if the crew consisted of two of each type mechanic?

3. A "Little Sis" restaurant has been opened as a prototype to test the concept of a smaller facility with a limited menu. Experience during the first two years were as follows:

|Year |Annual Volume |Total Cost ($) |
| |(Customer visits) |(Fixed plus variable cost) |
|Year 1 |40,000 |600,000 |
|Year 2 |60,000 |700,000 |

The average sale is $10 per customer. Determine the break-even quantity graphically and by solving algebraically

4. The "Hill O'Beans" Coffee Company operates a chain of coffee shops downtown, and has decided to open a new store. The demand will be weak, fair, or strong; probabilities are 0.25, 0.30, and 0.45, respectively.

If the company installs a small booth that only sells coffee, the associated payoffs are -$25,000, 25,000, and $100,000 for weak, fair, and strong demand. If the company chooses an expanded facility that offers sandwiches and breakfast foods, it must build a kitchen and rent additional space. The payoffs for an expanded facility are -$200,000, -$25,000, and $500,000.
a. Draw a decision tree for this problem.
b. What should management do to achieve the highest expected payoff?

5. A company is screening ideas for new services. Four alternative service ideas are being considered. Management identified four criteria and weighted them as follows: A = 40, B = 30, C = 20, D = 10. They have also come up with scored values for the five alternatives and the four criteria as shown below. Management has decided that if an alternative has less than a total scored value of 600, it should automatically be rejected. Use the preference matrix technique to determine which idea should be accepted.

|Alternative |1 |2 |3 |4 |
|Criteria | | | | |
|A |9 |8 |4 |3 |
|B |6 |7 |5 |10 |
|C |9 |5 |8 |6 |
|D |2 |5 |9 |8 |

6. A medium sized retail electronics and electrical appliances chain of stores is considering building a regional warehouse. The company is considering four alternatives sites. The fixed cost and variable cost with respect to units of output is given below.

|Alternative sites |Fixed cost |Variable cost/unit |
|A |450,000 |12.50 |
|B |326,000 |9.00 |
|C |425,000 |7.20 |
|D |400,000 |8.00 |

Given the above costs determine which alternative is cost effective at what volume levels.

7. Harrison Condominiums, Inc. recently purchased land near a beach and is attempting to determine the size of the condominium development it should build. It is considering three sizes of developments, small, medium, and large. An uncertain economic condition makes ascertaining the demand for new condominiums difficult. However, the demand is narrowed to low, medium, and high. The expected profit for the three development sizes under the three demand conditions are given in the following payoff table.

| | |Demand |
| | |Low |Medium |High |
|Decision |Small |400 |400 |400 |
|Alternatives | | | | |
| |Medium |100 |600 |600 |
| |Large |-300 |300 |900 |

a) Determine the recommended decision under the optimistic, pessimistic, Laplace, Minimax regret criteria. b) What is the recommended decision using the expected value approach? Assume the probabilities for the three demand conditions to be .2, .35, and .45 respectively. c) What is the expected value of perfect information?

8. A U.S. based electronic chip manufacturer is planning to build a new manufacturing and distribution facility in South Korea, China, Taiwan, Philippines, or Mexico. It will take approximately five years to build the necessary infra-structure (roads, etc.), construct the new facility, and put it into operation. The eventual cost of the facility will differ between countries and will vary within countries depending on the financial, labor, and political climate. The company has estimated the facility cost (in $ millions) in each country under three different future economic/political climates as follows.

| | |Economic/political climate |
| | |Decline |same |Improve |
|Country |South Korea |21.7 |19.1 |15.2 |
| |China |19.0 |18.5 |17.6 |
| |Taiwan |19.2 |17.1 |14.9 |
| |Philippines |22.5 |16.8 |13.8 |
| |Mexico |25.0 |21.2 |12.5 |

a) Determine the recommended decision under the optimistic, pessimistic, Laplace, Minimax regret criteria. b) What is the recommended decision using the expected value approach? Assume the probabilities for the three demand conditions to be .2, .5, and .3 respectively? c) What is the expected value of perfect information?

9. Par, Inc., is a small manufacturer of golf equipment and supplies whose management decided to move into the market for medium (standard) and high-priced (deluxe) golf bags. After a thorough investigation of the steps involved in manufacturing a golf management has determined that each golf bag produced will require the four operations, namely, (1) Cutting and dyeing the material, (2) Sewing, (3) Finishing, and (4) Inspection and packaging

The standard model bag will require 7/10 hours in the cutting and dyeing department, ½ hour in the sewing department, 1 hour in finishing department, and 1/10 hour in the inspection and packaging department. The deluxe model will require 1 hour for cutting and dyeing, 5/6 hour for sewing, 2/3 hour for finishing, and 1/4 hour for inspection and packaging. The profit contribution for every standard bag is estimated to be $10 and $9 for every deluxe bag produced.

The director of manufacturing estimates that labor of 630 hours for cutting and dyeing, 600 hours for sewing, 708 hours for finishing, and 135 hours for inspection and packaging will be available for the production of golf bags during the months.

The company's problem is to determine how many standard and deluxe bags it should produce to maximize the total profit contribution.
(a) Develop an LP model and solve using graphical method
(b) Solve the problem using Excel Solver.
(c) Identify binding an non-binding constraints and calculate the value of slack/surplus variables of each constraints and interpret it.
(d) Compute the sensitivity range for each objective function coefficient and right hand side value of each constraint.
(e) Give an interpretation for each shadow price.
(f) Assume that a premium of $5 per hour must be paid for additional labor hours. If you have $500 budget for additional labor how would you use it and how much net additional profit you could make.

10. Greentree Kennels, Inc. provides overnight lodging for a variety of pets. A particular feature at Greentree is the quality of care pets receive, including excellent food. The kennel’s dog food is made by mixing two brand-name products to obtain what the kennel calls the “well balanced dog diet.” The data for the two dog foods are as follows.

|Dog food |Cost/Ounce |Protein % |Fat % |
|Bark bits |0.06 |30 |15 |
|Canine Chow |0.05 |20 |30 |

Greentree wants to be sure that the dogs receive at least 5 ounces of protein and at least 3 ounces of fat per day.

(a) Formulate a linear program and determine the minimum cost mix of the two dog food products using the graphical method.
(b) Solve this problem in Excel
(c) Identify binding an non-binding constraints and calculate the value of slack/surplus variables of each constraints and interpret it.
(d) Identify and fully interpret the shadow prices of the constraints.
(e) What change in the diet would you make if you wish to cut feed cost by $0.35?

11. The Two-River Oil company near Pittsburgh transports gasoline to its distributors by truck. The company has recently contracted to supply gasoline distributors in southern Ohio, and it has $600,000 available to spend on the necessary expansion of its fleet of gasoline tank trucks. Three models of gasoline tank trucks are available.

|Truck Model |Capacity |Purchase Cost |Monthly operating cost|
| |(Gallons) | | |
|Super Tanker |5000 |67000 |550 |
|Regular Line |2500 |55000 |425 |
|Econo-Tanker |1000 |46000 |350 |

The company estimates that the monthly demand for the region will be 550,000 gallons of gasoline. Because of the size and speed differences of the trucks, the number of deliveries or round trips possible per month of each truck will vary. Trip capacities are estimated at 15 trips per month for the super tanker, 20 trips per month for the regular line, and 25 trips per month for the Econo-Tanker. Based on the maintenance and driver availability, the firm does not want to add more than 15 new vehicles to its fleet. In addition, the company has decided to purchase at least three of the Econo-Tankers for use on short run, low demand routes. As a final constraint, the company does not want more than half the new models to be super tankers. The company wishes to satisfy the gasoline demand with minimum monthly operating expense. Model this problem as a linear programming problem and determine an optimum solution. Interpret the answers, sensitivity ranges, and shadow prices wherever appropriate.

12. Customers at a local post office arrive at the average rate of 2 every minute during the peak period of 11 a.m. to 1:00 p.m. During the peak period, three clerks serve regular customers. Service time for regular customers follows exponential distribution with a mean of 2 minute. Assume that a maximum of fifteen customers can wait for service. At present 5 customers are in the line.

Bulk mailers arrive at the post office at the rate of three per hour. One of the three clerks is cross trained for bulk mailers. The cross-trained clerk gives priority to bulk mail customer. The service time for bulk mailers follows normal distribution with a mean of 15 minutes and a standard deviation of 7 minutes. There are no bulk milers waiting for service at this time. There can be only one bulk-mail customers waiting for service.

After the bulk mailing is processed, the bulk mail customer directly moves to the bulk-mail payment window. This payment window is served by one of the regular clerks including the cross trained clerk. The bulk-mail payment window has priority over the regular customers. The time to make the payment follows a normal distribution with a mean of 2 minutes and standard deviation of .25 minutes.

Develop a SimQuick flow chart for this simulation problem.

13. A small fertilizer manufacturer produces and sells two types of fertilizers in bulk. At present, the company follows the same inventory policy for both products, namely, reorder 100 tons of the product if the on-hand inventory reached 50 tons. The setup cost for setting the line up for each product is $500 per set up. Inventory carrying cost is $3 per ton per day for each product. The contribution margin before inventory related costs is estimated as $50 per ton for the first product and $30 per ton for the second product. A Simqucik model was developed for this problem. The simulation results for a duration of 90 days are shown below.

|Element types |Element names |Statistics |Overall means|
| | | | |
|Work Station(s) |Produce-A |Final status |NA |
| | |Final inventory (int. buff.) |20.00 |
| | |Mean inventory (int. buff.) |11.26 |
| | |Mean cycle time (int. buff.) |0.47 |
| | |Work cycles started |22.00 |
| | |Fraction time working |0.49 |
| | |Fraction time blocked |0.44 |
| | | | |
| |Produce-B |Final status |NA |
| | |Final inventory (int. buff.) |0.00 |
| | |Mean inventory (int. buff.) |6.72 |
| | |Mean cycle time (int. buff.) |0.22 |
| | |Work cycles started |29.00 |
| | |Fraction time working |0.33 |
| | |Fraction time blocked |0.27 |
| | | | |
|Buffer(s) |Initiate |Objects leaving |51.00 |
| | |Final inventory |49.00 |
| | |Minimum inventory |49.00 |
| | |Maximum inventory |100.00 |
| | |Mean inventory |74.28 |
| | |Mean cycle time |131.15 |
| | | | |
| |ROP-A |Objects leaving |2186.50 |
| | |Final inventory |43.50 |
| | |Minimum inventory |0.00 |
| | |Maximum inventory |50.00 |
| | |Mean inventory |32.99 |
| | |Mean cycle time |1.36 |
| | | | |
| |ROP-B |Objects leaving |2850.00 |
| | |Final inventory |0.00 |
| | |Minimum inventory |0.00 |
| | |Maximum inventory |50.00 |
| | |Mean inventory |20.20 |
| | |Mean cycle time |0.64 |
| | | | |
|Exit(s) |Demand-A |Objects leaving process |2186.50 |
| | |Object departures missed |327.00 |
| | |Service level |0.87 |
| | | | |
| |Demand-B |Objects leaving process |2850.00 |
| | |Object departures missed |2379.00 |
| | |Service level |0.55 |

Complete the following table:

|Item |Chemical A |Chemical B |
|ROP | | |
|Order Quantity | | |
|Service Level | | |
|No. of orders | | |
|Ordering cost | | |
|Average inventory | | |
|Inventory carrying cost | | |
|Orders quantity satisfied | | |
|Profit before inventory costs | | |
|Net profit | | |

Answers:
1. The energy modifications did not generate the expected savings; labor and capital productivity decreased.

|Productivity |Last Year |This Year |Change |
|Labor (hrs) |11.429 |10.667 |-6.67% |
|Capital ($) |0.267 |0.222 |-16.67% |
|Energy (kWh) |1.333 |1.538 |15.38% |
|Multifactor productivity |0.196 |0.170 |-13.34% |

2. (a) $52.5, (b) $1.525 3. 80,000 4. Expand; $167,500 5. Alternative 1, with a weighted score of 740. 6. B for 0-55,000; C for > 55,000 7. (a) Optimistic: Large, 900; Pessimistic: Small, 400; Laplace: Medium, 433.33; Minimax regret: Medium, 300; (b) Medium, 500; (c) 195 8. (a) Optimistic: Mexico, 12.5; Pessimistic: China, 19; Laplace: Taiwan, 17.067; Minimax regret: Taiwan, 2.4; (b) Taiwan, 16.86; (c) .91
9. Max 10 x1 + 9 x2 s.t. 7/10 x1 + x2 < 630 1/2 x1 + 5/6 x2 < 600 x1 + 2/3 x2 < 708 1/10 x1 + 1/4 x2 < 135 x1 , x2 > 0

(b) (540,252) Z = 7668

(c) Cutting & Dyeing and Finishing are binding.

(d)
Sensitivity range for objective function coefficients:
For x1: 6.300 to 13.500
For x2: 6.667 to 14.286

Sensitivity range for RHS of constraints:
Cutting and dyeing 495.6 to 682.364
Sewing 480 to ∝
Finishing 580 to 900
Inspection and packaging 117 to ∝

(f) Add 100 hours to Finishing. Increase in net profit will be $193.75.

10) Min .06 x1 + .05 x2 s.t. 0.30 x1 + 0.20 x2 > 5 0.15 x1 + 0.30 x2 > 3 x1 , x2 > 0

(15, 2.5); z = 1.025;
(c) Both constraints are binding.

(d) shadow prices: .175, .05; (i) the cost of increasing the minimum requirement of 5 ounces of protein per day is $0.175 per ounce. All other parameters are constant; (ii) the cost of increasing the minimum requirement of 3 ounces of fat per day is $0.05 per ounce. All other parameters are constant.
(d) decrease minimum protein requirement by 2 ounces.

11) Min 550x1 + 425x2 + 350x3
s.t. 67x1 + 55x2 + 46x3 < 600 Budget (15x5) x1 + (20x2.5)x1 + (25x1)x3 > 550 Demand x1 + x2 + x3 < 15 No more than 15 x3 > 3 At least 3 econo x1 < .5 (x1 + x2 + x3) , or 0.5x1 - 0.5 x2 – 0.5 x3 < 0 No more than 50% Super x1 , x2 , x3 > 0

X1=5, X2=2, X3=3; Z = 4650

Budget and number of new trucks are not binding. Other constraints are binding.