PROBLEM 1 A. Matin-Pro, a real estate development firm, is considering several alternative development projects. These include building and leasing an office park, purchasing a parcel of land and building and office building to rent, buying and leasing a warehouse, building a strip shopping center, and building and selling condominiums. The financial success of these projects depends on interest rate movement in the next five years. The various development projects and their five-year financial return ($ millions) given that interest rates will decline, remain stable, or increase are shown in the following payoff table. Interest Rates Project Decline Stable Increase Office Park 0.5 1.7 4.5 Office Building 1.5 1.9 2.4 Warehouse 1.7 1.4 1.0 Shopping Center 0.7 2.4 3.6 Condominiums 3.2 1.5 0.6 Determine the best investment using the following decision criteria. a. Maximax b. Maximin c. Equal likelihood d. Hurwicz (α = 0.3) e. An economist hired by the firm has determined that there is a.50 probability that interest rates will decline, a.40 probability that rates will remain stable, and a.10 probability that rates will increase. Using expected value, determine the best project. What is the expected value of perfect information? B. The Palm Garden Greenhouse specializes in raising carnations that are sold to florists. Carnation are sold for RM3.00 per dozen; the cost of growing the carnation and distributing them to the florists is RM 2.00 per dozen. Any carnations left at the end of the day are sold to local restaurants and hotels for RM 0.75. the estimation of customer ill will if demand is not met is RM1.00 per dozen. The expected daily demand for the carnations is shown as follows. Daily Demand probability 20.05 22.10 24.25 26.30 28.20 30.10 1.00 a. Develop the payoff table for this decision situation. b. Compute the expected value of each alternative number of carnations that could be stocked, and select the best decision. c. Construct the opportunity loss table and determined the best decision. d. Compute the expected value of perfect information.
PROBLEM 2 A. ITSworks is a large computer discount store that sells computers and ancillary equipment and software in the town where State University is located. ITSworks has collected historical data on computer sales and printer sales for the past 10 years as follows. Year Personal Computer Sales Printers Sold 1 1045 326 2 1610 510 3 860 296 4 1211 478 5 975 305 6 1117 506 7 1066 612 8 1310 560 9 1517 590 10 1246 676 i. Develop a linear regression model for these data and forecast printer demand in year 11 if 1,300 computers are sold. ii. Develop a linear trend line forecast to forecast printer demand in year 11. iii. Compare the forecasts developed in parts (i) and (ii) and indicate which one appears to be more accurate. B. Briefly explain each of the following time series forecasting method: a. moving averages b. Weighted moving averages c. Exponential smoothing d. Given the following data on the number of CitChat brand prepaid card (in units) that has been sold in the first eight months in a telecommunication shop in Jitra, Kedah: Bulan/Month Jualan/sales 1 785 2 600 3 578 4 590 5 770 6 805 7 710 8 900 Compute a 3-months moving average for the period from month 5 until 8 (of the next year). C. Explain briefly the following description: - Seasonal pattern - Exponential smoothing - Adjusted exponential smoothing
PROBLEM 3 A. Vantage Sdn Bhd has decided to conduct cash planning for the next three months using simulation. Net cash flows (receipts minus disbursement) during the month are random variables given by the probability distribution below (where, negative values represent net cash outflows and positive values represent net cash inflows). Net Cash Flows per Month (RM000) Probability -150 0.20-100 0.40 100 0.25 150 0.15 Vantage Sdn Bhd currently has a beginning cash balance of RM200,000 (at the beginning of month 1). The firms s required minimum cash balance, to keep on hand for future transactions, is RM150,000, determined after each month s cash flow reconciliation. Thus, after considering the month s net cash flow results, if the resulting cash flow balance for the month is less than RM150,000, Vantage Sdn Bhd will borrow sufficient funds to bring the balance up to RM150,000. On the other hand, if the resulting balance exceeds the required RM150,000, Vantage Sdn Bhd will repay outstanding accumulated borrowings (to the extent possible given the available cash balance in excess of RM150,000, and given the amount of accumulated borrowings outstanding). Vantage Sdn Bhd has no accumulated borrowings currently (at the beginning of month 1). Simulate the cash flows of Vantage Sdn Bhd for one year and indicate the total amount borrowed during the year and how much is owed at the end of the year. B. The time between arrivals of cars at the Petroco Service Station is defined by the following probability distribution: Time Between Probability Arrivals (min.) 1 0.15 2 0.30 3 0.40 4 0.15 1.00 i. Simulate the arrival of cars at the service station for 20 arrivals and compute the average time between arrivals. ii. Simulate the arrival of cars at the service station for I hour, using a different stream of random numbers from those used in (i) and compute the average time between arrivals. iii. Compare the results obtained in (i) and (ii). C. Explain briefly the following descriptions: - Monte Carlo process - Random number - Analogue simulation - Pseudorandom numbers
PROBLEM 4 D. MdBurger s fast-food restaurant has a drive through window with single server. The window operator is assisted by other employees who prepare the orders. Customers arrive at the ordering station every 4.5 minutes (Poisson distribution) and the service time is 2.8 minutes. i. Determine the average length of the waiting line and the waiting time. ii. What is the probability that no customers are in the system and the service idle. iii. What is the probability a customer will have to wait to be served? Discuss the quality of the service. E. AquaTech Service Sdn. Bhd. has 4 stations to serve customers. Customers have to line up on a first in first out basis. The mean arrival rate is FOURTY (40) customers per hour, Poisson distributed and the mean service time per server is 4 minutes, exponentially distributed. Indicate whether the company operations are effective and efficient in terms of the following; i. Idle time of workers at the counters (servers). ii. iii. iv. The percentage of time a customer can walk in and get served without waiting at all Customer waiting time for service and number of customer waiting for service. Average time customer spends in the total queuing system. v. The average number of customers in the queuing system F. What are the elements of waiting line analysis? G. Explain briefly the following descriptions: - Operating characteristics - Utilization factor - Finite calling population - Multiple server model
PROBLEM 5 A. DDB-Builder has built a new elementary school so that the town now has a total of four schools Addeen, Bashiron, Cobbith and Daimman. Each has a capacity of 400 students. The school wants to assign children to schools so that their travel time by bus is as short as possible. The school has partitioned the town into five districts conforming to population density north, south, east, west, and central. The average bus travel time from each district to each school is shown as follows. District Travel Time (mins) Student Addeen Bashiron Cobbith Daimman population North 12 23 35 17 250 South 26 15 21 27 340 East 18 20 22 31 310 West 29 24 35 10 210 Central 15 10 23 16 290 Determine the number of children of children that should be assigned from each district to each school in order to minimize total student traveling time. B. A large manufacturing company is closing three of its existing plants and intends to transfer some of its more skilled employees to three plants that will remain open. The number of employees available for transfer from each closing plan and the number of employees can be accommodated at the three plants remaining open are as follows. Closing Plant Transferable Employees Open Plants Employees Demand X 60 A 45 Y 105 B 90 Z 70 C 35 Total 235 Total 170 Each transferred employee will increase product output per day at each plant as shown in the following table. The company wants to transfer employees so as ensure the maximum increase in product output. TO FROM A B C X 5 8 6 Y 10 9 12 Z 7 6 8 a. Find the initial solution using VAM b. Solve using MODI C. Explain briefly the following descriptions: - Unbalance transportation model - Sensitivity analysis - Modified distribution (MODI)