Practice Problems Upto Forecasting - Dec 2010 (1)

PRACTICE PROBLEMS UPTO FORECASTING

1. Weekly sales of copy paper at Cubicle Suppliers are in the table below. Forecast week 8 with a three-period moving average and with a four-period moving average. Compute MAD for each forecast. Which model is more accurate?

Week Sales (cases)1 172 223 274 325 196 187 22

SolutionThe forecast with 3-month moving average is 19.0 with 4-moving average the forecast is 22.0 The four-week moving average is more accurate (see below).

Week Sales (cases) 3MA |error| 4MA |error|1 172 213 274 31 21.7 9.35 19 26.3 7.3 24.0 5.06 17 25.7 8.7 24.5 7.57 21 22.3 1.3 23.5 2.58 19.0 22.0

MAD = 6.7 5.0

2. Use exponential smoothing with = 0.2 to calculate smoothed averages and a forecast for period 7 from the data below. Assume the forecast for the initial period is 7.

Period Demand1 102 83 74 105 126 9

SolutionPeriod Demand Forecast

1 10 7.02 8 7.63 7 7.74 10 7.55 12 8.06 9 8.8

3. The following trend projection is used to predict quarterly demand: Y = 250 - 2.5t, where t = 1 in the first quarter of 1998. Seasonal (quarterly) relatives are Quarter 1 = 1.5; Quarter 2 = 0.8; Quarter 3 = 1.1; and Quarter 4 = 0.6. What is the seasonally adjusted forecast for the four quarters of 2000?

SolutionPeriod Projection Adjusted

9 227.5 341.2510 225 180.0011 222.5 224.7512 220 132.00

4. The local convenience store makes personal pan pizzas. Currently, their oven can produce 50 pizzas per hour. It has a fixed cost of $2,000, and a variable cost of $0.25 per pizza. The owner is considering a bigger oven that can make 75 pizzas per hour. It has a fixed cost of $3,000, but a variable cost of $0.20 per pizza.a. What is the break-even point?b. If the owner expects to sell 9,000 pizza, should he get the new oven?

Solution(a) the breakeven is 20,000 units (b) no, stay with the current oven.

5. The local convenience store makes personal pan pizzas. Currently, their oven can produce 50 pizzas per hour. It has a fixed cost of $2,000, and a variable cost of $0.25 per pizza. The owner is considering a bigger oven that can make 75 pizzas per hour. It has a fixed cost of $3,000, but a variable cost of $0.20 per pizza.a. What is the break-even point?b. If the owner expects to sell 9,000 pizza, should he get the new oven?

By mistake, (5) is a repeat of (4). So same solution applies

6. A clothing chain is considering two different locations for a new retail outlet. The organization has identified the four factors listed in the following table as the basis for evaluation, and has assigned weights as shown on the right side of this table. The manager has rated each location on each factor, on a 100-point basis (higher scores are better), as shown in the right-hand table.a. Calculate the composite score for each alternative location.b. Which site should be chosen?c. Are you concerned about the sensitivity and subjectivity of this solution? Comment.

Factor Factor Description Weight Barclay Chester1 Average community income .40 75 702 Community growth potential .25 60 803 Availability of public transportation .15 45 904 Labor cost .20 80 65

Solution on next page

The higher rated site is Chester, 74.5 to 67.75. There is a margin of several points, which should overcome most levels of subjectivity. The site factor scores are quite different, so that a small swing in weights could produce swings in scores of a few points, but probably not the seven necessary to reverse the findings.

Data  Weight Barclay ChesterFactor 1 0.4 75 70Factor 2 0.25 60 80Factor 3 0.15 45 90Factor 4 0.2 80 65

ResultsTotal 1   Weighted sum 67.75 74.5Weighted average 67.75 74.5

7. East Texas Seasonings is preparing to build one processing center to serve its four sources of seasonings. The four source locations are at coordinates shown below. Also, the volume from each source is provided.a. What is the center of gravity?b. What is the rectilinear distance from center to Athens?

X-coordinate Y-coordinate VolumeAthens, Texas 30 40 100Beaumont, Texas 20 15 400Carthage, Texas 55 60 150Denton, Texas 20 70 250

SolutionCenter of gravity is X = 26.9, Y = 40.6. City block distance is √(40-26.9)2+(40-40.6)2 = 13.7 units. Data  Weight X coord Y coordAthens, Texas 100 30 40Beaumont, Texas 400 20 15Carthage, Texas 150 55 60Denton, Texas 250 20 70

ResultsSum 900 125 185Average 31.25 46.25Weighted Average 26.94444 40.55556

8. A manufacturing company preparing to build a new plant is considering three potential locations for it. The fixed and variable costs for the three alternative locations are presented below.

a. Complete a numeric locational cost-volume analysis.b. Indicate over what range each of the alternatives A, B, C is the low-cost choice.c. Is any alternative never preferred? Explain.

Costs A B CFixed ($) 2,500,000 2,000,000 3,500,000Variable ($ per unit) 21 25 15

SolutionB is cheapest up to 125,000 units; C is cheapest after 166,667 units. A is cheapest in between. The B-C crossover is not relevant. Thus each alternative has an attractive range.

Data  Option A Option B Option CFixed cost 2,500,000 2,000,000 3,500,000Variable cost 21 25 15   Volume(optional)      

ResultsBreak-even points Units Dollars  Option A vs. Option B 125000 5125000 Option A vs. Option C 166666.6667 6000000 Option B vs. Option C 150000 5750000    Volume analysis @ units    Option A Option B Option Ctotal cost $2,500,000.00 $2,000,000.00 $3,500,000.00

9. Cyclone Appliances has developed a new European-style convection oven that will be made on an assembly line. The schedule requires 80 ovens in an 8-hour day. The assembly includes seven tasks. The table below indicates the performance time and the sequence requirements for each task.

Task Performance Time (minutes) Task must follow Task listed belowA 1B 2 AC 3 BD 2 BE 4 C, DF 1 EG 2 F

a. What is the desired cycle time in seconds for this assembly operation?b. What is the minimum number of workstations?c. Draw the precedence diagram. d. Group the tasks into the minimum number of workstations using the longest task time

heuristic to minimize idle time at each station.d. What is the total idle time for your solution?e. What is the efficiency of the line?

Solution

10. An insurance claims processing center has six work centers, any of which can be placed into any of six physical departmental locations. Call the centers 1, 2, 3, 4, 5, and 6, and the departments A, B, C, D, E, and F. The current set of assignments is A-3, B-1, C-6, D-2, E-4, and F-5.

The (symmetric) matrix of departmental distances, in meters is

1 2 3 4 5 61 -- 5 30 20 15 202 -- 40 15 10 103 -- 50 20 54 -- 10 355 -- 56 --

The matrix of work flow (estimated trips per day) is among centers

A B C D E FA -- 15 20 0 30 0B 20 -- 50 0 160 10C 0 50 -- 30 0 30D 30 60 20 -- 70 0E 40 0 0 10 -- 60F 0 0 30 20 50 --

The firm estimates that each trip costs approximately $4.a. What is the cost of the current assignment?b. Use trial-and-error to find one improved assignment.c. What is that assignment, and what is its cost?

SolutionThe current assignment costs 13,875. Optimal is 10,450, with A-3, B-5, C-4, D-1, E-6, and F-2