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Exercises

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Submitted By bedrana
Words 1528
Pages 7
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|1. Producing widgets involves fourteen production tasks, lettered a through n, below. For each task, the time required to |
|accomplish it is given, and the immediately preceding task. |
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|Production Task |
| |
|Time (min.) |
| |
|Preceding Task |
| |
| |
|a |
|b |
|c |
|d |
|e |
|f |
|g |
|h |
|I |
|j |
|k |
|l |
|m |
|n |
| |
|.2 |
|.4 |
|.5 |
|.4 |
|1.0 |
|.5 |
|1.1 |
|.7 |
|.8 |
|.4 |
|1.2 |
|.9 |
|.6 |
|.4 |
|9.1 |
| |
|- |
|a |
|b |
|c |
|a |
|e |
|d, f |
|g |
|g |
|h |
|I |
|k |
|l |
|j, m |
| |
|The manager expects to produce 300 widgets per eight-hour shift. The workers are allowed two 10-minute coffee breaks per shift, |
|and 40 minutes is allocated to cleanup and maintenance tasks. |
|Is it possible to accomplish the objective of 300 widgets per shift with one workstation? |
|What is the maximum possible output with 14 workstations? |
|Draw the precedence diagram for this process. |
|What is the minimum number of workstations which will be required to achieve an output of 300 pieces per shift? |
| |
|. a. The operating time (OT) is (8)(60) - 20 - 40 = 420 minutes per shift. One workstation would require 9.1 minutes to produce |
|one widget. In one shift it could produce 420/9.1= 46 widgets, and the objective cannot be achieved. |
|b. With 14 workstations, the output is limited by the station with the longest time, which is station k with 1.2 minutes. In |
|eight hours, fourteen stations could produce 420/1.2 = 350 widgets, which is more than adequate. |
|c. |
|d. The minimum number of workstations = D*S t/OT = 300(9.1)/420 = 6.5 workstations. |
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|2. Refer to the data in Problem 1. |
|Assign the tasks to workstations according to the heuristic rule of the largest number of following tasks. |
|How many workstations are required under the rule of the largest number of following tasks? |
|What is the percent of idle time (or the balance delay) for this layout? |
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|2. a. Count the tasks which follow a particular task on a path through the precedence diagram which was obtained in #1c. |
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|Number |
| |
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|Task |
|Following |
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| |
|a |
|13 |
| |
| |
|b |
|10 |
| |
| |
|c |
|9 |
| |
| |
|d |
|8 |
| |
| |
|e |
|9 |
| |
| |
|f |
|8 |
| |
| |
|g |
|7 |
| |
| |
|h |
|2 |
| |
| |
|i |
|4 |
| |
| |
|j |
|1 |
| |
| |
|k |
|3 |
| |
| |
|l |
|2 |
| |
| |
|m |
|1 |
| |
| |
|n |
|0 |
| |
|The cycle time (CT) = OT/D = 420/300 = 1.4 minutes. Each workstation can spend a maximum of 1.4 minutes accomplishing a set of |
|tasks. |
|Here is a set of feasible assignments. (It may not be the only one.) The idle time per station is the maximum total time (1.4 |
|minutes) - the total station time. |
| |
|Station |
|Tasks |
|Total time |
|(minutes) |
|Idle time |
|(minutes} |
| |
| |
|1 |
|2 |
|3 |
|4 |
|5 |
|6 |
|7 |
|8 |
|9 |
|a,b,c |
|d,e |
|f |
|g |
|h,j |
|I |
|k |
|l |
|m,n |
|1.1 |
|1.4 |
|0.5 |
|1.1 |
|1.1 |
|0.8 |
|1.2 |
|0.9 |
|1.0 |
|0.3 |
|0 |
|0.9 |
|0.3 |
|0.3 |
|0.6 |
|0.2 |
|0.5 |
|0.4 |
|3.5 |
| |
|b. 9 workstations are required. |
|c. The percent of idle time = (Idle Time per Cycle)x100/(number of stations)×(maximum station time) = 3.5(100)/[(9)(1.4)] = |
|27.78%. |
|3. Refer to the data in Problem 1. |
|Assign the tasks to workstations according to the heuristic rule of the positional weight. |
|How many workstations are required under the rule of the greatest positional weight? |
|What is the percent of idle time (or the balance delay) for this layout? |
| |
|3. a. The positional weight of a task is the sum of its own time and the times of all following tasks on the precedence diagram |
|(#1 - c). |
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|Task |
|Positional Weight |
| |
| |
|a |
|9.1 minutes |
| |
| |
|b |
|7.4 |
| |
| |
|. |
|. |
| |
| |
|. |
|. |
| |
| |
|m |
|1.0 |
| |
| |
|n |
|0.4 |
| |
|The assignment of tasks to workstations will be identical with Problem #2a. Because there must be a high correlation between the |
|number of following tasks and the sum of the task times, these two rules must produce very similar layouts. |
|b. 9 workstations will be required. |
|c. The same as #3c. |
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|4. The XYZ Co. manufactures a variety of specialized products according to the orders of the customers. The plant consists of 5 |
|departments, numbered 1 through 5 below. While some variation in the work flow is experienced, depending on the composition of |
|the orders received, the following matrix is considered to be representative of the traffic between the departments per five-day |
|workweek, measured in the number of forklift loads or the number of pull truck loads. |
| |
|From |
|1 |
|2 |
|3 |
|4 |
|5 |
| |
| |
|1 |
|2 |
|3 |
|4 |
|5 |
|0 |
|70 |
|10 |
|50 |
|50 |
|100 |
|0 |
|30 |
|40 |
|40 |
|50 |
|60 |
|0 |
|0 |
|80 |
|0 |
|0 |
|140 |
|0 |
|10 |
|30 |
|80 |
|10 |
|60 |
|0 |
| |
|The floor plan of the factory is displayed in the diagram below. (See next page). The plant has an L shape, and the lettered |
|areas represent spaces that are to be occupied by the five departments. |
|In how many ways can these five departments be arranged in the factory? |
|Obtain the distance matrix by measuring from the center of one space to the center of the other space. For example, the distance |
|from area B to area E is 18 ft. + 24 ft. = 42 ft. The distances are the same, both ways. |
|Assign departments to the areas. Try to keep departments with heavy traffic close to each other. |
|Obtain the load-distance index for your layout. (The load-distance index is the sum of the products of the traffic between two |
|departments and the distance between the two departments.) |
|Have you obtained the minimum value of the load-distance index? |
| |
|4. a. 5! = 5(4)(3)(2)(1) = 120 possible layouts. |
|b. The distance matrix. |
| |
|From |
| |
| |
| |
| |
| |
| |
|To |
|A |
|B |
|C |
|D |
|E |
| |
| |
|A |
|0 |
|18 |
|36 |
|54 |
|24 |
| |
| |
|B |
|18 |
|0 |
|18 |
|36 |
|42 |
| |
| |
|C |
|36 |
|18 |
|0 |
|18 |
|60 |
| |
| |
|D |
|54 |
|36 |
|18 |
|0 |
|78 |
| |
| |
|E |
|24 |
|42 |
|60 |
|78 |
|0 |
| |
|c. One layout is shown in the diagram below. This one starts with departments 3 and 4, since they have the heaviest traffic. |
|d. Find the products of the loads and distances for every pair of departments. |
| |
|Departments |
|Loads |
|Areas |
|Distances |
|Products |
| |
| |
|3 to 4 |
|140 |
|D, C |
|18' |
|2,520 |
| |
| |
|3 to 5 |
|10 |
|D, B |
|36' |
|360 |
| |
| |
|. |
|. |
|. |
|. |
|. |
| |
| |
|. |
|. |
|. |
|. |
|. |
| |
| |
|1 to 5 |
|30 |
|E, B |
|42' |
|1,260 |
| |
| |
|1 to 2 |
|100 |
|E, A |
|24' |
|2,400 |
| |
| |
|Total (The Load-Distance Index) |
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|30,600 |
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|e. It is not known whether this is the minimum possible value among all of the 120 values of the load-distance index. |
| |
| |
|5. (One step beyond; based on matrix algebra) The textbook mentions some software packages which perform the lengthy computations|
|involved in obtaining the load-distance index and which also test several layouts in search of a low value of the index. If you |
|do not have access to any of these packages, you can obtain the load-distance index on your computer by multiplying the traffic |
|matrix and the distance matrix. Let us symbolize the traffic matrix as L(i,j) and the distance matrix as D(i,j). Then the product|
|matrix is: P(i,j) = L(i,j)*D(i,j). |
|Show how to construct the traffic matrix and the distance matrix so as to perform this multiplication for the layout in 4-c. |
|Hint: consider the traffic matrix to be fixed, and rearrange the distance matrix. |
|Show that the load-distance index is the trace of the product matrix. |
| |
|5. a. In the traffic matrix, the rows represented "from" and the columns represented "to." In the distance matrix, the rows will |
|represent "to" and the columns will represent "from." Use the diagram in #4c to align the elements of the distance matrix with |
|the elements of the traffic matrix. Thus, column 1 of the distance matrix must be "from E," since department 1 is in area E. Row |
|3 of the distance matrix must be "to D," since department 3 is in area D. Here is the rearranged distance matrix: |
| |
|From |
| |
| |
| |
| |
| |
| |
|To |
|E |
|A |
|D |
|C |
|B |
| |
| |
|E |
|0 |
|24 |
|78 |
|60 |
|42 |
| |
| |
|A |
|24 |
|0 |
|54 |
|36 |
|18 |
| |
| |
|D |
|78 |
|54 |
|0 |
|18 |
|36 |
| |
| |
|Cv |
|60 |
|36 |
|18 |
|0 |
|18 |
| |
| |
|B |
|42 |
|18 |
|36 |
|18 |
|0 |
| |
|b. Each element on the principal diagonal of the product matrix will be the sum of the products of the traffic from each |
|department and the distances from each department to all of the other departments. |
| |
| |
|6. Here is the Muther diagram for the departments in Problem 4. |
| |
|A = absolutely necessary to locate the departments next to each other. |
|U = undesirable to locate the departments next to each other. |
|X = departments must not be located next to each other. |
|Assign the departments to the areas so as to satisfy, as far as possible, the conditions of the Muther diagram. |
|What is the value of the load-distance index of this layout? |
|6. a. One assignment of departments to areas is shown in the diagram. |
|b. The Load-Distance Index = 36,000. Compare this value with the value in #4d. The constraints on the locations of the |
|departments have caused the value to increase. |
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Exercise Science

...Are you too busy to exercise? Or perhaps you find it too boring or confusing? After a long day at the office, no one feels like lugging yourself to the gym, but you can't neglect your health! Don't fret! You’re not alone… Studies show that 60% of American adults don't get the recommended amount of physical activity, and over 25% of adults are not active at all. These statistics affect our health, motivation and every day stress. We want to minimize these statistics in our community and build a new gym facility is right next door to our office! It will be available to all of our employees and other surrounding company employees for an affordable rate. White Plains is a city on the move. The population has grown by 10% each year for the past three years. The current population of White Plains is over 58,000. Most importantly, the growth has been fueled by the increased employment in the city's high-tech companies. This will attract a professional that is the target customer for our company’s new gym facility. This new facility will create profit and more productivity from our employees. Our office is 50,000 square feet and we are looking to open a 12,000 square feet gym next door located at 327 Central Avenue in White Plains. The focus of our gym is to keep the whole company involved by exposing everyone to the variety of activities and services we offer. In addition to our facility, there will be a daycare center that will keep members' children entertained while they...

Words: 1181 - Pages: 5