# ETM 430 HW of Week 4

**Chapter 8 (50 points)**

- What is the transfer-line manufacturing system? What are its advantages? What are its disadvantages? (10 pts)

- What is the flexible manufacturing? What are its advantages? What are its disadvantages? (15 pts)

- What is the just-in-time manufacturing? How to achieve it? How does it impact facilities design? (15 pts)

- What is the U-shaped flow-line manufacturing system? Why does it become so popular? (10 pts)

**Chapter 9 (100 points)**

- A classroom 80’x60’ with a 11’ ceiling will be illuminated for reading and transcribing handwriting in ink or medium pencil on good-quality paper. Uniform lighting is required throughout the room. Desks in the classroom are 3’ high. All ceilings and walls are to be painted medium-color and soft 40 watt fluorescent lamps are selected for long-term eye comfort, 2-lamp-and-4’-long luminaries are used, luminaries are to be ceiling mounted, and all luminaries are to be cleaned every six months. Please determine the numbers of lamps and luminaries and develop the light layout. (50 pts)

- Everything remains the same as that of Question 1 except that the luminaries are suspended from 25’ ceiling. Please determine the numbers of lamps and luminaries and develop the light layout. (50 pts)

**Chapter 10 (50 points)**

- There are six Walmart stores in Eastern Kentucky. Their coordinates are identified (in mile): P1 (60, 180), P2 (150, 250), P3 (5, 90), P4 (210, 120), P5 (70, 10), and P6 (170, 50). A new distribution center is planned to supply merchandise to these six stores. The cost per unit distance traveled between the distribution center and each store is the same. The number of freight truck trips per week between the distribution center and the store 1, 2, 3, 4, 5 and 6 are expected to be 20, 10, 50, 60, 25 and 30, respectively. (50 pts)

1) Please identify the best location for the new distribution center. Your submission needs to include:

- a) The m-file
- b) The calculated minimum cost and the location coordinates

2) The best place identified in 1) is unfortunately located in the middle of a lake. Thus, an iso-cost contour map is needed to figure out possible alternative locations. Please calculate the iso-cost contour map of this question. Your submission needs to include:

- a) The m-file.
- b) A large-area, coarse map with labels. Please mark the identified best location, P1, P2, P3, P4, P5, and P6 on this contour map.
- c) A small-area (zoom in on the center), fine map without labels.

3) Compare 1) and 2)’s results and check if the coordinate location in 1) matches the center of the contour lines in 2).

**Example 10.2:**A new machine needs to be added into a maintenance department among five existing machines, which are currently located in coordinates: P1 (1, 1), P2 (6, 2), P3 (2, 8), P4 (3, 6) and P5 (8, 4). The cost per unit distance traveled between the new machine and each existing machine is the same. The number of trips per day between the new machine and the existing machines 1, 2, 3, 4 and 5 are 10, 20, 25, 20 and 25, respectively. (50 pts)

1) Please identify the best location for the new machine. Your submission needs to include:

- a) The m-file

% 430 HW 10 Problem 1

% Define x values for calculating the cost along the x axis

x=1:0.1:8;

% Calculate the sub-total cost along the x axis

sumx=10*abs(x-1)+20*abs(x-6)+25*abs(x-2)+20*abs(x-3)+25*abs(x-8);

% Calculate the minimum x sub-total cost and the corresponding x value

[xmin, indexx]=min(sumx);

% Figure out the x value at which the total cost along the x axis is

% minimum

xvalue=x(indexx)

xmin

% Define y values for calculating the cost along the y axis

y=1:0.1:8;

% Calculate the sub-total cost along the y axis

sumy=10*abs(y-1)+20*abs(y-2)+25*abs(y-8)+20*abs(y-6)+25*abs(y-4);

% Calculate the minimum y sub-total cost and the corresponding y value

[ymin, indexy]=min(sumy);

% Figure out the y value at which the total cost along the y axis is

% minimum

yvalue=y(indexy)

ymin

MinTotalCost=xmin+ymin

%End%

- b) The calculated minimum cost and the location coordinates

The minimum total cost is 440 at (3, 4)

2) Alternatives are required for the best location of 1). Thus, an iso-cost contour map is needed to identify possible alternative locations. Please calculate the iso-cost contour map of this question. Your submission needs to include:

- a) The m-file.

% 430 HW 10 Problem 1 Iso-Cost Contour

% Define [x,y] grid for the region

[x, y]=meshgrid(1:0.1:8, 1:0.1:8)

% Calculate the total cost

TotalCost=10*abs(x-1)+20*abs(x-6)+25*abs(x-2)+20*abs(x-3)+25*abs(x-8)…

+10*abs(y-1)+20*abs(y-2)+25*abs(y-8)+20*abs(y-6)+25*abs(y-4);

% Generate the iso-cost contour

contour(x,y,TotalCost, 15)

[Xu, h]=contour(x,y,TotalCost, 15);

clabel(Xu, h)

%End%

- b) A large-area, coarse map with labels. Please mark the identified best location, P1, P2, P3, P4, and P5 on this contour map.
- c) A small-area (zoom in on the center), fine map without labels.

3) Compare 1) and 2)’s results and check if the coordinate location in 1) matches the center of the contour lines in 2).

Yes, the coordinate location in 1) matches the center of the contour lines in 2).