Questions: Problem 8-8 (Algo) An initial solution has been given to the following workcenter layout problem. Each location is 180 feet long and 90 feet wide as shown in the following figure. Use the centers of departments for distances and measure distance rectilinearly. For example, the distance between A and B in the initial layout is 180 feet and the distance between A and D is 450 feet. DEPARTMENT A B C D --------------- A 0 10 25 55 B 0 10 5 C 0 15 D 0 90' 180' 180' 180' ------------ A B C D Given the flows described and a cost of 3 per unit per foot, compute the total cost for the layout.

Solution Steps

To solve this problem, we need to calculate the total cost of the layout based on the given distances and flows between departments. The cost is determined by multiplying the flow between departments by the distance and the cost per unit per foot.

1. Extract the flow matrix and the distances between departments.
2. Calculate the cost for each pair of departments using the formula: cost = flow * distance * cost per unit.
3. Sum up all the individual costs to get the total cost.

We are given the flow between departments and the distances between them. The cost per unit per foot is also provided.

• Flows: \[ \begin{align_} f_{AB} &= 10, \\ f_{AC} &= 25, \\ f_{AD} &= 55, \\ f_{BC} &= 10, \\ f_{BD} &= 5, \\ f_{CD} &= 15 \end{align_} \]

• Distances: \[ \begin{align_} d_{AB} &= 180, \\ d_{AC} &= 360, \\ d_{AD} &= 450, \\ d_{BC} &= 180, \\ d_{BD} &= 270, \\ d_{CD} &= 180 \end{align_} \]

• Cost per unit: \( c = 3 \)

For each pair of departments, calculate the cost using the formula: \[ \text{Cost} = \text{Flow} \times \text{Distance} \times \text{Cost per unit} \]

• \( \text{Cost}_{AB} = 10 \times 180 \times 3 = 5400 \)
• \( \text{Cost}_{AC} = 25 \times 360 \times 3 = 27000 \)
• \( \text{Cost}_{AD} = 55 \times 450 \times 3 = 74250 \)
• \( \text{Cost}_{BC} = 10 \times 180 \times 3 = 5400 \)
• \( \text{Cost}_{BD} = 5 \times 270 \times 3 = 4050 \)
• \( \text{Cost}_{CD} = 15 \times 180 \times 3 = 8100 \)

Add all the individual costs to find the total cost: \[ \begin{align_} \text{Total Cost} &= 5400 + 27000 + 74250 + 5400 + 4050 + 8100 \\ &= 124200 \end{align_} \]

Final Answer