? Question 4: This question is from chapter 5. The question is worth 20 points.

Question

?Question 4: This question is from chapter 5. The question is worth 20 points. (Please show step by step work to receive full credits)

The following diagram shows a four step process that begins with operation 1 and ends with operation 4. The rates shown in each box represent the effective capacity of that operation.

? ? ?Operation 1 Operation 2    Operation 3 Operation 4
? (15units/hr) ------ (10 units/hr)---(5 units/hr)--- (25 Units/hr)

a)      Determine the capacity of the process? (5 points)

b)     Which action would yield the greatest increase in process capacity: (1) Increase the capacity of operation 1 by 10%; (2) Increase the capacity of operation 2 by 15%; (3) Increase the capacity of operation 3 by 5%. ( 15 points)

Explanation / Answer

Solution:

(a) The capacity of a process is determined by the capacity of the bottleneck process. A bottleneck process in a system is the process that takes the most amount of time or yields the lowest output in a given time period. A bottleneck process reduces the capacity of the whole system. The capacity of a system is equal to the capacity of the bottleneck process in the system.

In the given scenario,

Capacity of Operation 1 = 15 units/hr

Capacity of Operation 2 = 10 units/hr

Capacity of Operation 3 = 5 units/hr

Capacity of Operation 4 = 25 units/hr

It can be observed that Operation 3 yields the lowest output i.e. 5 units/hr. Hence, it is the bottleneck process of the system.

Capacity of the process = 5 units/hr

(b) Among the given actions - (1), (2) and (3), Action (3) i.e. Increasing the capacity of operation 3 by 5% would yield the greatest increase in process capacity. This is because Operation 3 is the bottleneck process and the capacity of a system is equivalent to the capacity of the bottleneck process. Actions (1) and (2) would not have any impact on the process capacity as the process capacity would still be equal to the capacity of the bottleneck process i.e. operation 3 which is equal to 5 units/hr.

This can be proved mathematically using the calculations below:

Action 1: Increase the capacity of operation 1 by 10%

Increased Capacity of Operation 1 = 16.5 units/hr

Capacity of Operation 2 = 10 units/hr

Capacity of Operation 3 = 5 units/hr

Capacity of Operation 4 = 25 units/hr

Capacity of the process = 5 units/hr (Bottleneck process)

Percentage increase in process capacity = 0%

Action 2: Increase the capacity of operation 2 by 15%

Capacity of Operation 1 = 15 units/hr

Increased Capacity of Operation 2 = 11.5 units/hr

Capacity of Operation 3 = 5 units/hr

Capacity of Operation 4 = 25 units/hr

Capacity of the process = 5 units/hr (Bottleneck process)

Percentage increase in process capacity = 0%

Action 3: Increase the capacity of operation 3 by 5%

Capacity of Operation 1 = 15 units/hr

Capacity of Operation 2 = 10 units/hr

Increased Capacity of Operation 3 = 5.25 units/hr

Capacity of Operation 4 = 25 units/hr

Capacity of the process = 5.25 units/hr (Bottleneck process)

Percentage increase in process capacity;

% increase = [(New process capacity - Old process capacity) / Old process capacity] x 100

% increase = [(5.25 - 5) / 5] x 100

Percentage increase in process capacity = 5%

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