How do I answer in an Excel file? A manufacturing work station is preceded by 16

Question

How do I answer in an Excel file?

A manufacturing work station is preceded by 1600 units of inventory. The workstation's flow rate (i.e., throughput) is 800 units per 8-hour shift. Using Little's Law, calculate the average flow time (in hours) for the work station. A major change of managers and redesign of the workstation is made. As a result, the new flow time is 90 minutes. Assuming that the flow rate remains the same at 800 units per shift, what is the new average inventory level?

Consider an oil change facility. The daily throughput averages 75 cars and the facility is opened for 10 hours per day. Three bays operate simultaneously and the average service time per car at each bay is 18 minutes. What is the utilization of the bays during a typical day?

A manufacturing faculty includes an assembly process, where each product is assembled by one of two assembly workers. Each worker assembles a product in 7.5 minutes. Parts arrive at this department at the rate of 15 parts per hour. Calculate the utilization of the assembly process.   If the target utilization were 75% or below, how many assembly workers would be needed?

Explanation / Answer

As per Little’s law :

Flow rate x Flow time= In-process inventory

Given,

In process Inventory = 1600 units

Flow rate = 800 units / 8 hours = 100 units / hour

Since,

Flow rate x flow time = In-process inventory

100 x Flow time ( hours) = 1600

Or, Flow time = 1600/100 = 16

Flow time = 16 hours

AVERAGE FLOWTIME FOR THE WORKSTATION = 16 HOURS

Revised flow time = 90 minutes = 1.5 hours

Flow rate ( unchanged ) = 100 units/ hour

Therefore,

New average inventory level = Flow rate x Revised flow time = 100 x 1.5 = 150 units

NEW AVERAGE INVENTORY LEVEL = 150 UNITS

Daily throughput i.e. flow rate of cars at oil change facility =75 cars / 10 hours = 7.5 cars/ hour

That means , 1 car arrives every 60/7.5 = 8 minutes

Service time of each bay ( out of 3 bays ) = 18 minutes

Hence, average service time of 3 bays combined = 18 /3 = 6 minutes for every car

Utilization of the bays in a typical day = Average service time of 3 bays combined / Arrival rate of cars x 100 = 6/8 x 100 = 75%

UTILIZATION OF BAYS DURING A TYPICAL DAY = 75 %

Rate of assembling a product = 7.5 minutes for each product

Arrival rates of parts = 15 parts per hour = 4 minutes for each part

Since there are 2 Assembly workers , we assume that 2 products can be assembled simultaneously.

Therefore , effective assembling rate for 2 workers = 7.5/2 = 3.75 minutes per product

Thus, Utilization of the assembly process = Effective assembling rate / Arrival rate for parts x 100 = 3.75/4 x 100 = 93.75 %

Let the number of assembly workers = N when the target utilization rate is max. 75 %

Effective assembling rate for N workers = 7.5/ N minutes

Arrival rate of parts = 4 minutes for each part

Therefore, Utilization of the assembly process

( 7.5/N) / 4 x 100 = 75

Or, 7.5/N = 3

Or, N = 2.5

Thus, number of assembly workers required = 2.5

UTILIZATION OF THE ASSEMBLY PROCESS = 93.75%

NUMBER OF ASSEMBLY WORKERS REQUIRED FOR UTILIZATION OF 75% MAX = 2.5

AVERAGE FLOWTIME FOR THE WORKSTATION = 16 HOURS

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