How capacity of Receiving Department will be measured: # of orders of

How capacity of Receiving Department will be measured:  # of orders of raw materials orders processed per unit of time

Steps to operational process of Receiving Department:

1. unload order of raw materials from truck using one of the available unloading docks
2. inspect the order (both quality and quantity)
3. stage the order for the Production Department to use

Definition of Capacity, Variables, Assumptions, Constraints, and Mathematical Formulas

Definition of Capacity: number of orders of raw materials processed by Receiving Department in a specific time period (hour, shift, day, etc.) 

Variables:

o = average number of orders on a truck 
d = number of loading docks
u = average time to unload each order from a truck
i = average time to inspect an order
p = number of inspectors
s = average time to stage an order for Production Department
f = number for forklifts moving orders from inspection station to Production staging station.
t = time period being analyzed

Assumption: There is little variance in the data to compute the averages

Constraints: # loading docks, # inspectors, and # forklifts

Formulas: Since the steps are sequential in the operational process, the total is a sum of the individual formula results for each step. Orders are unloaded from trucks, inspected, and then staged for production, in that sequence. Note that we have orders in each step in steady state.

Number of orders unloaded from trucks per unit of time: NU = d*o*u

Number of orders inspected per unit of time: NI = NU*i*p

Number of orders staged for production per unit of time: NS = NU*s*f

Total Number of units processed per unit of time: NT = NU + NI + NS

Design (Max) Capacity in number of orders that can be processed in time period = t*NT

This formula gives you the Design Capacity which is the maximum number of orders Receiving can process using historical averages, per the stated assumptions and constraints.

It should be noted we are using averages, i.e. means, in this model and ignoring variance in the time it takes to do a task. To be more accurate we would use the mean and standard deviation to set up a confidence interval and that will yield the expected best and worst cases for a task.

Worked Example.

Note: the unit of time being used for calculations is hours. Since the unit of time is hours each of the formulas must use hours.

Assumption: The variance of time to perform each step is small enough that an average is accurate enough.

Constraints: there are three loading docs, one inspector, and one forklift to move orders from inspection staging to production staging.

o =2 
d = 3
u = 45 minutes (which is .75 hours)
i = 15 minutes (which is .25 hours)
s = 30 minutes (which is .5 hours)
t = one 8 hour shift

Formulas:

Number of orders unloaded per unit of time:   NU = d*o*u = 2*3*.75  = 4.5 orders per hour

Number of orders inspected per unit of time: NI = NU*i = 4.5*.25 = 1.125 orders per hour

Number of orders staged per unit of time: NS = NU*s = 4.5*.5 = 2.25 orders per hour

Total Number of units processed per unit of time: NT = NU + NI + NS = 4.5 + 1.125 + 2.25 = 7.875

Design (Max) Capacity = t * NT = 8*7.875 = 63 orders per 8 hour shift

What this tells me is that based on historical data, i.e. averages, and stated constraints, the maximum number of orders the Receiving Department can handle in an 8 hour shift is 63.

Here’s the capacity utilization formula from Chapter 5 in the textbook.

We know the denominator is equal 63 based on our analysis above. If we have a shift and we unload 50 orders our utilization will be 73%, which means we have 27% slack capacity and that is 13 additional orders we could have unloaded if needed.