Capacity planning Operations Management

It is important for a company to adjust the output rate or its capacity to fulfill customers’ demand at an affordable rate.

Capacity refers to the ability of a company to produce a sustained level of products and services.

A company may leverage its capacity to accomplish long-term goals.

A company should not construct more than what is needed and should have an excellent inventory and capacity planning.

There doesn’t exist a single formula to determine the exact capacity a company may require, mainly because of external factors, but mostly because of the changes in the demands.

To develop a great capacity plan, a company may begin by stating answers to the following questions:

How variable is the customer demand?
How much inventory can it accommodate?
How expensive is establishing and preserving capacity?
How long would a customer be willing to wait for the product or service?
How long does it take to expand new capacity?

Building and maintaining capacity is a tough job for managers, as their decisions may or may not lead to a disaster. Poor capacity planning can be very expensive to sustain or the company may lose some revenues.

The relationship of the customer demands to the company’s inventory must be directly proportional.

If the demand has high variability, the inventory availability must also be high.

One method that the company may follow regarding its inventory is to prepare beforehand. The company may opt to carry an inventory when the demand is less than the capacity.

This inventory can then be sold when the demand is greater than the capacity. This way, the return of investment can be improved while establishing a high rate of usage of company resources.

Capacity should be added in terms of chunks rather than as one unit, sometimes known as “step increases”.

A company can increase its capacity by hiring more personnel or acquiring more equipment.

One essential note to remember is that the company should increase the capacity to the correct process parts to avoid allocation of resources to efforts that do not assist to satisfy company goals.

The demand forecast for this month is much more accurate than a demand forecast a year from now.

This is because the longer the company takes to increase the capacity, the demand for that specific time would be less certain.

The best way to determine the company’s capacity level is to analyze the inventory build-up over the long run.

Shown above is a diagram on balancing the supply and demand of a company having inventories where supply represents the inflow and demand represents outflow.

Ideally, supply should be equal to demand. However, this will not occur in a million years as there are variations or factors that affect demand.

The two events in balancing supply and demand are: when supply is greater than demand, the products accumulate or get stored over time and, when demand is greater than supply, the products get pulled from the inventory.

Alternatives a company may adopt:

Produce products only when a customer orders it
Observe a constant number of output to cover increased demand
Increase the company’s capacity

It is better for a company to have excess inventory than idle capacity. There are certain ways to deal with the excess amount of products, like selling them with discounts or having sales.

When a company produces to match demand, it pertains that the supply is less than its capacity, which usually leads to higher utilization rate of the company’s resources and a possible tremendous loss in profit.

Instead, a company may utilize the level production strategy which permits it to increase its capacity and inventory level.

The company may utilize an inventory buildup diagram or IBD. An IBD is a visual representation of the company’s current level in certain periods of time.

The company may use the following formula for its operations:

I_B = I_A+ ( T_B – T_A) (S – D )

where :

I_B= Inventory at time b

I_A= Inventory at time a

T_B = Time b

T_A = Time a

S = Supply

D = Demand

To better demonstrate these concepts, for example there is a bakery that has the capacity to produce 2,000 cakes per month.

The demand for the first half of the year is 1,800 cakes per month and 2,500 cakes per month for the second half of the year.

If the bakery produces at the rate of demand (chase demand strategy), it will suffer a tremendous loss of about 500 cakes per month for the second half of the year as it can only bake cakes at a maximum capacity of 2,000 cakes per month.

If the bakery produces at capacity (level production strategy), it will have an excess of 200 cakes per month which will be stored in the freezer (inventory). The total number of stored cakes would be 1,200.

Over the second half of the year, the bakery would need to have 15,000(2,500 * 6) cakes, of which 12,000 it can produce (2,000 * 6) and 1,200 from the freezer. It will still experience a loss of 3,000 cakes.

Employing the formula mentioned, the loss of profit is less compared to not having an inventory.

One method that the company may adopt regarding its inventory is to prepare beforehand. The company may opt to carry an inventory when the demand is less than the capacity.

To further minimize the loss of sales, the bakery may increase its maximum capacity. The best way is to acquire a capacity equal to the average demand of about 2,150 cakes per month ((1,800 * 6) + (2,500 * 6)12).

With this analysis, the bakery will have extra 350 (2,150 – 1,800) cakes per month for the first half of the year and will cause an inventory of 2,100 cakes.

For the second half of the year, it will pull 350(2,500 – 2,150) cakes per month from the inventory and will cause a zero inventory at the end of the year.

Waiting matters in a customer’s perception of quality service.

In general, customers hate waiting.

A customer leaves if he/she feels that he/she has waited too long and may or may not return. In a domino effect, these actions may lead to lesser customer demand, which then takes a hit on the overall profit of the company.

Reasons customers wait:

Insufficient capacity
Variability and lumpiness in customer arrival rates
Variability in the duration of a customer to finish the processes

If the average demand is greater than the average capacity, the tendency is that the customers’ line would grow indefinitely.

However, even if the average demand is less than the capacity, the time a customer finish the company’s process or procedures grows with increasing resource utilization.

Fluctuations in demand is a major cause of waiting.

If demand is equal to customers arriving per hour, capacity is greater than the average customer arrival rate (average demand).

Customers arrive at a varied, unpredictable, and unsteady pace.

Customers also vary in time to process the company’s products or services.

This variation happens because customers are independent of one another.

Knowing one customer’s arrival or process time tells nothing about another customer.

This is called the Poisson arrival process in which people do not coordinate their arrival and duration times.

It is normal to assume that under these conditions, the time between each customer is exponentially distributed.

Exponential distribution does not follow a normal or bell curve distribution (waiting times are greater because of customers clumping) and the mean is equal to the standard deviation.

The Queueing Theory

Queue- a line for servers

Servers – operations in queue

Arrival rate (,lambda) – mean number of arrivals per unit time

Service rate (μ, mu) – mean number of customers that can be served at 100 percent utilization

Thruput – number of customers served

Channel (M) – number of parallel operations

Utilization (u) – measure of how busy the system

Phase -collective noun for queue and its servers

Line length (Lq) – average number of customers in a line

Wait time (Wq) – average time a customer waits

Little law’s equation can be used to determine waiting time assuming the throughput value is always constant:

Wq=LqThruput

When using this equation or any other queueing equations, the process utilization must be less than 100 percent. Another variation of the Little law’s equation:

Wq=Lq

To further determine the average line length and waiting time, this equation developed by Hirotaka Sakesagawa of Waseda University, Japan may be used:

Lq=u2(M + 1)1-u

For example, 72 customers arrive at random each hour at a fast-food restaurant that has five cash registers. Assuming customers divide themselves equally, 14.4 (72/5) customers arrive per hour for every cash register.

A cashier has the capacity to process 15 customers per hour and since it only has to process 14.4 customers, it has a utilization of 96 percent ((14.4/15) * 100). This leads to a M of 1.

Using the above equation and Little law’s equation, the following can be concluded.

Lq=.962(1 + 1)1-.96= 23 people Wq=2314.4= 1.6 hrs

The wait time is still long. The best strategy is for the fast food restaurant to increase its number of cash registers.

First, the restaurant must determine the arrival rate of customers given an utilization of 85 percent to avoid burst of waiting times:

= Utilization – Capacity = .85 – 15 = 12.75

7212.75= 5.65 6 cashiers

With 6 cashiers, and 12 customers per hour per register (72/6) and a utilization of 80 percent ((12/15) * 100):

Lq=.82(1 + 1)1-.8= 3.2 people

Wq=3.212= 16 minutes

Increasing the fast food restaurant’s capacity to 6 cash registers allowed it to have an average waiting time of 16 minutes per person.

Instead of adding an extra cash register, the fast food restaurant may opt to perform another method by forming one line for all of the cash registers.

With this method, it still has a utilization of 96 percent and now has a M of 5 (1 line, 5 cashiers):

Lq=.962(15+ 1)1-.96= 21.7 people

Wq=21.772= 18.1 minutes

This method makes a customer wait for 18.1 minutes before getting served.

One last method to reduce waiting time is to lessen its variability usually through appointments or reservations, and standardizing the process.

This further means that there will no longer be exponential distributions and the following equation can be used:

Lq=u2(M + 1)1-u(CV2TBA + CV2ST2)

where :

CVTBA = coefficient of variation of time between arrivals

CVST = coefficient of variation of service time duration

Going back to the fast food restaurant example with single line, introducing reservations results to CVTBA of 0.4 and a CVST of 0.5. With this:

Lq=.962(5 + 1)1-.96(0.42 +0.522) = 4.45 people

Wq=4.4572= 3.71 minutes

This would be the best strategy among all that have been mentioned as it was able to cut down the waiting time of a customer to approximately 4 minutes.

As long as the arrival rates are Poisson and that service times are exponentially distributed, the Sakesagawa equation may be applied as long as the output rate of an operation is equal to the arrival rate and that the total arrival rate is the sum of all the arrival rates of the queue.

From a customer’s perspective, two theories are in play: how long he/she has to wait and how long he thinks he is waiting.

If a customer must wait, the company must at least make the customer feel comfortable by managing the customer’s perception.

Things to remember when managing a customer’s perception:
Customers do not mind waiting, as long as they are comfortable.
The pre-process wait time feels longer than in-process wait time.
Unoccupied time feels longer than occupied time.
Uncertain waits are perceived to be the worst waits.
Unexplained and unfair waits are the worst.

These principles may apply to back orders too. For these cases, the company must offer a website link where the customer can see the status and track his/her order.