Capacity Planning

Capacity Planning

• Capacity denotes in general the extent of availability of these resources for use by various processes

• It also denotes the maximum output of products and services one can achieve using these resources

• Capacity planning is a systematic approach to – Estimate the amount of capacity required,

– Evaluation of alternative methods of augmenting capacity

– Devise methods to use capacity effectively

• Capacity planning is important– It has a significant impact on the cost of operation of the system due to

large fixed costs associated with capacity

• Economies of scale is an concept in economics related to capacity

Economies of ScaleAn illustration

2000 units per month

5000 units per month

10,000 units per month

Units of output

Avera

ge u

nit

cost

of

ou

tpu

t

Capacity buildup Alternative modes

Units

Units

Units

TimeTime

Units

Capacity

Demand

Typical mode

Proactive modeReactive modeTime

Input measures of capacity

• Firms operating in low volume, high variety situation find it relevant – Refining capacity of BPCL refinery in Mumbai is

260,000 barrels of crude per day – Television manufacturer often measures its capacity

by millions of picture tubes that it produces – Tool room facility will measure its capacity in terms of

machine hours– A hospital will measure the capacity in terms of

number of beds.

Output measures of capacity

• When the volume of production is high and the variety is relatively low output measures are useful– Toyota Kirloskar Auto Parts measures it capacity in terms

of number of transmission gear boxes it can produce

– Tata Bearings, a division of Tata Steel, has a capacity of 25 million pieces per annum

– MICO Bosch has an installed capacity of one lakh distributor pumps at its Jaipur plant

– An automated car wash facility’s capacity can be measured in terms of number of cars serviced per day

Japanese notion of capacity

• Capacity = Work + Waste• Nine types of waste according to Canon

production system:– Waste in Operations– Waste in Startup– Waste in Equipment– Waste in Defects– Waste in Materials– Waste in Indirect Labour– Waste in Human Resources– Waste in expense

Capacity PlanningTime Horizon

Long term Medium term Short-termTime frame 2 - 5 years Typically 1 year 1 week to 3 months

Planning premiseAugmenting capacity for projected growth

Balancing demand - supply Maximising availability; Efficent use of resources

Key decisions made

Capacity Augmentation; Capital Budgeting Exercises

Adjusting demand and supply attributes to balance available capacity to requirement

Resource deployment strategies, Maintenance routines, Improvement projects to be undertaken

Tools & Techniques used

Investment planning; Break-even analysis, Discounted cash flow techniques; Decision Trees

Aggregate Production Planning; Make or Buy

Planning & Scheduling, Total Productive Maintenance, Waste elimination by continuous improvement; Simulation; Heuristics;Waiting line models

Time Horizon for planningCriterion

Capacity Planning Framework

Estimate the capacity requirements for the

planning horizon

Compute the available capacity & identify

quantum of capacity to be augmented

Identify available alternatives & select the

best one for capacity augmentation

Capacity PlanningComputational steps

• Estimate the total requirement for the planning horizon

• Estimate Labour and Machine requirements

• Compute Capacity Availability• Compare availability with Requirement• Evaluate alternative methods for capacity

augmentation

Capacity requirements

• Projected demand per unit time during the = D

planning horizon

• Standard labour hours required per unit of product = SL

• Efficiency of labour = EL

• Capacity requirements (Labour) =

• Capacity requirements (Machine) =

L

L

E

SD*

M

M

E

SD*

Capacity Availability

• System availability– Number of working days in the planning horizon: Nd

– Number of working hours per day: h

– System availability (Hours) = Nd * h

• Resource availability– Number of machines available: Nm

– Machine: Time lost in breakdowns & maintenance = b %

– Number of workers available: NL

– Labour: Absenteeism of the workers = a %

• Capacity available in the system (Hours)– Machine: Nd * h * Nm * (1 – b/100)

– Labour: Nd * h * NL * (1 – a/100)

Capacity AugmentationAlternatives

• Waste Elimination

• Multi-tasking of workforce

• Sub-contracting/Outsourcing

• De-bottlenecking

• Addition of new capacity

Problem

• A product is manufactured in a shop using a five-stage process. The first step in the process is to cut the sheet metal to required shapes and sizes using a shearing process. After the shearing process, the components are subjected to pressing operations to alter the shape of the flat sheet as per the design. In the third stage of the process welding is done to join the components. The next step in the process is a painting operation. After painting, the components are packed and kept ready for dispatch.

• The time take for each of these operations are 20, 30, 15, 12 and 6 minutes respectively.

• Presently, each stage has only one machine for operation. • Map the process and analyse the capacity with respect to the following scenarios:

– If the shop works for an 8-hour shift with an effective available time of 450 minutes, what is the production capacity of the shop?

– Where is the bottleneck in the system? If we want to add one machine, where should we make the investment?

– Identify the additional capacity required for a daily production target of 25 units. Compute the utilisation of the machines as per the revised capacity calculations.

Shearing (20 minutes)

Pressing (30 minutes)

Welding (15 minutes)

Painting (12 minutes)

Packing (6 minutes)

The production capacities are:

– Shearing: 450/20 = 22.50 Pressing: 450/30 = 15.00

– Welding: 450/15 = 30.00 Painting: 450/12 = 37.50

– Packing: 450/6 = 75.00

• The smallest number in the above calculation limits the production capacity for the shop. Therefore, the current production capacity is 15 units per day.

Shearing (20 minutes)

Pressing (30 minutes)

Welding (15 minutes)

Painting (12 minutes)

Packing (6 minutes)

Bottleneck

The production capacities are:

– Shearing: 450/20 = 22.50 Pressing: 450/30 = 15.00

– Welding: 450/15 = 30.00 Painting: 450/12 = 37.50

– Packing: 450/6 = 75.00

• The smallest number in the above calculation limits the production capacity for the shop. Therefore, the current production capacity is 15 units per day.

Shearing (20 minutes)

Pressing (30 minutes)

Welding (15 minutes)

Painting (12 minutes)

Packing (6 minutes)

Shearing (20 minutes)

Pressing (30 minutes)

Welding (15 minutes)

Painting (12 minutes)

Packing (6 minutes)

Pressing (30 minutes) Bottleneck

• The production target is 25 per day now. Since a day has 450 minutes, the maximum time that the process can take in each stage is 18 minutes. – Packing, Painting and Welding sections have timings less than 18.

Therefore, they do not need any more investment in capacity.

– By adding one more machine at the pressing stage, the effective time will be less than 18 minutes.

– Similarly, by adding one more machine at the shearing stage, the effective time will be 10 minutes.

– Utilisation of Shearing =

– Utilisation of Pressing =

– Utilisation of Welding =

– Utilisation of Painting = 66.67% Utilisation of Packing = 33.33%

%56.55450*2

20*25

*

*

timeavailablemachinesofnumber

timeprocessproductionDaily

%33.83450*2

30*25

%33.83450*1

15*25

Bottleneck & Capacity Analysis The Wandering Bottleneck

Shearing (20 minutes)

Pressing (30 minutes)

Welding (15 minutes)

Painting (12 minutes)

Packing (6 minutes)

Shearing (20 minutes)

Pressing (30 minutes)

Welding (15 minutes)

Painting (12 minutes)

Packing (6 minutes)

Pressing (30 minutes)

Hierarchies in capacity estimation

First operation

Fabrication Shop

Paint Shop

Electrical & Wiring

Assembly & Testing

Shearing Unit

Pressing Unit

Welding Unit

CNC Turret Press

Hydraulic Press

NC Press Brake

63 Tonne ECC Press

Denotes bottleneck in the process

Capacity Planning under uncertaintyUse of waiting line models

• Often demand placed on resources is uncertain making capacity requirement estimation difficult

• In such cases, waiting line models – make use of queueing theory fundamentals

– to analyse the impact of alternative capacity choices

– on important operational measures such as queue length, waiting time and utilisation of resources

• In service systems, waiting time is an important operational measure that determines the service quality – Computerised passenger reservation facility of Indian Railways

– Banking system or BSNL’s bill payment counters

Components of Queuing System

ArrivalsServer Served

customersWaiting

Line

Calling Populatio

n

Components of Queuing Systems

Calling Population

Arrival Parameters

System Structure & Parameters

Service Parameters

Infinite

Finite

Rate

Pattern

Markovian, General Distbn., Deterministic

Single, Bulk, Special group

Servers

Stages

Routing

Capacity

Single, Multiple

Single, Multiple

Single, Serial, Network

Finite, Infinite

Markovian, General Distbn., Deterministic

Performance Metrics

Queue length, Waiting time, Utilisation, Cost based

Queue Parameters

FCFS, LCFS, Random, Balk, Renege, Jog

Single-Channel Structures

Servers

Waiting line

Single-server, multiple stages

Waiting line Server

Single-server, single-stage

Multi-Channel Structures

Servers

Servers

Waiting line

Multiple-servers, single stage

Multiple-servers, multiple-stages

Single Server QueueFormulae for Lq

Lq =

Single server Queue

(Exponential service time)

Ls Average number of customers in the system (waiting to be served)

Lq Average number of customers in the waiting line

Ws Average time a customer spends in the system (waiting and being served)

Wq Average time a customer spends waiting in line

mean arrival rate

mean service rate

S Number of servers in a multi-server queue

Performance MetricsRelationships

Ws =Ls

Wq =

Average time customerspends in system

Average time customer spends in queue

Lq

Ls = Lq +

Average number of customers in system

Little’s Formula

S

Server utilisation

In the case of single server:

In the case of multiple servers:

In the case of a Single Server

Problem• The teller facility of a bank has a one-man operation at present.

Customers arrive at the bank at the rate of one every 4 minutes to use the teller facility. The service time varies randomly across customers on account of some parameters. However, based on the observations in the past, it has been found that the teller takes on an average 3 minutes to serve an arriving customer. The arrivals follow Poisson distribution and the service times follow exponential distribution.

– What is the probability that there are at most three customers in front of the teller counter?

– Assess the various operational performance measures for the teller facility.

– Of late the bank officials notice that the arrival rate has increased to one every three and a half minutes. What is the impact of this change in the arrival rate? Do you have any observation to make?

Solution to Problem

• Arrival rate at the bank: = = 15 per hour• Service rate at the teller: = = 20 per hour

• Utilisation of teller facility:

• Probability of at most three customers in the system =

• Using equation, we compute Pn for values of n = 0 to 3P0 = (1- ) = 0.25; P1 = 0.25*0.751 = 0.1875; P2 = 0.25*0.752 = 0.1406; P3 = 0.25*0.753 = 0.1055.

• Probability of at most 3 customers =0.25 + 0.1875 + 0.1406 + 0.1055 = 0.6836

75.020

15

3

0

n

nnP

Operational Performance Measures

Avg. No. of customers in the waiting line:

Avg. No. of customers in the system:

Avg. time a customer spends waiting in line:

Avg. time a customer spends in the system:

)(

2

qL

qs LL

q

q

LW

s

s

LW

Operational Performance Measures

Avg. No. of customers in the waiting line:

Avg. No. of customers in the system:

Avg. time a customer spends waiting in line:

Avg. time a customer spends in the system:

25.2)1520(20

15

)(

22

qL

00.320

1525.2

qs LL

min915.015

25.2 Hr

LW qq

min1220.015

00.3 Hr

LW ss

Impact of Arrival Rate

Arrival rate = 15 per hour

Arrival rate = 17.143 per hour

Utilisation of the teller facility 75% 85.7%

Avg. number of customers in waiting line

2.25 5.14

Avg. number of customers in the system

3.00 6.00

Average time a customer spends waiting in line

9 minutes 18 minutes

Average time a customer spends in the system

12 minutes 21 minutes

Capacity Design issue Flexibility/Utilization Trade-

off

Utilization () 100%0 Op

era

tional Perf

orm

an

ce

Measu

res

High utilizationLow cost of operationPoor service

Low utilizationHigh cost of operationGood service

Cost Relationship in QueuingE

xpe

cte

d c

ost

s

Level of service

Total cost

Service cost

Waiting Costs

Formulae For Lq

Three types of Queuing systems

Lq =

Single server QueueExponential service time

Lq =

Single server QueueGeneral service time

Lq =

=

=

Single server QueueDeterministic service time

Multi-Server QueuesApproximation for Lq based

on dataXa_ Mean Inter-Arrival Time

(IAT)Xs

_

Mean Service Time (ST)Sa Standard deviation of inter-arrival

timeSs Standard deviation of service timeCa Coefficient of variation of IATCs Coefficient of variation of ST

=_

Mean arrival rate = Xa

_1/

=Ss/Xs

_

Utilisation of the ‘s’ servers = S Mean service rate Xs

_

1/=

2*

)1(

22)1(2sa

S

qCC

L

Sa/Xa

Source: Chase, R.B, F.R. Jacobs, and N. J. Aquilano, (2003), “Operations Management for competitive advantage”, Tata McGraw Hill, 10th Edition, pp 261 – 262.

_

Capacity ManagementServices

Peak HourPeak Hour• Assemble to order• Service Portfolio

(narrow)• Demand Mgmt.

– Reservations

• Exploiting – Multi-skill labour– Flexible work force

Non-Peak HourNon-Peak Hour• Made to order• Service Portfolio

(wide)• Demand Mgmt.

– Special Tariffs, offers