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4 Work Study

A firm must plan its manufacturing

activities at a variety of levels and

operate these as a system. Aggregate

planning is medium-range capacity

planning which typically covers a time

horizon of anywhere from three to 18

months. The goal of aggregate

planning is to achieve a production

plan which will effectively utilize the

organization’s resources to satisfy

expected demand. Planners must make

decisions on output rates, employment

levels and changes, inventory levels

and changes, back orders, and

subcontracting. Aggregate planning

determines not only the output levels

planned but also the appropriate

resource input mix to be used.

Aggregate planning might seek to

influence demand as well as supply. If

this is the case, variables such as price,

advertising, and product mix might be

used. If changes in demand are

considered, then marketing, along with

operations, will be intimately involved

in aggregate planning.

Aggregate planning is essentially a

big-picture approach to planning.

Planners generally try to avoid

focusing on individual products or

services unless, of course, the

organization has only one major

product or service. Instead, they focus

on overall, or aggregate, capacity.

Aggregate planning is closely related

to other corporate decisions involving,

for example, budgeting, personnel, and

marketing. The relationship to

budgeting is a particularly strong one.

Most budgets

assumptions about aggregate output,

personnel levels, inventory levels,

purchasing levels, etc. An aggregate

plan should thus be the basis for initial

budget development and for budget

revisions as conditions warrant.

A majority of aggregate planning

approaches incorporate continuous

decision variables and require frequent

adjustments to both production and

workforce settings. Despite the

availability and diversity of these

approaches, few

applications have been reported.

are based on

significant

Complex models with restrictive

assumptions and infeasible decisions

are cited as contributing to the lack of

acceptance of aggregate planning in

the business environment[1].

Aggregate planning in

perspective

Characteristics of aggregate

planning

In the broad sense of the definition, the

aggregate-planning problem[2] has the

following characteristics:

●

a time horizon of about 12 months,

with updating of the plan on a

periodic basis (perhaps monthly);

●

an aggregate level of product

demand consisting of one or a few

categories of product – the

demand is assumed to be

fluctuating, uncertain, or seasonal;

●

the possibility of changing both

supply and demand variables;

●

a

objectives which might include

low inventories, good labour

relations, low costs, flexibility to

increase future output levels and

good customer service;

variety of management

●

facilities that are considered fixed

and cannot be expanded.

Aggregate

important link between facilities

planning on the one hand and

scheduling on the other. Facilities

planning determines the physical

capacity which cannot be exceeded by

aggregate planning. Thus facilities

planning extends further into the future

than aggregate planning and constrains

the aggregate-planning decisions.

Scheduling, on the other hand, refers to

the short range (a few months or less)

and is constrained by aggregate-

planning decisions. While aggregate

planning deals with the acquisition of

resources, scheduling is concerned

with allocating available resources to

specific jobs and orders. Thus, a basic

distinction should be made between

planning forms an

acquiring resources through aggregate

planning and allocating them through

scheduling.

Decision options

The aggregate-planning problem can

be clarified by a discussion of the

various decision options available.

These will be divided into two types:

(1) those modifying demand;

(2) those modifying supply.

Demand can be modified or influenced

in several ways:

●

pricing;

●

advertising and promotion;

●

backlog or reservation;

●

development of complementary

products.

There are also a large number of

variables available to modify supply

through aggregate planning[3]. These

include: hiring and layoff of

employees; using overtime and

undertime; using part-time or

temporary labour; carrying inventory;

subcontracting; and making co-

operative arrangements.

In considering all these options, it is

clear that an aggregate-planning

problem is extremely broad and affects

all parts of the firm. The decisions

which are made must, therefore, be

strategic and reflect all the firm’s

objectives. Some of the multiple trade-

offs which should be considered are

customer service level (through back

orders or lost demand), inventory

levels, stability of the workforce and

costs.

Basic strategies

There are a number of strategies[4]

which aggregate planners might adopt.

Some of the more prominent ones are:

maintain a level workforce;

maintain a steady output rate;

match demand period by period;

use a combination of decision

variables.

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●

●

●

Aggregate planning today

Lin Pan and Brian H. Kleiner

CONTRIBUTED PAPERS

Vol. 44 No. 3, 1995, pp. 4-7, © MCB University Press, 0043-8022

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The first three strategies are pure

strategies in that each has a single focal

point; the last strategy is a mixed one.

Under the level workforce strategy,

variations in demand are met by using

some combination of inventories,

overtime, part-time

subcontracting, and back ordering.

Maintaining a steady rate of output

implies absorbing demand variations

with inventories, subcontracting, or

backlogging. Matching capacity to

demand implies a “chase” strategy; the

planned output for any period would be

the expected demand for that period.

Whatever strategy an organization is

considering, two important factors are

company policy and costs. Company

policy may set constraints on the

available options or the extent to which

they can be used. As a general rule,

aggregate planners seek to match

supply and demand within the

constraints imposed on them by

policies or agreements and at a

minimum cost.

workers,

Aggregate-planning costs

When demand is considered given, the

following costs[3]

considered:

should be

●

hiring and layoff costs;

●

overtime and undertime costs;

●

inventory carrying costs;

●

subcontracting costs;

●

part-time labour costs;

●

cost of stockout and back order.

Some or all of these costs may be

present in any particular aggregate-

planning problem. The applicable costs

will be used to select alternative

strategies.

Review of aggregate-planning

models

Overview of models

Essentially, the aggregate-planning

problem can be stated as follows: given

a set of forecasts (Ft), determine

production, inventory, and workforce

levels (Pt, It, and Wt, respectively),

t = 1,2, ..., N, which minimizes cost

subject to appropriate constraints.

Typically, the planning is done on a

monthly basis over a six-to-18-month

horizon, N. Most of the existing

aggregate-planning models found in

the literature try to minimize an

objective function representing “total

relevant costs”.

At first, based on intuitive feasible

solutions, Barter and Graphs are used

as simple methods[5].

Based on explicit cost, the three

classic analytic optimization methods –

the linear decision rule, the transport

method, and the linear programming –

have traditionally assumed deter-

ministic demand. These methods

further require the estimation of

several uncertain, obscure costs

(hiring, firing, shortage, carrying, etc.)

and impose rigid cost functions[5].

“Goalnn

programming

attempts to

minimize the

deviations from

prioritized

goals”

The cost-based simulation and

heuristics models more adequately

reflect specific conditions. An

iterative, trial-and-error procedure is

used to find minimum total variable

costs. The simulation model, while

more flexible than optimization

models, ensures only local (rather than

global) optimization. Other cost-based

heuristics include

production planning, the search

decision rule, and the more recent

production-switching heuristic. All of

these models tend to sacrifice

mathematical optimality in favour of

less rigid cost functions and more

realistic models. What management

actually wants is a tool to assist them in

planning and decision making. To this

end, firms were found to prefer a

deterministic simulation model over

the more elegant optimal or near-

optimal solution approaches. A cost

simulation with stochastic demand

model called the production decision

framework has been developed[5].

All models for aggregate planning

discussed above depend on the

estimation of a number of cost

parameters. Some other approaches –

parametric

which do not require explicit cost

parameter estimates – bring us closer to

the model to be proposed here. Based

on implicit costs, the management

coefficients model focuses on making

decisions consistent rather than

mathematically optimal. This approach

uses linear regression of historical

decision variables to determine

preferred sets of coefficients. To

accommodate the multiple and often

conflicting objectives inherent in

aggregate production-planning

decisions, goal programming, an

extension of linear programming,

attempts to minimize the deviations

from prioritized goals and to get away

from rigid cost formulations.

Techniques for aggregate

planning

There are numerous techniques which

can be used to help decision makers

with the task of aggregate planning.

Approaches vary from simplistic,

graphical methods to the highly

sophisticated linear decision rule and

the parametric production-planning

method. The most sophisticated

techniques can be classified as

optimizing, search, heuristic, and

dynamic methods. Within each of these

categories are numerous alternative

approaches, resulting in an abundance

of theoretical solution procedures. The

following are some of the common

techniques used:

●

Informal techniques. These

approaches consist of developing

simple tables or graphs which

enable planners to compare

projected demand requirements

visually with existing capacity,

and this provides them with a basis

for developing alternative plans

for achieving intermediate-range

goals. Alternatives are usually

evaluated in terms of their overall

costs. The chief disadvantage of

such techniques is that they do not

necessarily result in an optimum

aggregate plan.

●

Mathematical techniques. A

number of

techniques[6] have been proposed

over the last two decades to handle

aggregate planning.

mathematical

●

Linear

extensions.

assumptions the setting of

production rates and workforce

sizes can be viewed as a linear

programming problem. A linear

programming

Under

and

certain

WS May/June, 1995 5

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programming problem consists of

selecting the values for several

non-negative variables so as to

minimize a linear function (the

total relevant costs) of these

variables subject to several linear

constraints on the variables.

One of the basic weaknesses of

linear programming is the

assumption of determinism; in

most applications there is

considerable uncertainty in the

forecasts of demand. Another

shortcoming is the requirement of

linear cost functions. An important

benefit of a linear programming

model is the potential use of the

dual solution to obtain the implicit

costs of constraints such as the

maximum allowable inventory

level.

There are several extensions

which have been made to the basic

linear programming model: the

removal of convexity and/or

inclusion of a set-up type cost;

inclusion of many products;

production at several locations;

worker productivity and wages;

and inclusion of effects of the

detailed scheduling that will

follow in the short run.

●

Linear decision rule. When

various costs can be approximated

by linear and quadratic functions it

turns out that the decision rules[6]

for setting the workforce sizes and

production rates are of simple

linear form. The objective of this

method is to derive linear

equations or “decision rules”

which can be used to specify the

optimal production rate and

workforce level over some

prescribed production planning

horizon.

The linear decision rule has

been shown to lead to costs

significantly lower than those

encountered under the existing

management procedure. The

behaviour of the rule is quite

insensitive to errors in estimating

the cost coefficients. However,

one potential drawback of the

linear decision rule is that the costs

may not be really quadratic.

Another drawback is that the

model does not allow for costs of

changing production

workforce levels which depend on

the point of departure. Finally,

there is no easy way of including

constraints on the inventory or

production levels.

and

●

Heuristic

techniques. A broad definition of

this term would be methods which

help the decision maker learn from

his or her own experience and

facilitate the development of

procedures by which complicated

problems can be satisfactorily

solved.

and simulation

●

Management coefficients app-

roach. It assumes that managers

behave in a rational fashion. Past

behaviour of managers is used to

estimate the unknown coefficients

in plausible decision rules.

The strong point of this method

is that it has intuitive appeal to

management.

implementation

easier than in the case of a

sophisticated

decision model. A serious

drawback is the essentially

subjective selection of the form of

the rule. The assumption that the

past is a good description of the

future may prevent the manager

from quickly adapting to new

conditions in a rapidly changing

competitive environment.

This

considerably

makes

mathematical

●

Simulation search procedures. The

philosophy here is that a closed-

form mathematical solution

cannot be obtained when the

model is made truly representative

of the prototype situation.

Therefore, a mathematical model

is developed which represents

quite accurately the actual cost

functions and constraints. Then,

by a trial and error procedure, the

variables are varied until there

results no further reduction in the

total relevant costs. A computer is

often used to facilitate this search

procedure. These procedures

include search decision rule,

parametric production planning,

and a manual simulation approach.

New developments in

aggregate planning

A reformulation of the aggregate-

planning problem

Reformulation of the aggregate-

planning problem[5,7] will more

closely agree with situations frequently

encountered in practice. The proposed

reformulation assumes that a firm’s

production planners want to determine

the expected service and inventory

levels for a given production profile in

the face of uncertain seasonal demand.

By using several different production

profiles which are each consistent with

the firm’s staffing, subcontracting, and

overtime policies, it is possible to pick

the profile that best meets the firm’s

preferences for service level and

inventory turns. Actually, the trade-offs

between inventory and service level

are examined so that an informed

choice can be made by all those

concerned.

While most methods rely on explicit

cost estimates, this method proposes an

approach which utilizes inventory/

service level trade-offs to facilitate

effective aggregate planning. One of

the advantages is that communications

can be established among production,

marketing, and finance managers who

often have conflicting goals. Also,

levels for inventory turns, service, and

production can be set which are

consistent with one another. Further-

more, several alternative production

profiles can be examined in a relatively

short time through the use of the

simulation model.

Production decision framework – a

heuristic method

The production decision framework[7]

is a dynamic model proposed to assist

the manager in the planning process.

Emphasis was placed on developing a

logical, understandable, and straight-

forward model.

“The planningnn

problem is

subdivided into

one of nine

states”

The development phase utilizes a ratio,

named RPCC, which represents the

relative value of the cost of changing

the production level to the cost of

carrying inventory. This ratio is used to

determine the length of an effective

planning horizon. Two indicators, the

current period ratio and the planning

horizon ratio, are calculated to reflect

the demand to current production rate

over different time periods. Based on

6 Work Study

Page 4

the joint values of these indicators, the

planning problem is subdivided into

one of nine mutually exclusive and

exhaustive states. A set of action

statements, representing logical

responses to each of the subproblems,

is formulated.

A discrete production-switching rule

The trend towards high-volume batch

and continuous flow process within

American manufacturing has resulted

in increasing numbers of crew-loaded

facilities. Most available aggregate-

planning models contain continuous

variables and require frequent

adjustments to both production and

workforce settings.

The production-switching rule[8]

was developed to accommodate

discrete production environments

which rely on crew loading. Inventory

costs are estimated using an interval

approach rather than traditional point

estimates. The

incorporation of overtime options and

is interactive in nature. Decision

variables from the model can be

disaggregated and linked directly to

lower-level planning activities.

model allows

Improved hierarchical production

planning

The hierarchical approach, by

partitioning the problem into a series of

subproblems, is able to reduce the

complexity of the solution process,

trading off mathematical optimality for

good, feasible solutions with reduced

costs. Such an approach is desirable in

practice.

The improved

production-planning model[9] consists

of four modules:

hierarchical

(1) forecasting;

(2) aggregate production planning;

(3) disaggregate production planning;

(4) sequencing.

When no forecasts for individual

products are provided, the improved

hierarchical production-planning

model overcomes this weakness by

appending a front-end forecasting

module. In addition to reducing direct

costs, this model provides efficient

tools to aid managers in their decision-

making process. It is not confined to

one decision level only; in fact, middle

management, production-planning

personnel, schedulers, etc. can all

benefit from the use of the various

modules within the hierarchical

production-planning system.

Conclusion

Intermediate-range planning est-

ablishes general levels of employment,

output, and inventories for periods of

two months to one year. In the

spectrum of planning, it falls between

the broad design decisions of long-

range planning and the very specific

and detailed short-term planning

decisions. It begins with an overall

forecast for the planning horizon and

ends with preparations for applying the

plans to specific products and services.

The essence of intermediate

planning is the aggregation of products

or services into one product or service.

This permits planners to consider

overall levels of employment and

inventories without having to become

involved with specific details which

are better left to short-range planning.

Obviously, no one aggregate-

planning decision model can capture

all the nuances of a complex

manufacturing environment. However,

to be realistic, a model must reflect the

realities of the production environment

in which it is to be used. It appears that

the complexity and the restrictive

assumptions of these techniques limit

their widespread acceptance in

practice. Attention must also be

focused on providing managers with

the tools necessary to calculate the

appropriate costs that are used as inputs

to these models.

References

1. DuBois, F.L. and Oliff, M.D.,

“Aggregate production planning in

practice”, Production and Inventory

Journal, Third Quarter, 1991, pp.

26-30.

2. Schroeder, R.G., Operations Man-

agement, McGraw-Hill, New York,

NY, 1985.

3. Stevenson,

Operations Management, Irwin,

Homewood, IL, 1986.

4. Chase, R.B. and Aquilano, N.J.,

Production

Management, Irwin, Homewood, IL,

1985.

5. Schroeder, R.G. and Larson, P.D.,

“A reformulation of the aggregate

planning problem,” Journal of

Operations Management, Vol. 6 No.

3, May 1986, pp. 245-56.

6. Silver, E.A.,

aggregate production planning: state

of the art”, Production and Inventory

Management, First Quarter, 1972,

pp. 15-39.

7. Holt, J.A., “A heuristic method for

aggregate planning: production

decision framework”, Journal of

Operations Management, Vol. 2 No.

1, October 1981, pp. 41-51.

8. Oliff, M.D. and Leong, K., “A

discrete production-switching rule

for aggregate planning”, Decision

Sciences, Vol. 18 No. 4, 1987, pp.

582-97.

9. Leong, K. and Oliff, M.D.,

“Improved hierarchical production

planning”, Journal of Operations

Management, Vol. 8 No. 2, 1989, pp.

90-114.

W.J., Production/

and Operations

“Medium-range

WS May/June, 1995 7

Lin Pan and Brian H. Kleiner are based at

the Department of Management, School of

Business Administration and Economics,

California State University Fullerton,

Fullerton, California, USA.