30079_32a.pdf

CHAPTER 32

PRODUCTION PLANNING

Dennis B. Webster

Thomas G. Ray

Department of Industrial & Manufacturing Systems Engineering

Louisiana State University

Baton Rouge, Louisiana

32.1 INTRODUCTION 987

32.2 FORECASTING 988

32.2.1 General Concepts 988

32.2.2 Qualitative Forecasting 988

32.2.3 Quantitative Forecasting 988

32.2.4 Forecasting Error Analysis 993

32.2.5 Conclusions on Forecasting 994

32.3 INVENTORY MODELS 994

32.3.1 General Discussion 994

32.3.2 Types of Inventory Models 995

32.3.3 The Modeling Approach 996

32.4 AGGREGATE

PLANNING—MASTER

SCHEDULING 10 03

32.4.1 Alternative Strategies to

Meet Demand Fluctuation s 1003

32.4.2 Aggregate Planning Costs 1004

32.4.3 Approaches to Aggregate

Planning 10 04

32.4.4 Levels of Aggregation and

Disaggregation 10 05

32.4.5 Aggregate Planning

Dilemma 10 05

32.5 MATERIALS REQUIREMENTS

PLANNING 1006

32.5.1 Procedures and Required

Inputs 1006

32.5.2 Calculations 1010

32.5.3 Conclusions on MRP 1010

32.5.4 Lot-Sizing Techniques 1010

32.6 JOB SEQUENCING AND

SCHEDULING 1014

32.6.1 Structure of the General

Sequencing Problem 1014

32.6.2 Single-Machine Problem 1015

32.6.3 Flow Shops

1017

32.6.4 Job Shops

1018

32.6.5 Heuristics/Priority

Dispatching Rules 1020

32.6.6 Assembly Line Balancing 1023

32.7 OTHER RELATED TOPICS 1029

32.7.1 Japanese Manufacturing

Philosophy 1029

32.7.2 Time-Based Competition 1030

32.1 INTRODUCTION

Changes that were unforeseen prior to the 1970s are now sweeping the field of manufacturing.

Competition from outside the United States is driving the forces of change. There is a relentless push

for improvement in total quality, which includes the quality of service to the customer. Service to

the customer is related to two concepts: the delivered product quality and the timeliness of customer

service.

The topics discussed in this section relate primarily to the second concept of customer service,

timeliness. These topics relate either directly or indirectly to accomplishing the job in a timely

manner. Forecasting, for example, provides the manufacturer with a basis for anticipating consumer

demand so as to have adequate product on hand when it is demanded. Of course, the preferred

approach would be to wait for a customer order and then produce and ship immediately when the

order arrives. This approach is, for practical purposes, impossible for products with any significant

lead time. What the manufacturer must do is to perform as well or better than his competition for

the business area.

Job sequencing is an approach to reduce the completion times of the jobs to be performed.

Materials requirements planning (MRP) is a technique for assuring that adequate inventory is available

to complete the work required on products needed to meet a customer schedule. Inventory models

are used in an effort to provide components for a manufacturing process in a timely manner at

minimum cost when the demand for the item is constant.

Mechanical Engineers' Handbook, 2nd ed., Edited by Myer Kutz.

In a similar manner, each of the topics in this section relates to the subject of meeting customer

demand, on time and at the lowest cost possible.

32.2 FORECASTING

32.2.1 General Concepts

The function of production planning and control is based upon establishing a plan, revising it as

required, and adhering to it to accomplish desired objectives. Plans are based upon a forecast of

future demand for the related products or services. Good forecasts are a requirement for a plan to

be valid and functionally useful. Managers, when faced with a forecast, plan what actions must be

taken to meet the requirements of the forecast. These actions prepare the organization to cope with

the anticipated future state of nature that is predicated upon the forecast.

Forecasting methods are traditionally grouped into one of three categories: qualitative techniques,

time-series analysis, or causal methods. Qualitative techniques are normally based on opinions or

surveys. Time-series analysis is based on historical data and the study of its trends, cycles, and

seasons. Causal methods try to find relationships between independent and dependent variables,

determining which variables are predictive of the dependent variable of concern. The method selected

for forecasting must relate to the type of information available for analysis.

Definitions

DESEASONALIZATION. The removal of seasonal effects from the data for the purpose of further

study of the residual data.

ERROR ANALYSIS. The evaluation of errors in the historic forecasts, done as a part of forecasting

model evaluation.

EXPONENTIAL SMOOTHING. An iterative procedure for the fitting of polynomials to data for use

in forecasting.

FORECAST. Estimation of a future outcome.

HORIZON. A future time period or periods for which a forecast is required.

INDEX NUMBER. A statistical measure used to compare an outcome which is measured by a cardinal

number with the same outcome in another period of time, geographic area, profession, etc.

MOVING AVERAGE. A forecasting method in which the forecast is an average of the data for the

most recent n periods.

QUALITATIVE FORECAST. A forecast made without using a quantitative model.

QUANTITATIVE FORECAST. A forecast prepared by the use of a mathematical model.

REGRESSION ANALYSIS. A method of fitting a mathematical model to data by minimizing the sums

of the squares of the data from a theoretical line.

SEASONAL DATA. Data that cycle over a known seasonal period, such as a year.

SMOOTHING. A process for eliminating unwanted fluctuations in data; normally accomplished by

calculating a moving average or a weighted moving average.

TIME-SERIES ANALYSIS. A procedure for determining a mathematical model for data correlated

with time.

TIME-SERIES FORECAST. Forecast prepared with a mathematical model from data correlated with

time.

TREND. Underlying patterns of movement of historic data that become the basis for prediction of

future forecasts.

32.2.2 Qualitative Forecasting

These forecasts are normally used for purposes other than production planning. Their validity is more

in the area of policy-making or in dealing with generalities to be made from qualitative data. Among

these techniques are the Delphi method, market research, consensus methods, and other techniques

based upon opinion or historic relationships other than quantitative data.

The Delphi method is one of a number of nominal group techniques. It involves prediction with

feedback to the group that gives the predictor's reasoning. Upon each prediction, the group is again

polled to see if a consensus has been reached. If no common ground for agreement has occurred,

the process continues moving from member to member until agreement is reached.

Surveys may be conducted of relevant groups and their results analyzed to develop the basis for

a forecast. One group appropriate for analysis is customers. If a company has relatively few customers,

this select number can be an effective basis for forecasting. Customers are surveyed and their re-

sponses combined to form a forecast.

Many other techniques are available for nonquantitative forecasting. An appropriate area to search

if these methods seem relevant to a subjective problem at hand is the area of nominal group

techniques.

32.2.3 Quantitative Forecasting

Quantitative forecasting involves working with numerical data to prepare a forecast. This area is

further divided into two subgroups of techniques, according to the data type involved. If historic data

are available and it is believed that the dependent variable to be forecast relates only to time, time-

series analysis is used. If the data available suggest relationships of the dependent variable to be

forecast to one or more independent variables, then the techniques used fall into the category of

causal analysis. The most commonly used method in this group is regression analysis.

Methods of Analysis of Time Series

The following material will discuss in general several methods for analysis of time series. These

methods provide ways of removing the various components of the series, isolating them, and pro-

viding information for their consideration should it be desired to reconstruct the time series from its

components.

The movements of a time series are classified into four types: long-term or trend movements,

cyclical movements, seasonal movements, and irregular movements. Each of these components can

be isolated or analyzed separately. Various methods exist for the analysis of the time series. These

methods decompose the time series into its components by assuming that the components are either

multiplicative or additive. Assuming that the components are multiplicative, the following relationship

holds:

Y=TxCXSx/

Where Y is the outcome of the time series, T is the trend value of the time series, and C, S, and 7

are indices respectively for cyclical, seasonal, and irregular variations.

To process data for this type of analysis, it is best first to plot the raw data in order to observe

their form. If the data are yearly, they need no deseasonalization. If the data are monthly or quarterly,

they can be converted into yearly data by summing the data points that would add to a year before

plotting. (Seasonal index numbers can be calculated to seasonalize the data later if required.) By

plotting yearly data, the period of apparent data cycles can be determined or approximated. A centered

moving average of appropriate order can be used to remove the cyclical effect in the data. Further,

cyclical indices can be calculated when the order of the cycle has been determined. At this point,

the data contain only the trend and irregular components of variation. Regression analysis can be

used to estimate the trend component of the data, leaving only the irregular, which is essentially

forecasting error.

Index Numbers. Index numbers are calculated by grouping data of the same season together,

calculating the average over the season for which the index is to be prepared, and then calculating

the overall average of the data over each of the seasons. Once the seasonal and overall averages are

obtained, the seasonal index is determined by dividing the seasonal average by the overall average.

Example Problem 32.1

A business has been operational for 24 months. The sales data in thousands of dollars for each of

the monthly periods are as shown in Table 32.1.

Table 32.1

Yearl

Year 2

Jan.

Feb.

Mar.

Apr.

May

Jun.

Jul.

Aug.

Sep.

Oct.

Nov.

Dec.

The overall average is 584 divided by 24, or 24.333. The index for January would be

= (20 + 24)

Jan ~~ 24.333

- .904

The index for March would be

= (28 + 30)

Mar 24.333

- 1.192

To use the index, a trend value for the year's sales would be calculated, the average monthly sales

would be obtained, and then this figure would be multiplied by the index for the appropriate month

to give the month's forecast.

It should be noted that a season can be defined as any period for which the data is available for

appropriate analysis. If there are seasons within a month, i.e., four weeks in which the sales vary

considerably according to a pattern, a forecast could be indexed within the monthly pattern also. This

would be a second indexing within the overall forecast. Further, seasons could be chosen as quarters

rather than months or weeks. This choice of the period for the analysis is dependent upon the

requirements for the forecast.

Data given on a seasonal basis can be deseasonalized by dividing them by the appropriate seasonal

index. Once this has been done, they are labeled deseasonalized data. They still contain the trend,

cyclical, and irregular components after this adjustment.

Moving Average. A moving average can normally be used to remove the seasonal or cyclical

components of variation. This removal is dependent upon the choice of a moving average that contains

sufficient data points to bridge the season or cycle. For example, a seven-period-centered moving

average should be sufficient to remove seasonal variation from monthly data. A disadvantage to the

use of moving averages is the loss of data points due to the inclusion of multiple points into the

calculation of a single point. For the monthly data related to the calculation of index numbers given

in the previous section, only the months of April of Year 1 through September of Year 2 would be

available for analysis when a seven-month-centered moving average is used. Six data points are not

available for calculation due to the requirements of the method.

Example Problem 32.2

See Table 32.2. Note that in this case the five-year moving average lost four data points, two on each

end of the data series. Observation of the moving average indicated a steady downward trend in the

data. The raw data had fluctuations that might tend to confuse an observer, initially due to the apparent

positive changes from time to time.

Weighted Moving Average. A major disadvantage of the moving average method, the effect of

extreme data points, can be overcome by using a weighted moving average. In this average, the effect

of the extreme data points may be decreased by weighing them less than the data points at the center

Table 32.2

5-Year

Moving Total

5-Year

Moving Average

Year

Data

56.5

53.0

54.6

51.2

53.9

48.4

49.1

48.3

42.4

44.6

275.3

269.2

261.1

257.2

250.9

242.1

232.8

55.1

53.8

52.2

51.4

50.2

48.4

46.6

Table 32.3

5-Year

Moving

Total

5-Year Total

Less Center

Value

Weighted Average

(.5 Col 2/4 + .5 Col 4)

Year

Data

56.5

53.0

54.6

51.2

53.9

48.4

49.1

48.3

42.4

44.6

275.3

269.2

261.1

257.2

250.9

242.1

232.8

222.3

214.6

209.9

203.3

202.5

193.0

184.5

54.3

54.1

51.8

52.4

49.5

48.7

47.2

of the group. There are many ways to do this. One method would be to weight the center point of

a five-period average as 50% of the total, with the remaining points weighted for the remaining 50%.

For the example in the previous section, the yield would be as shown in Table 32.3.

Example Problem 32.3

See Table 32.3.

Table 32.4 displays the two forecasts. The results are very comparable, with the weighted average

forecast distinguishing a slight upswing from period 5 to 6 that was ignored by the moving average

method.

Exponential Smoothing. This method determines the forecast (F) for the next period as the

weighted average of the last forecast and the current demand (Z)). The current demand is weighted

by a constant a and the last forecast is weighted by the quantity 1 — a (0 ^ a < 1.0).

new forecast = a (demand for current period) + (1 — a) (forecast for current period)

This can be expressed symbolically as

Ft = a D,_! + (!-<*) F,_!

Normally the forecast for the first period is taken to be the actual demand for that period (i.e.,

forecast and demand are the same for the initial data point). The smoothing constant is chosen as a

result of analysis of error by a method such as mean absolute deviation coupled with the judgment

of the analyst. A high value of a makes the forecast very responsive to the occurrence in the last

period. Similarly, a small value would lead to a lack of significant response to the current demand.

Evaluations must be made in light of the cost effects of the errors to determine what value of a is

best for a given situation. The following example problem shows the relationship between actual data

and forecasts for various values of a.

Table 32.4

Moving Average

Forecast

55.1

53.8

52.2

51.4

50.2

48.4

46.6

Weighted Average

Forecast

54.3

54.1

51.8

52.4

49.5

48.7

47.2

Period

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