BDPA IT Showcase: Production Planning Tools

Production Planning Tools
JESSYE BEMLEY
AND
BENIKA JOHNSON

NORTH CAROLINA A&T STATE UNIVERSITY
GREENSBORO, NC

Introduction
Many companies have different products that they use or make on a regular basis. To help them through
this process they use different production planning tools such as forecasting, Materials Requirement
Planning System (MRP), Linear Programming, Inventory plan and Aggregate Plan or workforce plan.
During INEN 355 or Production Control class we were given a case study project of a company called
Mike’s Bikes. From the information given, we were to use all of the tools listed above to help the owner of
the company have a successful business.

Forecasting: Basic Characteristics
Most companies use forecasting to determine future sales and demand to predict how they will profit in the
coming year. Forecasting methods can be classified as either subjective or objective. Subjective forecasting
methods are based on human judgment while objective forecasting methods derive the forecasts from
analyzed data. There are five characteristics that categorize forecasts: 1.) Forecasts are usually wrong, 2.) A
good forecast has some measure of error, 3.) The longer the forecast horizon the less accurate the forecast,
and 4.) All information should be included into forecasts.

Different Forecasting Methods

Moving Average

Moving averages take the arithmetic average of the most recent N periods. The forecast is given by
t −1
Ft = (1 / N ) ∑D
i =t − N
i = (1 / N )( Dt −1 + Dt −2 +  + Dt − N ) . This example shows a forecast with a
moving average of 3. Period Demand MA(3)
1 300
2 150
3 425
4 70 875
5 227 645
6 387 722
7 100 684
8 290 714

Exponential Smoothing

In exponential smoothing the current forecast is the weighted average of the last forecast and demand
value. What is happening is
NewForecast = α (Current observation of demand ) + (1 − α )( Last forecast ) . In symbols
the equation would read Ft = αDt −1 + (1 − α ) Ft −1 .

Period Demand ES(.1)
1 300 300
2 150 165
3 425 399
4 70 102.9
5 227 214.59
6 387 369.759
7 100 126.9759
8 290 273.6976

This table shows a forecast with an exponential smoothing constant of (.1).

Regression Analysis

Regression analysis fits a straight line over a set of data to show a trend. This straight line is computed by
ˆ
Y = a + bX . Next we have to determine the slope and intercept which can found by the next two
S xy
equations: b= ; a = D − b( n + 1) / 2 . To find our regression parameters we use:
S xx
n
n( n + 1) n
∑ Di ; S xx = n (n + 16 2n + 1) − n (n4+ 1) .
2 2 2
)(
S xy = n∑ iDi −
i =1 2 i =1

Forecast for Mike’s Bikes

For our project we used a subjective forecasting method called Winters’ Model. Winters’ Model is used
for a seasonal series. Seasonal series have a pattern that repeats after some value of N periods. The
Winters’ Model consists of three exponential smoothing equations that can be used as information is
updated. The three equations represent the series, the trend and the seasonal factors. To begin the process
we need initial estimates of at least two seasons. From this data we can calculate the sample means for both
−N 0
1 1
sets of data. The calculations are as follows: V1 =
N
∑ D j ; V2 =
j = −2 N +1 N
∑D
j = − N +1
j . Next, we define the

initial slope that connects mean 1 to mean 2. This can be found by using this equation Go = (V2 − V1 ) / N
. Then we find the estimated value of the series of time at time zero by the given equation
S o = V2 + Go [( N − 10 / 2] . Last we determine the initial seasonal factors that can be computed for each
period and then averaged to get the set seasonal factors. This equation calculates the seasonal factors
Dt
ct = .
Vi − [( N + 1) / 2 − j ]Go

Table 1. Below is an example of how we found each of these factors.

2005
Demand
110 117 V1= 122.5
127
113
133
2007
Demand
110 141 V2= 146
136
122
185

Go= 5.875
So= 154.8125

New C Norm.
c-7 1.029137 c-3 1.028464 0.949089
c-6 1.117097 c-2 1.054221 0.972858
c-5 0.993953 c-1 0.992648 0.916038
c-4 1.169874 c-0 1.259196 1.162015
c-3 1.02779 Sum= 4.334529 4
c-2 0.991344
c-1 0.889294
c-0 1.348519

F 0,1 152.5068
F 0,2 162.0417
F 0,3 157.9593
F 0,4 207.2017
F 0,5 174.8104
F 0,6 184.9039
F 0,7 179.4862
F 0,8 234.5091

Aggregate Planning

After being in business for a while companies need to take a look at their workforce and production line.
Using an aggregate plan allows them to determine when to hire, fire workers and also determine the mix or
quantity of products being manufactured. To begin making an aggregate plan we have to determine the
aggregate unit. An aggregate unit is when items on a production line are similar. This can be calculated by
Production rate/#of workers. There are two different plans you can use to calculate an aggregate plan zero
inventory and constant workforce. A zero inventory plan changes the workforce each month in order to
produce the amount of units that are close to demand pattern. A constant workforce plan tries to maintain a
constant workforce to satisfy the net demand. For the purposes of our project we used the zero inventory
plan. Under this plan we found the cumulative demand, number of aggregate units/ worker, minimum
workers, workers hired, and workers fired. Once all these factors were calculated we can created a linear
program to give us an optimal cost to see which model would be the best to use. There are many programs

that can be used to create a linear program such as GAMS, LINGO, LINDO and Excel. Below is an
example of the linear program we used to find the minimized cost using Microsoft Excel.

MinC h ( H 1 + H 2 + H 3........) + C f ( F1 + F 2 + F 3 + .........) + C I ( I1 + I 2 + I 3 + ............)

Subject to: I1= Inventory in stock + P1- Demand
I2= I1 + P2 - Demand
I3= I2 + P3 - Demand

P1= W1*K*# of working days/month

W1=beginning #of workers+ H1 - F1
W2= W1 + H2 - F2
W3=W2 + H3 - F3

I1>=buffer
I2>=buffer
I3>=buffer

All variables>=0

Materials Requirements Planning System

This systems allows personnel to plan when materials should arrive that are needed to make certain
products. There are three phases to this system. The first phase is getting the information needed to make
the Master Production Plan also known as a Bill of Materials. This shows the amounts and timing of
production for each item.
Figure 1. Shows an example of a Bill of Materials.

110

A(2) C(1)

D(2) E(3)

Lead Lot On Safety
Item time Size Hand Allocation Stock
110 3 1 31 10 20
A 2 50 56 0 30

C 1 50 23 0 10
D 2 150 118 0 100
E 1 250 160 0 150

Table 2. Shows the amount and timing of items produced.

The next phase of the MRP is to determine the amount of planned ordered receipts. Phase 3 is the
development of detailed shop floor schedules and resources requirements based on the planned order
receipts. Below is an example of the MRP. Safety Stock
Lead Time

Low level
Allocated
On Hand
Lot Size

Item
PD 1 2 3 4 5 6 7 8

Gross requirements 0 0 0 0 0 0 0 235
Scheduled receipts 0 0 0 0 0 0 0 0
Projected on hand 1 1 1 1 1 1 1 1 0
1 3 31 20 10 0 110
Net requirements 0 0 0 0 0 0 0 234
Planned order receipts 0 0 0 0 0 0 0 234
Planned order releases 0 0 0 0 234 0 0 0
PD 1 2 3 4 5 6 7 8
1 4 22 20 0 0 210
PD 1 2 3 4 5 6 7 8
50 2 56 30 0 1 A
PD 1 2 3 4 5 6 7 8
100 2 78 50 0 1 B
PD 1 2 3 4 5 6 7 8
50 1 23 10 0 1 C
PD 1 2 3 4 5 6 7 8
150 2 118 100 0 2 D
PD 1 2 3 4 5 6 7 8
250 1 160 150 0 2 E
PD 1 2 3 4 5 6 7 8

Inventory Control

Basics of Inventory

It is important for businesses or companies to keep a record of what items or products they have in
inventory. Inventory can be classified into four different types raw materials, components, Work-in-
process, and finished goods. Raw materials are the resources needed to produce a product. Components are
either raw materials or subassemblies that will be included in the final product. Work-in-process is
inventory in the plant waiting to be processed. Finished goods are completed and waiting to be shipped out
to distributors. There are different characteristics that describe inventory systems such as pattern of

demand, replenishment lead times, review times, and treatment of excess demand. The pattern of demand
can either be a constant versus variable which assumes that the demand is constant and the known versus
random assumes the demand is constant but still random which means it still has some uncertainty. The
lead time tells us the exact amount of time it takes to receive an item from when its order was placed.
Review time allows time to accurately record inventory levels at all times. Excess demand is how the
system reacts to having more inventory than the systems can handle. Three different costs are associated
with inventory holding, order, and penalty costs. These costs are used to help with different inventory
models to minimize costs.

Different Inventory Models

Economic Order Quantity
One model that is used for known demand is the Economic Order Quantity Model or (EOQ). This system
deals with products that are already made to buy. This model assumes that the demand is known and
constant. Shortages are not permitted. There is no order lead time. It has setup, order and holding costs. The
basic job for this model is to determine the optimal quantity order or Q*. First, the total annual cost is
Kλ hQ
calculated G (Q ) = + λc + . From this we can find the optimal Q* by using this equation
Q 2
2 Kλ
Q* = .
h

Quantity Discount Model
In the EOQ model cost is independent of the size of the order. But, using the quantity discount model the
supplier will charge less based on the retailer or customer buying a higher batch of products. There are two
types of discounts that can be applied to all units, fixed and incremental which applies the discount to
anything addition or beyond the breakpoint.
All units use a similar equation like the EOQ but has, a fixed order cost and interest rate defined as:
G j (Q) = λc j + λK / Q + Ic j Q / 2 . The incremental discount uses a piece wise type of function and the
Go (Q) for 0 ≤ Q < t

G (Q) = G1 (Q) for t ≤ Q < u
same order quantity function: G (Q) .
 2 for u ≤ Q

Inventory Plan
To keep an accurate record you need to know the demand, certain costs, the mean demand during lead time
and standard deviation. These factors are key to helping us determine the order quantity of items, the
reorder point, safety stock and the value of asset pooling. Given the data below for six distributors we
created an accurate Inventory plan for Mike’s Bikes.

East Seast Midwest West Mtn Nwest
Model 110 Annual Demand 58 117 88 105 123 94
Model 210 Annual Demand 90 180 135 162 189 144
Order cost( both bikes ordered together) $1,000 $800 $800 $1,400 $1,000 $1,500
Annual Holding Cost (same for both models) $326 $403 $387 $391 $249 $390
Total
Model 110 Mean Demand During Leadtime 19.3 39 29.3 35 41 31.3 194.9
Model 110 Demand Std. Dev. During Leadtime 0.49 14.12 14.21 9.59 6.15 3.02 47.58
Model 210 Mean Demand During Leadtime 30 60 45 54 63 48 300
Model 210 Demand Std. Dev. During Leadtime 8.65 4.9 19.47 0.94 27.76 0.49 62.21

As discussed earlier in different inventory plans was the order quantity which can be found using the
optimal Q* equation. Then we determine the reorder point which is the point where the inventory on hand
is getting low and an order should be placed. We determine the reorder point by using this equation:
R = λ + Z α σ . We chose to use a 95% confidence interval because we wanted to consider only 5% of
error in the bikes made. The safety stock is the extra products that are left in stock this can be defined as:
SS = Z α σ .The value of asset pooling allows different companies to pull from each others inventory if
they do not have a particular product. We determine this amount by using the same data as the safety stock.
All of our results were found using Microsoft Excel and are shown below.

19.0741
Order Quanity Model 110 18.86341 21.55264 8 27.42113 31.4317 26.89009
23.6249 38.9624
Order Quanity Model 210 23.49781 26.73276 8 34.06027 5 33.28201

Reorder point Model 110 20.1036 62.1568 52.6044 50.7276 51.086 36.2528
108.526
Reorder point Model 210 44.186 68.036 76.9308 55.5416 4 48.8036
Total
Safety Stock for Model 110 0.8036 23.1568 23.3044 15.7276 10.086 4.9528 78.0312
102.024
Safety Stock for Model 210 14.186 8.036 31.9308 1.5416 45.5264 0.8036 4

ALL Ware.
468.1872
612.1464

Value of Asset Poolin for Model 110 78.0312
Value of Asset Poolin for Model 210 102.0244

Results
Table 3 shows the original data provided for the case study.

Based on the data given for Mike’s Bike Shop, our process consisted of generating a forecast, workforce
plan and MRP for the next two years. Our method selection for forecasting was Winters Model because of
the seasonal trend in the initial demand from the previous years. We chose to forecast the future based on
the first year and the final year of demand. The workforce plan was generated using a zero inventory plan
and compared with a linear program that solved the workforce plan optimally. In the provided workbook
set, the aggregate unit for each model was determined by solving for the average production rate and the
number of workers. Based on the defined aggregate units for both models, Mike can determine his
quarterly workforce needed. The linear program consisted of four major constraints and five variable
components. This allowed us to minimize the cost to hold inventory, hire workers, and fire workers for
each model. The MRP was concluded by combining both Bills of Materials needed to produce both
models. We used both models because both models had similar products in order to be considered a
finished good. The initial gross requirements were also the final forecasted demand for the last year. From
there, we were able to find the actual amount of materials required in order to meet the scheduled plan.
Finally, the inventory plan consisted of six distributors defined by regions. From the data given, we were
able to determine the reorder point, order quantity, safety stock, and the value of asset pooling. Using
EOQ, the order quantity was able to be computed. EOQ was the selection of choice because the parts were
being bought instead of being made which is used in EPQ. Using a confidence interval of 95%, the reorder
point for both models this would assist Mike with his inventory plan.

Conclusion
Production Planning Tools can be used in everyday companies to help provide better efficient services.
Each of these techniques are easy to use and can be done with different software programs such as Excel,
GAMS, LINDO and LINGO. These tools help companies to look at their overall business and make
changes that will save them money, create safer environments, create a better production line, plan efficient
scheduling and be aware of inventory coming and going out. As shown through the Case Study on Mike’s
Bikes the techniques work and show that any company can be successful but save money.

Reference
Nahmias, Steven. Production and Operations Anaylsis. New York, McGraw Hill. 2005

BDPA IT Showcase: Production Planning Tools

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