1. operational planning & control
CHAPTER 7

2. 6.1. Introduction Production Planning & Control
All activities related to purchasing, storing, and manufacturing materials, products, & components. Involve different functions
Forecasting: predicting future customer demands
Planning: planning for future.
Long range: capacity (aggregate) planning,
Short range: materials requirements planning (MRP)
Inventory Control: raw material, components, finished products
Production scheduling: time, machine, workers, for each job

3. 7.3. Demand Forecasting 7.3.1. Moving Average (MA) method:
Forecast = Average of actual demand in last (n) time periods
Weighted MA (WMA): higher weight to more recent data or

4. 7.3.1. Moving Average (MA) Choice of (n) and weights (wi) Arbitrary,
Based on experience
Can be determined by experimentation
The last forecast (Ft) is forecast for all the future.
It will be updated when a new time period brings a new actual demand value

5. 7.3.1. Moving Average (MA) Example
Given the data below, forecast using the moving average method with(n = 4)
Given weights (0.4, 0.8, 1.2, 1.6), calculate the forecast using the weighted moving average method t 1 2 3 4 5 6 7 8 9 10 Xt

6. 7.3.1. Moving Average (MA) Examplet 1 2 3 4 5 6 7 8 9 10 11 Xt Ft (4 +6
+3 +6) /4
= 4.75 (6 +3
+6 +5) /4 = (3 +5
+4)
4.5
5.25
4.25
+4 +5)

7. 7.3.1. Moving Average (MA) Example
WMA(4): Normalized weights ( 4) = 0.1, 0.2, 0.3, 0.4 t 1 2 3 4 5 6 7 8 9 10 11 Xt Ft
(1*4
+2*6
+3*3 +4*6) /10 =
4.9
(1*6
+2*3
+3*6 +4*5)
/10
(1*3
+3*5
+4*4)
4.6
5.2
4.3
4.1
+3*4 +4*5)
4.4

8. 7.3.2. Exponential Smoothing (ES)
Weights decrease exponentially with the age of data
Similar to WMA but more efficient, especially for computer
Need 3 pieces of data:
last period demand (Xt-1),
last period forecast (Ft-1),
smoothing constant ().

9. 7.3.2. Exponential Smoothing (ES)
Choice of ()
Arbitrary, based on experience
Can be determined by experimentation
Initial Value (F1).
Set F1 = X1. or
F1 = average of first few actual demands

10. 7.3.2. Exponential Smoothing (ES) Example
For the data below, calculate the forecast using the exponential smoothing method with
 = 0.2
F1 = X1 t 1 2 3 4 5 6 7 8 9 10 Xt

11. 7.3.2. Exponential Smoothing (ES) Example
WMA(4): Normalized weights ( 4) = 0.1, 0.2, 0.3, 0.4 t 1 2 3 4 5 6 7 8 9 10 11 Xt Ft
.2*4 +
.8*4 =
.2*6
4.4
2*3
+ .8*4.4
4.12
2*6
+ .8*4.12
4.496
4.597
4.477
4.782
4.426
4.34
4.472

12. Regression Analysis
Regression models assume the same pattern (curve) of demand will continue in the future
Least-Squares Regression
Minimize the sum of squared errors
Linear Regression
Ft = a + bt
a = intercept, b = slope

13. 7.3.3. Regression Analysis Linear Regression
Forecasted demand: Ft = a + bt
Actual demand: Xt
Error: a + bt - Xt
Sum of Squared Errors:  (a + bt – Xt)2
Minimizing gives

14. 7.3.3. Linear Regression Example
For the data below, calculate the forecast using linear regression t 1 2 3 4 5 Xt 7 8 10

15. 7.3.3. Linear Regression Example t 1 2 3 4 5 15 Xt 7 8 10 33
t*Xt 21 32 50
116 t2 9 16 25 55

16. 7.3.3. Linear Regression Example
Ft = t F6 = (6) = 11.7 F7 = (7) =

17. 7.5. Inventory Planning & Control
Objective:
Determine proper inventory levels to satisfy customer demands & minimize total cost
Decisions:
What to order
How much to order
When to order

18. 7.5. Inventory Planning & Control
Types of inventory costs
Procurement cost (PC): order processing, paper work, supplier fees, receiving, & inspection (per order)
Carrying cost (CC): investment opportunity, storage, obsolescence, spoilage, insurance, taxes (per unit/per time unit)
Total cost (TC) = PC + CC

19. 7.5. Inventory Planning & Control
Basic inventory (EOQ) model
Assumptions
Demand rate is constant & known
A complete order arrives when inventory level drops to 0
Definitions:
T = cycle time (time between successive orders)
D= demand rate (unit/time unit)
Q = quantity of each order (lot size)

20. 7.5. Inventory Planning & Control
Basic inventory (EOQ) model

21. 7.5. Inventory Planning & Control
Basic inventory (EOQ) model
Number of orders/yr =D/Q
Ordering cost/yr = PC*D/Q
Average inventory level = Q/2
Holding cost/yr = CC*Q/2
Total cost/yr: TC(Q) = PC*D/Q + CC*Q/2

22. 7.5. Inventory Planning & Control
Basic inventory (EOQ) model
To minimize TC, set: TC’ = 0
- PC*D/Q2 + CC/2 = 0
Solving gives the Economic Order Quantity (EOQ)

23. 7.5. Inventory Planning & Control
EOQ Example: Given D = 50 units/month
PC = $72/order
CC = $6/unit/year
Find Q, T, TC
CC = 6/12 = $0.5/unit/month
= 120 units
T = Q/D = 120/50 = 2.4 months
TC = 72(50/120) + 0.5(120/2) = $60/month

24. End of Chapter 7
Questions?