Description
The documentation containing the important formulas of Operations Management.
KEY EQUATIONS CHAPTER 3: Project Management 1. Start and finish times: ES = max (EF times of all activities immediately preceding activity) EF = ES + t ; LS = LF – t ; LF = min (LS times of all activities immediately following activity) 2. Activity slack: S = LS – ES or S = LF – EF 3. Project costs:Cost to crash per unit of time = 4. Activity time statistics:
Crash cost – Normal cost CC – NC = Normal time – Crash time NT – CT
2
a + 4m + b ?b?a? (Expected activity time) ; ? 2 = ? ? 6 ? 6 ? T ? TE 5. z-transformation formula: z = Where: T = due date for the project ; ?2 te =
(Variance)
TE = (expected activity times on the critical path)= mean of normal distribution ?2 = ?(variances of activities on the critical path) 6. Cost Performance Index (CPI) = Earned Value(EV)/Actual Cost; Scheduled Performance Index(SPI) = EV/Planned Cost (PC) CHAPTER 11: Location 1. Load–distance score: ld = ? l i d i
i
2.
Center of gravity:
x? =
?l x ?l
i i i
i i
and
y? =
?l y ?l
i i i
i i
CHAPTER 12: Inventory Management 1.
Cycle inventory =
Q ; 2
2.
Pipeline inventory = dL Q D ( H ) + (S ) 2 Q
TBO EOQ = EOQ (52 weeks/year) D
3. Total annual cost (C) = Annual holding cost + Annual ordering or setup cost = C = 4. Eco. order quantity:
EOQ = 2 DS H
; 5.
Time between orders, expressed in weeks:
6. Inventory position = On-hand inventory + Scheduled receipts – Backorders=IP = OH + SR – BO 7. Continuous review system: Reorder point(R)= Average demand during the protection interval + Safety stock=dL+ z?L Protection interval = Lead time (L) ; Order quantity = EOQ ; Replenishment rule: Order EOQ units when IP ? R. Total Q system cost:
C= Q D ( H ) + ( S ) + Hz? L 2 Q
Standard deviation of demand during the lead time = ? L = ? t
L
8. Periodic review system: Target inventory level (T) = Avg. demand during the protection interval + Safety stock= d(P + L) + ?P+L Protection interval = Time between orders + Lead time=P+L ; Review interval = Time between orders = P Standard deviation of demand during the protection interval =
? P+ L = ? t P + L
Order quantity = Target inventory level – Inventory position = T – IP Replenishment rule: Every P time periods order T – IP units. Total P system cost:
1.
C=
dP D (H ) + ( S ) + Hz? P + L 2 dP
CHAPTER 15: Resource Planning:Master Production Scheduling
Projected On-Hand Inventory ? Projected on - hand ? ? On - hand ? ? MPS quantity ? ? Projected ? ? ? ? ? ? ? ? ? ? inventory at the end ? = ? inventory at the ? + ? due at the start ? ? ? requirements ? ? ? ? end of last week ? ? of this week ? ? this week ? of this week ? ? ? ? ? ? ? ? 1. Available to promise
1
? Available - to - ? ? On - hand ? ? Orders booked up ? ? ? ? ? ? MPS quantity ? ? ? ? ? ? to week S when the ? ? promise in ? = ? quantity in ? + ? ? in week 1 ? week 1: ? ? ? week 1 ? ? ? ? next MPS arrives ? ;week t: week 1 ? ? ? ? ? ?
? Available - to - ? ? Orders booked up ? ? ? ? MPS quantity ? ? ? ? ? ? to week S when the ? ? promise in ? = ? ? in week t ? ? ? ? ? ? next MPS arrives ? week t ? ? ? ? Dt + Dt ?1 + Dt ? 2 + ? + Dt ? n+1 n
13. FORECASTING 1. Linear regression: Y = a + bX 4. Weighted moving average: 2. Naive forecasting: Forecast = Dt 3. Simple moving average: 7. Forecast error: Et
CFE = ? Et CFE n ? Et2 MSE = n E=
Ft +1 =
= Dt ? Ft
5. Exponential smoothing: 8. Exponentially smoothed error: Trend-adjusted exponential smoothing: MAD t = ? E t + (1 ? ? )MAD t –1 Sigma = 1.25 MAD 9. Tracking Signal:
CFE MAD or CFE MAD t
Ft +1 = Weight 1 ( Dt ) + Weight 2 ( Dt ?1 ) +
6.
Weight 3 ( Dt ? 2 ) + ? + Weight n ( Dt ? n +1 )
Ft +1 = ?Dt + (1 ? ? ) Ft
At = ? Dt + (1 ? ? )( At ?1 + Tt ?1 ) Tt = ? ( At ? At ?1 ) + (1 ? ? )Tt ?1 Ft +1 = At + Tt
?=
MAD =
?( Et ? E ) 2 n ?1 ? Et
CHAPTER 16: Scheduling 1. Performance measures:
n (? Et / Dt )(100%) MAPE = n
Ch.14 Workforce Planning Period1.. Inputs Forecasted Demand Workforce level Undertime Overtime Vacation time Subcontracting time Backorders derived Utilized time Inventory Hires Layoffs Calculated Utilized time cost Undertime cost Overtime cost Vacation time cost Inventory cost Backorder cost Hiring cost Layoff cost Subcontracting cost Ch. 15 INVENTORY/MRP RECORD Total Cost Total
Job flow time = time of completion –Time job was available for first processing operation
Makespan = Time of completion of last job –Starting time of first job Sum of flow times Average WIP inventory = Makespan Sum of time in system Average inventory = Makespan Total inventory = Scheduled receipts for all items + On-hand inventories of all items Utilization = Productive work time Total work time available
Due date – Today' s date Total shop time available 3. Slack per remaining operations: (Due date – Today' s date) – Total time remaining S RO = Number of operations remaining
2. Critical ratio: CR =
Ch. 15 MPS RECORD Quantity at Hand Week1 Forecast Customer orders booked Projected OH inventory MPS Qty. MPS Start ATP invenory Order Policy: Lead Time: Week2 Week3
Item: Description..Rule Week1 Gross Requirement Scheduled Receipt Projected OH inventory Planned Receipts Planned Order Releases
Lot size: Lead Time: Week2 Week3
Ch.3 Project Management
Stage Crash activity Time reduction
Activity Resulting critical path
Normal Time Project duration
Normal Cost Project direct costs, Last trial
Crash Time Crash cost added
Crash Cost Total indirect cost
Immediate Predecessors Total penalty cost Total project cost
2
3
doc_123626193.doc
The documentation containing the important formulas of Operations Management.
KEY EQUATIONS CHAPTER 3: Project Management 1. Start and finish times: ES = max (EF times of all activities immediately preceding activity) EF = ES + t ; LS = LF – t ; LF = min (LS times of all activities immediately following activity) 2. Activity slack: S = LS – ES or S = LF – EF 3. Project costs:Cost to crash per unit of time = 4. Activity time statistics:
Crash cost – Normal cost CC – NC = Normal time – Crash time NT – CT
2
a + 4m + b ?b?a? (Expected activity time) ; ? 2 = ? ? 6 ? 6 ? T ? TE 5. z-transformation formula: z = Where: T = due date for the project ; ?2 te =
(Variance)
TE = (expected activity times on the critical path)= mean of normal distribution ?2 = ?(variances of activities on the critical path) 6. Cost Performance Index (CPI) = Earned Value(EV)/Actual Cost; Scheduled Performance Index(SPI) = EV/Planned Cost (PC) CHAPTER 11: Location 1. Load–distance score: ld = ? l i d i
i
2.
Center of gravity:
x? =
?l x ?l
i i i
i i
and
y? =
?l y ?l
i i i
i i
CHAPTER 12: Inventory Management 1.
Cycle inventory =
Q ; 2
2.
Pipeline inventory = dL Q D ( H ) + (S ) 2 Q
TBO EOQ = EOQ (52 weeks/year) D
3. Total annual cost (C) = Annual holding cost + Annual ordering or setup cost = C = 4. Eco. order quantity:
EOQ = 2 DS H
; 5.
Time between orders, expressed in weeks:
6. Inventory position = On-hand inventory + Scheduled receipts – Backorders=IP = OH + SR – BO 7. Continuous review system: Reorder point(R)= Average demand during the protection interval + Safety stock=dL+ z?L Protection interval = Lead time (L) ; Order quantity = EOQ ; Replenishment rule: Order EOQ units when IP ? R. Total Q system cost:
C= Q D ( H ) + ( S ) + Hz? L 2 Q
Standard deviation of demand during the lead time = ? L = ? t
L
8. Periodic review system: Target inventory level (T) = Avg. demand during the protection interval + Safety stock= d(P + L) + ?P+L Protection interval = Time between orders + Lead time=P+L ; Review interval = Time between orders = P Standard deviation of demand during the protection interval =
? P+ L = ? t P + L
Order quantity = Target inventory level – Inventory position = T – IP Replenishment rule: Every P time periods order T – IP units. Total P system cost:
1.
C=
dP D (H ) + ( S ) + Hz? P + L 2 dP
CHAPTER 15: Resource Planning:Master Production Scheduling
Projected On-Hand Inventory ? Projected on - hand ? ? On - hand ? ? MPS quantity ? ? Projected ? ? ? ? ? ? ? ? ? ? inventory at the end ? = ? inventory at the ? + ? due at the start ? ? ? requirements ? ? ? ? end of last week ? ? of this week ? ? this week ? of this week ? ? ? ? ? ? ? ? 1. Available to promise
1
? Available - to - ? ? On - hand ? ? Orders booked up ? ? ? ? ? ? MPS quantity ? ? ? ? ? ? to week S when the ? ? promise in ? = ? quantity in ? + ? ? in week 1 ? week 1: ? ? ? week 1 ? ? ? ? next MPS arrives ? ;week t: week 1 ? ? ? ? ? ?
? Available - to - ? ? Orders booked up ? ? ? ? MPS quantity ? ? ? ? ? ? to week S when the ? ? promise in ? = ? ? in week t ? ? ? ? ? ? next MPS arrives ? week t ? ? ? ? Dt + Dt ?1 + Dt ? 2 + ? + Dt ? n+1 n
13. FORECASTING 1. Linear regression: Y = a + bX 4. Weighted moving average: 2. Naive forecasting: Forecast = Dt 3. Simple moving average: 7. Forecast error: Et
CFE = ? Et CFE n ? Et2 MSE = n E=
Ft +1 =
= Dt ? Ft
5. Exponential smoothing: 8. Exponentially smoothed error: Trend-adjusted exponential smoothing: MAD t = ? E t + (1 ? ? )MAD t –1 Sigma = 1.25 MAD 9. Tracking Signal:
CFE MAD or CFE MAD t
Ft +1 = Weight 1 ( Dt ) + Weight 2 ( Dt ?1 ) +
6.
Weight 3 ( Dt ? 2 ) + ? + Weight n ( Dt ? n +1 )
Ft +1 = ?Dt + (1 ? ? ) Ft
At = ? Dt + (1 ? ? )( At ?1 + Tt ?1 ) Tt = ? ( At ? At ?1 ) + (1 ? ? )Tt ?1 Ft +1 = At + Tt
?=
MAD =
?( Et ? E ) 2 n ?1 ? Et
CHAPTER 16: Scheduling 1. Performance measures:
n (? Et / Dt )(100%) MAPE = n
Ch.14 Workforce Planning Period1.. Inputs Forecasted Demand Workforce level Undertime Overtime Vacation time Subcontracting time Backorders derived Utilized time Inventory Hires Layoffs Calculated Utilized time cost Undertime cost Overtime cost Vacation time cost Inventory cost Backorder cost Hiring cost Layoff cost Subcontracting cost Ch. 15 INVENTORY/MRP RECORD Total Cost Total
Job flow time = time of completion –Time job was available for first processing operation
Makespan = Time of completion of last job –Starting time of first job Sum of flow times Average WIP inventory = Makespan Sum of time in system Average inventory = Makespan Total inventory = Scheduled receipts for all items + On-hand inventories of all items Utilization = Productive work time Total work time available
Due date – Today' s date Total shop time available 3. Slack per remaining operations: (Due date – Today' s date) – Total time remaining S RO = Number of operations remaining
2. Critical ratio: CR =
Ch. 15 MPS RECORD Quantity at Hand Week1 Forecast Customer orders booked Projected OH inventory MPS Qty. MPS Start ATP invenory Order Policy: Lead Time: Week2 Week3
Item: Description..Rule Week1 Gross Requirement Scheduled Receipt Projected OH inventory Planned Receipts Planned Order Releases
Lot size: Lead Time: Week2 Week3
Ch.3 Project Management
Stage Crash activity Time reduction
Activity Resulting critical path
Normal Time Project duration
Normal Cost Project direct costs, Last trial
Crash Time Crash cost added
Crash Cost Total indirect cost
Immediate Predecessors Total penalty cost Total project cost
2
3
doc_123626193.doc