Description
The PPT explains Inventory management covers topics of EOQ economic order quantity, standard inventory model, problems, lot size, inventory control techniques and other topics.
Inventory Management
Inventory Management
?
What is inventory?
? ?
Quantity
?
Why do we carry inventories? Objectives of scientific Inventory Control Fixed Order Quality or ‘Q’ system. E.g. (EOQ)
Max Level
EOQ
Re-order level Buffer Stock or L.T. cons. Min Level
LT
Safety stock Time
R1
S1
R2
S2
R3
S3
R4
S4
R5
S5
Fixed Order Period or ‘P’ system Quantity OQ 3 OQ 4 y4 Time
The models are under VARYING consumption rates
OQ 1
y2
y1
LT
R1 R2 R3 R4 reorder points R1 S1 R1-R2 = R2 – R3 = R2 –R = Re-order period
R2
OQ 2
y3
S2
R3
S3
R4
S4
(y1 + OQ1) should be sufficient (?) for consumption for periodR1 to S2 (i.e. Fixed order period + Lead time)
Effect of ORDER QUANTITY on COST
Annual Total Cost
Annual Inventory Carrying Cost
Annual Procurement Cost EOQ 0 ORDER QUANTITY
For inventory decisions, two costs are involved 1) Procurement cost and 2) Inventory carrying cost Annual procurement cost = {No of orders/year} X {Procurement Cost / Order} = S X Cp q Annual inventory carrying cost = {Average inventory investment} X {Inventory carrying cost} = ½ (Order quantity X Price/unit) X Inventory carrying cost = {1/2 X q X Cu} X i i = inventory carrying cost expressed as a percentage of average inventory investment. Annual Total Cost = Annual Procurement Cost + Annual Inventory Carrying Cost (A.T.C) = S X Cp + S X Cu X i q 2 To minimize A.T.C., we differentiate expression for A.T.C. with respect to the decision variable ‘q’ and set the first derivative to zero. D (ATC) = - SCp + Cu X i = 0 dq q2 2 q2 = 2 SCp When total cot is minimum, we call the ‘q’ as q0 i.e.E.O.Q. ? q2 0 = 2 SCp Cu X i Cu X i E. O. Q. = q0 = E. O. Q = 2SCp 2 X Annual Requirement X Procurement Cost / Order Price / unit X Inventory carrying cost Cu X i
Standard Inventory Model
Annual Total Cost (a + b) Annual Inventory Carrying Cost (b)
Cost
Annual Procurement Cost ( a )
q0
EOQ
Order quantity (units)
EOQ = q0
S = Annual consp. in units Cp = Procurement cost /order Cu = Price per unit i = Inventory carrying cost as % of average inventory investment Proof of Optimal buying : - For order quantity = q0 Annual Procurement Cost (a) = Annual inventory carrying cost ( b )
2. S. Cp Cu X i
Assumptions for EOQ model
1.
Demand of items uniform over the period, at known rate
2.
3. 4. 5.
Replenishment instantaneous
Cu fixed and independent of order size Cp is fixed, does not vary with lot size The inventory carrying cost vary directly and linearly with size of inventory Item can be procured without any restrictions
6.
?
Alternative formula for EOQ When EOQ is in terms of value i.e. Q0 = q0 X Cu Q0 = 2. A. Cp i A= annual consumption in value i.e. A = S. Cu
? 1) 2)
Inventory Replenishment Systems Fixed Order Quantity (Q) Fixed Order Period (P) Modified Fixed Order Quantity System : - Two Bin System e.g. EOQ
?
Material Requirement Planning (MRP I) Sales Planning
Inventory
MRP I
Bill of Materials
*
Purchasing Make or Buy decisions Just-In-Time (JIT)
Orders
Internal Manufacturing
Problems on EOQ 1] In a manufacturing unit a certain type of bearing is required in quantity of 2500 numbers in a year. The procurement cost of this inventory is Rs 200 per order. The cost of bearing is Rs 1000 per unit , regardless of the quantity of the order. The inventory carrying cost is 10 % of the average inventory investment. Find out 1] Economic Order Quantity in units 2] Frequency of the ordering if there are 300 days in a year. 3] Total annual ordering cost.
2] M/s Fax Fit require 6,00,000oil seals per year for their production activity . The ordering cost is found to be Rs 100 per order. The oil seals are available at Rs 200 per piece flat. The inventory carrying cost is found to be 60 % of the average inventory investment. The company has a practice of placing orders of 600 pieces. You join the company as G.M.[ Materials] and wish to optimize the inventory management of this item. How would you go about it and what is the maximum saving you would obtain in the inventory management of this item per year?
Economic Lot Size of Manufactured Items
Items are manufactured (in lots or batches) in the factory to meet internal or external demand (consumption) over a period (till then it is stored as inventory) Here, Economic Lot Size ? Economic order quantity for purchase (procurement) Set up cost for the batch ? Cost of ordering (procurement)
Two main situations 1) Instantaneous replenishment Under this system item is manufactured according to its lot size. Then the entire lot is given to the stores (instantaneous inventory buildup) and from stores the consumption is gradual. If Annual requirement of the item (units) S Manufacturing cost per unit Cu Set-up cost per production run (batch) Cp Inventory carrying cost as a percentage of average inventory investment i Quantity per production run (Lot size) q ? Economic Lot Size q0 = 2. S. Cp Cu X i
Economic Lot Size of Manufactured Items
2)
Non-instantaneous (Gradual ) replenishment * Many times production batch takes long time to complete. Hence we may not wait for the entire batch (lot) quantity to get completed but start meeting demand (via stores) when the batch is being processed. Thus the inventory (of the manufactured item) receipt at stores is not instantaneous but gradual and consumption (issue from stores) starts before the entire batch quantity is received by stores. The inventory build up at stores is gradual and at the rate of (p-d) per day where p = daily production (units) hence receipt at stores. and d = daily demand (consumption) (units ) hence issue from stores If t is the production run in days The inventory build up at stores @ (p-d) / day and is maximum at the end of the production run. i.e. (p-d) t ? Average inventory level = (p-d)t = (p-d) X q 2 2 p ( ? q = p X t) = q 1- d 2 p
Annual inventory carrying cost == q d Cu . i ____________ (1) 2 1- p Annual set-up cost = (No of production runs) X (Set-up cost per production run) = S X Cp __________________ (2) q Annual Total Cost (A. T. C) = (1) + (2) = S. Cp + q (1- d) Cu X i q 2 p d (ATC) = -SCp + ½ (1- d ) Cu X i = 0 for q q0 dq p q0 = 2. S. Cp q0 = Economic lot size (1- d /p) Cu. i Example: - Q9 (b) 21/4/2004 Data:- S= 25,000 units/year p = 250 units/day Cp = Rs. 30,000 per prod. run Cost of holding one unit Rs.2500 per annum Consumption (demand) rate d = 25,000 = 100 units/day (since no of working days in year = 250) 250 ?q0 = = 6,00,000 / 0.6 = 10 6 = 1000 2 X 25000 X 30000 (1- 100 /250 ) X 2500
3] A telecommunication appliances manufacturing company , a certain gadget is
manufactured in the quantity of 25,000 units per year. An internal supplier [ department] in the same company is having a capacity of producing and supplying the vital component [ a transmitter] required for this gadget at the rate of 250 units per day while the demand of this vital component by the gadget manufacturing department [ internal customer] is at a fixed and uniform daily rate lower than 250. Hence the supplier department can produce this vital component in batches, using its spare capacity for some other work. The cost of setting for starting the manufacture of this vital component batch is Rs 30,000 per production run. The cost of holding one transmitter in inventory for one year is Rs 2500. The company is working for 250 days in a year.
Find out the Economic Batch Quantity [ EBQ or ELQ] for manufacture of the vital component [ transmitter] by the internal supplier department and the frequency of taking up the batches for its manufacture.
Inventory Control Techniques (Selective)
1) 2) 3)
4)
5)
6) 7) 8)
Classification ABC Analysis HML Analysis (High-Medium-Low) VED Analysis (Vital-Essential-Desirable) SDE Analysis (Scare-Difficult-Easy) GOLF Analysis (Govt-Ordinary-Local- Foreign) SOS Analysis (Seasonal- off seasonal) FSN Analysis (Fast-Slow-Non moving) XYZ Analysis
Criterion used Usage value (consumption X unit price) Unit price (consumption not taken into account) Criticality (for loss of production) Procurement difficulties
Source of procurement
Seasonality Issues from stores Inventory investment (cost of inventory on hand)
ABC Analysis – Example
Class Inventory Item
1001 1002 1003 1004 1005 1006 1007 1008 1009 1010 1011 1012 1013 1014 1015 1016 1017 1018 1019 1020 Total 20 items
Annual usage in Rs.
3,000 40,000 2,000 10,000 5,000 4,00,000 7,000 9,000 8,000 3,00,000 1,000 50,000 15,000 20,000 90,000 8,000 7,000 11,000 9,000 5,000 Rs. 10,00,000
% of total inventory usage in Rs.
0.3% 4.0 0.2 1.0 0.5 40.0 0.7 0.9 0.8 30.0 0.1 5.0 1.5 2.0 9.0 0.8 0.7 1.1 0.9 0.5 100.0%
ABC Analysis – Example (Contd…)
Percentage of total annual usage
100
80
60
A
40
20/20
10/70
B
C
70/10
20
0
10
20
30
40
50
60
70
80
90
100
Percentage of total number of inventory
A 1. 2. 3. 4. 5. 6. 7.
8.
9. 10. 11.
B Moderate control Low safety stock Not so frequent ordering Monthly control statement Periodic follow up Moderate value analysis Two-Three reliable sources for each item
C Loose control High safety stock Bulk ordering Quarterly control statement Follow up in exceptional cases Minimum value analysis Two sources for each item
Strict control No/very low safety stock Frequent ordering Weekly control statement Maximum follow up Rigorous value analysis Maximum sources for each item
Accurate material planning
Minimization of waste Centralized purchase Maximum effort to reduce
Estimates based on past data Rough estimates
Moderate checks Combination purchase Moderate efforts Periodic checks Decentralized purchase Minimum efforts Delegated to lower levels Group posting
lead time
12.
Handled by senior management Handled by middle management Individual posting Small group posting
13.
Inventory Data
Code [1] Usage-units [2] Unit Price Rs [3] Usage Value-Rs [2] * [3] Percentage of Total cost
1001 1002 1003 1004
50 4 8 100
600 200 1000 10
30000 800 8000 1000
1005
1006 1007 1007 1008
150
250 30 12 2
100
8 400 100 750
15000
2000 12000 1200 1500
1009
1010 1011 1012 TOTAL
20
200 8 1000 1834
25
11 100 25
500
2200 800 25000 1,00,000 100
EOQ model under quantity –discount Total Cost =
Per annum
S X Cu +
Annual Purchase Cost (3)
S X Cp + ½ X q X Cu X I q
Annual ordering cost (2) Annual Inv. Carrying cost (1)
(4)
(4) = (1) + (2) + (3) Total annual cost
Total Cost = (1) +(2) Costs (1) Annual Inv-carrying cost (3) Annual cost of items
EOQ
(2) Annual ordering cost (q) Order quantity (units)
When Total cost per annum can vary with the order size (quantity) i.e. Cu is dependent on q or when quantity discounts applicable.
For example : - If S = 10,000 units /year Cp = Rs. 20 per order Cu = Cost per unit (price) – variable I = 0.20 (20% of av.inventory investment) Slab Order size (q) Cost/unit (Cu) EOQ A 0.499 Rs.5.00 q0A = 633 B 500.999 Rs.4.50 q0B= 666 C 1000 and above Rs. 3.90 q0C = 716 Using q0 =
Feasibility No Yes No
2. S. Cp and calculating q0 A, q0 B& q0 C, Cu X i If all EOQs (or more than one EOQ) are ‘feasible’ then select the EOQ with the lowest unit cost (Cu) However, one practical consideration in quantity-discount problems is that the cost reduction from volume purchases frequency makes it seemingly economical to order quantities larger than EOQ.
Cu = Rs. 5.00 Cu = Rs. 4.50 Cu = Rs.3.90
Infeasible range
Feasible range
Total Cost
Rs. 39,590 Rs 45,600
666 500 q0 A 633 q0 B
716
1000 q0 C Order Size
In practical scenario, some EOQs may not be feasible i.e. EOQ does not fall within the feasible unit cost (Cu) range). In these situations, we have to calculate the Total Annual Cost for each unit cost (Cu) at the respective EOQs where it is feasible. Where it is not feasible we calculate the total cost at the minimum quantity where the respective unit cost (Cu) is first applicable. These total costs are then compared and the quantity or EOQ associated with the lowest total cost is the ‘order quantity’ that is selected. Procedurally, the largest order quantity (lowest unit price) is solved first, if the resulting q is valid or feasible, that is the answer. If not, the next largest order quantity (second lower price) is derived. If that is feasible, the cost of this q is compared to the cost of using the order quantity at the price break above and the lowest cost determines the optimal q.
(1)
Inv. Carrying cost
q X Cu X i 2
q0B = 666. Cu = 4.50 666 (0.2) (4.50)
Price break at 1000 Cu=3.90
2
= Rs. 299.70
1000 (0.2) X 3.90
= Rs. 390 10,000 (20) = Rs.200 1000 390 + 200 = 590 10,000 X 3.90 = 39,000 Rs. 39,590
(2)
Procurement Cost (1) + (2)
S X Cp q
10,000 X 20 = Rs. 300 666 300 + 300 = Rs. 600
(3)
Purchase Cost
S X Cu
10,000 X 4.50 = 45,000 Rs. 45,000
(4)
Total Cost (1) + (2) + (3)
Problem: A manufacturing unit producing electrical appliances require 4000 switches per year. The ordering cost is Rs 50 per order. The inventory carrying cost is 8 % of purchase price per unit on an annual basis. The switches are priced as follows:
Order Quantity-units
1 to 499 500 to 999
Unit price-Rs
9.00 8.50
1000 and above
8.00
Find out the optimum order quantity and the annual total cost .
Problem
? Data: ? Cp: Rs 64 per order. ? i=0.20, ? S=49 units per year. ? Cu: variable
Slab A B
Order Unit price Quantity-units [Cu]-Rs 1 to 199 200 and above 50.25 49.00
EOQ 79 80
Find the EOQ and the least total cost
doc_323132596.ppt
The PPT explains Inventory management covers topics of EOQ economic order quantity, standard inventory model, problems, lot size, inventory control techniques and other topics.
Inventory Management
Inventory Management
?
What is inventory?
? ?
Quantity
?
Why do we carry inventories? Objectives of scientific Inventory Control Fixed Order Quality or ‘Q’ system. E.g. (EOQ)
Max Level
EOQ
Re-order level Buffer Stock or L.T. cons. Min Level
LT
Safety stock Time
R1
S1
R2
S2
R3
S3
R4
S4
R5
S5
Fixed Order Period or ‘P’ system Quantity OQ 3 OQ 4 y4 Time
The models are under VARYING consumption rates
OQ 1
y2
y1
LT
R1 R2 R3 R4 reorder points R1 S1 R1-R2 = R2 – R3 = R2 –R = Re-order period
R2
OQ 2
y3
S2
R3
S3
R4
S4
(y1 + OQ1) should be sufficient (?) for consumption for periodR1 to S2 (i.e. Fixed order period + Lead time)
Effect of ORDER QUANTITY on COST
Annual Total Cost
Annual Inventory Carrying Cost
Annual Procurement Cost EOQ 0 ORDER QUANTITY
For inventory decisions, two costs are involved 1) Procurement cost and 2) Inventory carrying cost Annual procurement cost = {No of orders/year} X {Procurement Cost / Order} = S X Cp q Annual inventory carrying cost = {Average inventory investment} X {Inventory carrying cost} = ½ (Order quantity X Price/unit) X Inventory carrying cost = {1/2 X q X Cu} X i i = inventory carrying cost expressed as a percentage of average inventory investment. Annual Total Cost = Annual Procurement Cost + Annual Inventory Carrying Cost (A.T.C) = S X Cp + S X Cu X i q 2 To minimize A.T.C., we differentiate expression for A.T.C. with respect to the decision variable ‘q’ and set the first derivative to zero. D (ATC) = - SCp + Cu X i = 0 dq q2 2 q2 = 2 SCp When total cot is minimum, we call the ‘q’ as q0 i.e.E.O.Q. ? q2 0 = 2 SCp Cu X i Cu X i E. O. Q. = q0 = E. O. Q = 2SCp 2 X Annual Requirement X Procurement Cost / Order Price / unit X Inventory carrying cost Cu X i
Standard Inventory Model
Annual Total Cost (a + b) Annual Inventory Carrying Cost (b)
Cost
Annual Procurement Cost ( a )
q0
EOQ
Order quantity (units)
EOQ = q0
S = Annual consp. in units Cp = Procurement cost /order Cu = Price per unit i = Inventory carrying cost as % of average inventory investment Proof of Optimal buying : - For order quantity = q0 Annual Procurement Cost (a) = Annual inventory carrying cost ( b )
2. S. Cp Cu X i
Assumptions for EOQ model
1.
Demand of items uniform over the period, at known rate
2.
3. 4. 5.
Replenishment instantaneous
Cu fixed and independent of order size Cp is fixed, does not vary with lot size The inventory carrying cost vary directly and linearly with size of inventory Item can be procured without any restrictions
6.
?
Alternative formula for EOQ When EOQ is in terms of value i.e. Q0 = q0 X Cu Q0 = 2. A. Cp i A= annual consumption in value i.e. A = S. Cu
? 1) 2)
Inventory Replenishment Systems Fixed Order Quantity (Q) Fixed Order Period (P) Modified Fixed Order Quantity System : - Two Bin System e.g. EOQ
?
Material Requirement Planning (MRP I) Sales Planning
Inventory
MRP I
Bill of Materials
*
Purchasing Make or Buy decisions Just-In-Time (JIT)
Orders
Internal Manufacturing
Problems on EOQ 1] In a manufacturing unit a certain type of bearing is required in quantity of 2500 numbers in a year. The procurement cost of this inventory is Rs 200 per order. The cost of bearing is Rs 1000 per unit , regardless of the quantity of the order. The inventory carrying cost is 10 % of the average inventory investment. Find out 1] Economic Order Quantity in units 2] Frequency of the ordering if there are 300 days in a year. 3] Total annual ordering cost.
2] M/s Fax Fit require 6,00,000oil seals per year for their production activity . The ordering cost is found to be Rs 100 per order. The oil seals are available at Rs 200 per piece flat. The inventory carrying cost is found to be 60 % of the average inventory investment. The company has a practice of placing orders of 600 pieces. You join the company as G.M.[ Materials] and wish to optimize the inventory management of this item. How would you go about it and what is the maximum saving you would obtain in the inventory management of this item per year?
Economic Lot Size of Manufactured Items
Items are manufactured (in lots or batches) in the factory to meet internal or external demand (consumption) over a period (till then it is stored as inventory) Here, Economic Lot Size ? Economic order quantity for purchase (procurement) Set up cost for the batch ? Cost of ordering (procurement)
Two main situations 1) Instantaneous replenishment Under this system item is manufactured according to its lot size. Then the entire lot is given to the stores (instantaneous inventory buildup) and from stores the consumption is gradual. If Annual requirement of the item (units) S Manufacturing cost per unit Cu Set-up cost per production run (batch) Cp Inventory carrying cost as a percentage of average inventory investment i Quantity per production run (Lot size) q ? Economic Lot Size q0 = 2. S. Cp Cu X i
Economic Lot Size of Manufactured Items
2)
Non-instantaneous (Gradual ) replenishment * Many times production batch takes long time to complete. Hence we may not wait for the entire batch (lot) quantity to get completed but start meeting demand (via stores) when the batch is being processed. Thus the inventory (of the manufactured item) receipt at stores is not instantaneous but gradual and consumption (issue from stores) starts before the entire batch quantity is received by stores. The inventory build up at stores is gradual and at the rate of (p-d) per day where p = daily production (units) hence receipt at stores. and d = daily demand (consumption) (units ) hence issue from stores If t is the production run in days The inventory build up at stores @ (p-d) / day and is maximum at the end of the production run. i.e. (p-d) t ? Average inventory level = (p-d)t = (p-d) X q 2 2 p ( ? q = p X t) = q 1- d 2 p
Annual inventory carrying cost == q d Cu . i ____________ (1) 2 1- p Annual set-up cost = (No of production runs) X (Set-up cost per production run) = S X Cp __________________ (2) q Annual Total Cost (A. T. C) = (1) + (2) = S. Cp + q (1- d) Cu X i q 2 p d (ATC) = -SCp + ½ (1- d ) Cu X i = 0 for q q0 dq p q0 = 2. S. Cp q0 = Economic lot size (1- d /p) Cu. i Example: - Q9 (b) 21/4/2004 Data:- S= 25,000 units/year p = 250 units/day Cp = Rs. 30,000 per prod. run Cost of holding one unit Rs.2500 per annum Consumption (demand) rate d = 25,000 = 100 units/day (since no of working days in year = 250) 250 ?q0 = = 6,00,000 / 0.6 = 10 6 = 1000 2 X 25000 X 30000 (1- 100 /250 ) X 2500
3] A telecommunication appliances manufacturing company , a certain gadget is
manufactured in the quantity of 25,000 units per year. An internal supplier [ department] in the same company is having a capacity of producing and supplying the vital component [ a transmitter] required for this gadget at the rate of 250 units per day while the demand of this vital component by the gadget manufacturing department [ internal customer] is at a fixed and uniform daily rate lower than 250. Hence the supplier department can produce this vital component in batches, using its spare capacity for some other work. The cost of setting for starting the manufacture of this vital component batch is Rs 30,000 per production run. The cost of holding one transmitter in inventory for one year is Rs 2500. The company is working for 250 days in a year.
Find out the Economic Batch Quantity [ EBQ or ELQ] for manufacture of the vital component [ transmitter] by the internal supplier department and the frequency of taking up the batches for its manufacture.
Inventory Control Techniques (Selective)
1) 2) 3)
4)
5)
6) 7) 8)
Classification ABC Analysis HML Analysis (High-Medium-Low) VED Analysis (Vital-Essential-Desirable) SDE Analysis (Scare-Difficult-Easy) GOLF Analysis (Govt-Ordinary-Local- Foreign) SOS Analysis (Seasonal- off seasonal) FSN Analysis (Fast-Slow-Non moving) XYZ Analysis
Criterion used Usage value (consumption X unit price) Unit price (consumption not taken into account) Criticality (for loss of production) Procurement difficulties
Source of procurement
Seasonality Issues from stores Inventory investment (cost of inventory on hand)
ABC Analysis – Example
Class Inventory Item
1001 1002 1003 1004 1005 1006 1007 1008 1009 1010 1011 1012 1013 1014 1015 1016 1017 1018 1019 1020 Total 20 items
Annual usage in Rs.
3,000 40,000 2,000 10,000 5,000 4,00,000 7,000 9,000 8,000 3,00,000 1,000 50,000 15,000 20,000 90,000 8,000 7,000 11,000 9,000 5,000 Rs. 10,00,000
% of total inventory usage in Rs.
0.3% 4.0 0.2 1.0 0.5 40.0 0.7 0.9 0.8 30.0 0.1 5.0 1.5 2.0 9.0 0.8 0.7 1.1 0.9 0.5 100.0%
ABC Analysis – Example (Contd…)
Percentage of total annual usage
100
80
60
A
40
20/20
10/70
B
C
70/10
20
0
10
20
30
40
50
60
70
80
90
100
Percentage of total number of inventory
A 1. 2. 3. 4. 5. 6. 7.
8.
9. 10. 11.
B Moderate control Low safety stock Not so frequent ordering Monthly control statement Periodic follow up Moderate value analysis Two-Three reliable sources for each item
C Loose control High safety stock Bulk ordering Quarterly control statement Follow up in exceptional cases Minimum value analysis Two sources for each item
Strict control No/very low safety stock Frequent ordering Weekly control statement Maximum follow up Rigorous value analysis Maximum sources for each item
Accurate material planning
Minimization of waste Centralized purchase Maximum effort to reduce
Estimates based on past data Rough estimates
Moderate checks Combination purchase Moderate efforts Periodic checks Decentralized purchase Minimum efforts Delegated to lower levels Group posting
lead time
12.
Handled by senior management Handled by middle management Individual posting Small group posting
13.
Inventory Data
Code [1] Usage-units [2] Unit Price Rs [3] Usage Value-Rs [2] * [3] Percentage of Total cost
1001 1002 1003 1004
50 4 8 100
600 200 1000 10
30000 800 8000 1000
1005
1006 1007 1007 1008
150
250 30 12 2
100
8 400 100 750
15000
2000 12000 1200 1500
1009
1010 1011 1012 TOTAL
20
200 8 1000 1834
25
11 100 25
500
2200 800 25000 1,00,000 100
EOQ model under quantity –discount Total Cost =
Per annum
S X Cu +
Annual Purchase Cost (3)
S X Cp + ½ X q X Cu X I q
Annual ordering cost (2) Annual Inv. Carrying cost (1)
(4)
(4) = (1) + (2) + (3) Total annual cost
Total Cost = (1) +(2) Costs (1) Annual Inv-carrying cost (3) Annual cost of items
EOQ
(2) Annual ordering cost (q) Order quantity (units)
When Total cost per annum can vary with the order size (quantity) i.e. Cu is dependent on q or when quantity discounts applicable.
For example : - If S = 10,000 units /year Cp = Rs. 20 per order Cu = Cost per unit (price) – variable I = 0.20 (20% of av.inventory investment) Slab Order size (q) Cost/unit (Cu) EOQ A 0.499 Rs.5.00 q0A = 633 B 500.999 Rs.4.50 q0B= 666 C 1000 and above Rs. 3.90 q0C = 716 Using q0 =
Feasibility No Yes No
2. S. Cp and calculating q0 A, q0 B& q0 C, Cu X i If all EOQs (or more than one EOQ) are ‘feasible’ then select the EOQ with the lowest unit cost (Cu) However, one practical consideration in quantity-discount problems is that the cost reduction from volume purchases frequency makes it seemingly economical to order quantities larger than EOQ.
Cu = Rs. 5.00 Cu = Rs. 4.50 Cu = Rs.3.90
Infeasible range
Feasible range
Total Cost
Rs. 39,590 Rs 45,600
666 500 q0 A 633 q0 B
716
1000 q0 C Order Size
In practical scenario, some EOQs may not be feasible i.e. EOQ does not fall within the feasible unit cost (Cu) range). In these situations, we have to calculate the Total Annual Cost for each unit cost (Cu) at the respective EOQs where it is feasible. Where it is not feasible we calculate the total cost at the minimum quantity where the respective unit cost (Cu) is first applicable. These total costs are then compared and the quantity or EOQ associated with the lowest total cost is the ‘order quantity’ that is selected. Procedurally, the largest order quantity (lowest unit price) is solved first, if the resulting q is valid or feasible, that is the answer. If not, the next largest order quantity (second lower price) is derived. If that is feasible, the cost of this q is compared to the cost of using the order quantity at the price break above and the lowest cost determines the optimal q.
(1)
Inv. Carrying cost
q X Cu X i 2
q0B = 666. Cu = 4.50 666 (0.2) (4.50)
Price break at 1000 Cu=3.90
2
= Rs. 299.70
1000 (0.2) X 3.90
= Rs. 390 10,000 (20) = Rs.200 1000 390 + 200 = 590 10,000 X 3.90 = 39,000 Rs. 39,590
(2)
Procurement Cost (1) + (2)
S X Cp q
10,000 X 20 = Rs. 300 666 300 + 300 = Rs. 600
(3)
Purchase Cost
S X Cu
10,000 X 4.50 = 45,000 Rs. 45,000
(4)
Total Cost (1) + (2) + (3)
Problem: A manufacturing unit producing electrical appliances require 4000 switches per year. The ordering cost is Rs 50 per order. The inventory carrying cost is 8 % of purchase price per unit on an annual basis. The switches are priced as follows:
Order Quantity-units
1 to 499 500 to 999
Unit price-Rs
9.00 8.50
1000 and above
8.00
Find out the optimum order quantity and the annual total cost .
Problem
? Data: ? Cp: Rs 64 per order. ? i=0.20, ? S=49 units per year. ? Cu: variable
Slab A B
Order Unit price Quantity-units [Cu]-Rs 1 to 199 200 and above 50.25 49.00
EOQ 79 80
Find the EOQ and the least total cost
doc_323132596.ppt