Production Planning & Control: Inventory (Phase B)
Learning Outcomes 1. Identify or Define Define:: ♦ ♦
Economic Order Quantity (EOQ) Model Production Order Quantity (POQ) Model
Learning Outcomes 1. Identify or Define Define:: ♦ ♦
Economic Order Quantity (EOQ) Model Production Order Quantity (POQ) Model
Inventory Models ♦
Help answer the inventory planning questions!
Fixed order-quantity models Economic order quantity ♦ Production order quantity ♦ Quantity discount ♦
♦
Probabilistic models
♦
Fixed order-period models © 1984-1994 T/Maker Co.
EOQ
EOQ Assumptions Known and constant demand ♦ Known and constant lead time ♦ Instantaneous receipt of material ♦ No quantity discounts ♦ Only order (setup) cost and holding cost ♦ No stockouts ♦
Inventory Usage Over Time Order quantity = Q (maximum inventory level) l e v
Usage Rate
Average Inventory (Q*/2)
L y r o t n e v n I
Minimum inventory 0
Time
EOQ Model How Much to Order? Annual Cost
Minimum total cost
Order (Setup) Cost Curve Optimal Order Quantity (Q*)
Order quantity
Why Holding Costs Increase ♦
More units must be stored if more are ordered
Purchase Order Description Qty. Microwave 1
Order quantity
Purchase Order Description Qty. Microwave 1000
Order quantity
Why Order Costs Decrease Cost is spread over more units Example: You need 1000 microwave ovens 1 Order (Postage $ 0.33)
1000 Orders (Postage $330)
Purchase Order Description Qty.
PurchaseOrder Order Purchase PurchaseOrder Order Qty. Description Purchase Description Qty. Qty. Description Microwave Qty. 11 Description Microwave Microwave Microwave 11
Microwave
1000
Order quantity
Deriving an EOQ 1. Develop an expression for setup or ordering costs 2. Develo an ex ression for holdin cost 3. Set setup cost equal to holding cost 4. Solve the resulting equation for the best order quantity
EOQ Model When To Order Inventory Level Average Inventory (Q*/2)
Optimal Order Quantity
Reorder Point (ROP) Lead Time
Time
EOQ Model Equations 2 ×D ×S , Q* = H D Expected Number of Orders , N = Q * Optimal Order Quantity
Expected Time Between Orders
d =
D Working Days
ROP = d × L
, T =
or ng ays
N
D = Demand per year
/ Year
S = Setup (order) cost per order H = Holding (carrying) cost d = Demand per day L = Lead time in days
ear
Total cost
TC =
D Q
S+
Q 2
D = Demand per year Q = Optimal order quantity S = Setup (order) cost per order H = Holding (carrying) cost
H
The Reorder Point (ROP) Curve Q* Slope = units/day = d ) s t i
n u ( l v e l y r o t n e v n I
ROP (Units)
Time (days) Lead time = L
EOQ Model Problem 1 ABC Company supplies needles to hospitals. ♦ The annual demand is 1,000 units. ♦ The setup or ordering cost is $10 per order. ♦ The holding cost per unit per year is $0.50 Question: Determine the optimal number of units per order. ♦
Q* =
2 DS H
=
2(1,000)(10) 0.5
=
40,000
=
200 units
EOQ Model Problem 2 D = 1,000 units per year. ♦ S = $10 per order, H = $0.50 per unit per year. ♦ Total working day per year = 250. Question: Determine the optimal number of orders( N ) per year and the expected time between orders( T ). ♦
Q* =
N =
T =
2 DS H
=
2(1,000)(10)
Demand Order quantity
0.5
=
working days number of orders
1,000 200
=
250 5
=
=
=
40,000
=
200 units
5 orders per year
50 days between orders
EOQ Model Problem 3 D = 1,000 units per year. ♦ S = $10 per order, H = $0.50 per unit per year. Question: Determine the optimal total annual inventory cost. ♦
Q* =
TC =
=
H D Q
S +
,
=
Q
2
0.5
H
$50 + $50
=
=
=
40,000
=
1,000 200 ($10) + ($0.50) 200 2
$100
200 units
EOQ Model Problem 4 ♦ ♦ ♦
D = 8,000 units per year, working days = 250 per year. On average, delivery of an order takes 3 working days. Calculate the reorder point.
Demand per day, d =
working day per year
Reorder point, ROP = d × L = 32
unit day
×
=
, 250
=
32 units
3 day = 96 unit
Thus, when inventory stock drops to 96, an order should be placed. The order will arrive 3 days later, just as the firm' s stock is depleted.
POQ
Production Order Quantity Model Answers how much to order and when to order ♦ Allows partial receipt of material ♦
♦
♦
Suited for roduction environment ♦ ♦
♦
Other EOQ assumptions apply Material produced, used immediately Provides production lot size
Lower holding cost than EOQ model
POQ Model Inventory Levels Inventory Level Inventory level with no demand
Production Portion of Cycle
*
Supply Begins
Supply Ends
Max. Inventory Q·(1- d/p)
Demand portion of cycle with no supply
Time
Run Time Cycle Time
Reasons for Variability in Production Most variability is caused by waste or by poor management. Specific causes include:
employees, machines, and suppliers produce units that do not conform to standards are late or are not the ro er quantity inaccurate engineering drawings or specifications production personnel try to produce before drawings or specifications are complete customer demands are unknown
POQ Model Inventory Levels Inventory Level Inventory level with no demand
Production Portion of Cycle
*
Supply Begins
Supply Ends
Max. Inventory Q·(1-- d/p) Q·(1
Demand portion of cycle with no supply
Time
POQ Model Equations = Q * p
Optimal Order Quantity
Maximum inventory level
Setup Cost
Holding Cost
=
D
= Q *
=
1 -
( )
p D = Demand per year
* S
S = Setup cost
Q
= 0.5 * H * Q
2*D*S d H* 1 p
( ) 1-
d
p
H = Holding cost d = Demand per day p = Production per day
Example1 ♦
♦ ♦
Demand = 1,000 units per year, Setup = $10, Holding = $0.50 per unit per year, average daily demand = 4 units. Optimum production rate = 8 units per day. Total working days per year = 250 Calculate the optimum number of units per order.
=
Q p*
=
=
units,
2 DS d H [1 − ( )] p
20,000 0.5(0.5)
,
=
=
=
=
.
, p = units per ay,
2(1,000)(10) 4 0.5[1 − ( )] 8
80,000
=
282.8 ≈ 283 units
=
units per ay
Example 2 XYZ Computer Company uses 1,000 transistors each month for its computers assembly. The unit cost of each transistor is $10, and the cost of carrying one transistor in inventory for a year is $3. Ordering cost is $30 per order. Compute: (a) The optimal order quantity. (b) The expected number of orders placed each year. (c) The expected time between orders. (Assume 200 working day per year) D = 1000(12) units,
( a) Q*
=
(b) N =
2 DS
D Q*
H
=
S = $30,
=
12,000 490
H = $3
2(1,000 ×12)(30)
=
3
=
489.9 ≈
490 units
24.5 ≈ 25 orders per year
(c) Time between orders, T =
working day per year N
=
200 25
=
8 days
Example 3 Annual demand for notebook binders at Salina Stationery Shop is 10,000 units. The shop is operating 300 days per year and finds that deliveries from supplier generally takes 5 working days. Calculate the reorder point for the notebook binders. L
=
d =
5 days 10 ,000 300
=
ROP = d × L
33 .33 units per day
=
33 .33
unit day
×
5 day
=
166 .7 units
Salina Stationery Shop should reorder wh en her stock reaches 167 units
Example 4 Leonard Presby Inc. has an annual demand rate of 1,000 units but can produce at average production rate of 2,000 units. Setup cost is $10; carrying cost is $1. What is the optimal number of units to be produced each time.
=
Q p*
=
=
un s,
=
2 DS d H [1 − ( )] p
20,000 0.5
=
=
,
=
,
=
2(1,000)(10) 1,000 1[1 − ( )] 2,000
40,000
=
200 units
,
un s peryear ,
=
,
un s peryear
