Inventory Control [PDF]

Inventory Usage Over Tim e. Figure 12.3. Order quantity = Q. (maximum ... Optimal order quantity. The EOQ Model. Q = Num

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Idea Transcript


! "

# $ % % # ) *

& $' (

1

+, + # +

Percent of annual dollar usage

'

& 80 70 60 50 40 30 20 10 0

(

A Items – – – – – – – – B Items – |

10

|

20

&

(

+

C Items |

30

|

40

Percent of inventory items

|

50

|

60

|

70

Figure 12.2

2

'

%

.

&

(

+ / / + / +

0 1

# #

%

" /2 /2

3

3

'

4

'

"

!

Inventory level

" Order quantity = Q (maximum inventory level)

Usage rate

Average inventory on hand Q 2

Minimum inventory Time Figure 12.3

4

# Objective is to minimize total costs Curve for total cost of holding and setup

Annual cost

Minimum total cost Holding cost curve Setup (or order) cost curve Optimal order quantity

Table 11.5

$

Order quantity

Annual setup cost =

D S Q

Q = Number of pieces per order Q* = Optimal number of pieces per order (EOQ) D = Annual demand in units for the Inventory item S = Setup or ordering cost for each order H = Holding or carrying cost per unit per year Annual setup cost = (Number of orders placed per year) x (Setup or order cost per order) =

Annual demand Number of units in each order

=

D (S) Q

$

Setup or order cost per order

Annual setup cost = Annual holding cost =

Q = Number of pieces per order Q* = Optimal number of pieces per order (EOQ) D = Annual demand in units for the Inventory item S = Setup or ordering cost for each order H = Holding or carrying cost per unit per year

D S Q Q H 2

Annual holding cost = (Average inventory level) x (Holding cost per unit per year) =

Order quantity (Holding cost per unit per year) 2

=

Q (H) 2

5

D S Q Q Annual holding cost = H 2 Annual setup cost =

$ Q Q* D S H

= Number of pieces per order = Optimal number of pieces per order (EOQ) = Annual demand in units for the Inventory item = Setup or ordering cost for each order = Holding or carrying cost per unit per year Optimal order quantity is found when annual setup cost equals annual holding cost D Q S = H Q 2 Solving for Q*

2DS = Q2H Q2 = 2DS/H Q* =

2DS/H

% Determine optimal number of needles to order D = 1,000 units S = $10 per order H = $.50 per unit per year

Q* =

2DS H

Q* =

2(1,000)(10) = 0.50

40,000 = 200 units

% Determine optimal number of needles to order D = 1,000 units Q* = 200 units S = $10 per order H = $.50 per unit per year Expected Demand D number of = N = = Q* Order quantity orders 1,000 N= = 5 orders per year 200

6

% Determine optimal number of needles to order D = 1,000 units Q* = 200 units S = $10 per order N = 5 orders per year H = $.50 per unit per year Expected time between = T = orders

Number of working days per year N

T=

250 = 50 days between orders 5

% Determine optimal number of needles to order D = 1,000 units Q* = 200 units S = $10 per order N = 5 orders per year H = $.50 per unit per year T = 50 days Total annual cost = Setup cost + Holding cost TC =

D Q S + H 2 Q

TC =

1,000 200 ($10) + ($.50) 200 2

TC = (5)($10) + (100)($.50) = $50 + $50 = $100

& The EOQ model is robust It works even if all parameters and assumptions are not met The total cost curve is relatively flat in the area of the EOQ

7

' EOQ answers the “how much” question The reorder point (ROP) tells when to order ROP =

Demand Lead time for a per day new order in days

=dxL D

d = Number of working days in a year

Inventory level (units)

' Q*

Slope = units/day = d

ROP (units)

Figure 12.5

Lead time = L

'

Time (days)

%

Demand = 8,000 DVDs per year 250 working day year Lead time for orders is 3 working days d=

D Number of working days in a year

= 8,000/250 = 32 units ROP = d x L = 32 units per day x 3 days = 96 units

8

'

Inventory level

'

Part of inventory cycle during which production (and usage) is taking place Demand part of cycle with no production

Maximum inventory

t

Time Figure 12.6

' Q = Number of pieces per order p = Daily production rate H = Holding cost per unit per year d = Daily demand/usage rate t = Length of the production run in days Annual inventory Holding cost = (Average inventory level) x holding cost per unit per year Annual inventory = (Maximum inventory level)/2 level Maximum Total produced during inventory level = the production run



Total used during the production run

= pt – dt

9

' Q = Number of pieces per order p = Daily production rate H = Holding cost per unit per year d = Daily demand/usage rate t = Length of the production run in days Maximum = Total produced during inventory level the production run



Total used during the production run

= pt – dt

However, Q = total produced = pt ; thus t = Q/p Q Maximum inventory level = p p Holding cost =

–d

Q p

=Q 1–

d p

Maximum inventory level Q (H) = 2 2

1–

d p

H

' Q = Number of pieces per order H = Holding cost per unit per year D = Annual demand

p = Daily production rate d = Daily demand/usage rate

Setup cost = (D/Q)S Holding cost = 1/2 HQ[1 - (d/p)] (D/Q)S = 1/2 HQ[1 - (d/p)] Q2 = Q* =

2DS H[1 - (d/p)] 2DS H[1 - (d/p)]

' % D = 1,000 units S = $10 H = $0.50 per unit per year Q* =

2DS H[1 - (d/p)]

Q* =

2(1,000)(10) 0.50[1 - (4/8)]

p = 8 units per day d = 4 units per day

=

80,000

= 282.8 or 283 hubcaps

10

' When annual data are used the equation becomes 2DS annual demand rate H 1– annual production rate

Q* =

( Reduced prices are often available when larger quantities are purchased Trade-off is between reduced product cost and increased holding cost Total cost = Setup cost + Holding cost + Product cost TC =

D QH S+ + PD Q 2

( A typical quantity discount schedule 4 8

4 1

4

7

4

& 6(

&(

5 Table 12.2

11

( Steps in analyzing a quantity discount 1. For each discount, calculate Q* 2. If Q* for a discount doesn’t qualify, choose the smallest possible order size to get the discount 3. Compute the total cost for each Q* or adjusted value from Step 2 4. Select the Q* that gives the lowest total cost

( Total cost curve for discount 2

Total cost $

Total cost curve for discount 1

a

Q* for discount 2 is below the allowable range at point a and must be adjusted upward to 1,000 units at point b

1st price break

0

Total cost curve for discount 3

b

2nd price break

1,000

2,000 Order quantity

( Calculate Q* for every discount

Figure 12.7

% Q* =

2DS IP

Q1* =

2(5,000)(49) = 700 cars order (.2)(5.00)

Q2* =

2(5,000)(49) = 714 cars order (.2)(4.80)

Q3* =

2(5,000)(49) = 718 cars order (.2)(4.75)

12

(

%

Calculate Q* for every discount

2(5,000)(49) = 700 cars order (.2)(5.00)

Q2* =

2(5,000)(49) = 714 cars order (.2)(4.80) 1,000 — adjusted

Q3* =

2(5,000)(49) = 718 cars order (.2)(4.75) 2,000 — adjusted

% +

1

2DS IP

Q1* =

( 4 8

Q* =

+

+ "

7

3

Table 12.3

Choose the price and quantity that gives the lowest total cost Buy 1,000 units at $4.80 per unit

%

'

13

/ 71 % 9 '

+ 8

4 "

1

14

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