1 Inventory Control. 2 Week 1Introduction to Production Planning and Inventory Control Week...
-
Upload
janice-campbell -
Category
Documents
-
view
221 -
download
2
Transcript of 1 Inventory Control. 2 Week 1Introduction to Production Planning and Inventory Control Week...
1
Inventory Control
2
Week 1 Introduction to Production Planning and Inventory Control
Week 2 Inventory Control – Deterministic Demand Week 3 Inventory Control – Stochastic Demand Week 4 Inventory Control – Stochastic Demand Week 5 Inventory Control – Stochastic Demand Week 6 Inventory Control – Time Varying Demand Week 7 Inventory Control – Multiple Echelons
Lecture Topics
3
Week 8 Production Planning and Scheduling Week 9 Production Planning and Scheduling Week 12 Managing Manufacturing Operations Week 13 Managing Manufacturing Operations Week 14 Managing Manufacturing Operations Week 10 Demand Forecasting Week 11 Demand Forecasting Week 15 Project Presentations
Lecture Topics (Continued…)
4
Inventory in the US Economy
$290.40 billionWholesale(23.2%)
$122.10billionOther(9.8%
$98.60 billionFarm
(7.9%)
$424.60 billion
Manufacturing (33.9%)
$316.00 billionRetail (25.2%)
5
Inventory Types
6
Inventory Types
Raw Materials
Work-in-process (WIP)
Finished goods inventory (FGI)
7
Inventory Location
8
Inventory Location
Manufacturing Facility
In-Transit
Warehouse
Retailer
Customer
9
Benefits of Inventory
10
Benefits of Inventory
Reduces ordering, setup & transportation costs (economies of scale)
Buffer against demand fluctuations
Buffer against supply fluctuations Supply shortages
Variability in supply lead times
11
Benefits of Inventory (continued…)
Buffer against price fluctuations
Benefits from quantity discounts
Protects production capacity
Allows production smoothing
Reduces managerial complexity (eliminates the need for coordination)
Can increase demand
12
The Cost of Inventory
13
The Cost of Inventory
Tied up capital
Warehousing cost
Deterioration
Obsolescence
Demand shortfall
Quality defects
Changes in raw material prices
Changes in product design specifications
14
What if demand uncertainty and variability are
eliminated?
15
What if demand uncertainty and variability are
eliminated?
What if replenishment lead times are made
insignificant?
16
What if demand uncertainty and variability are
eliminated?
What if replenishment lead times are made
insignificant?
What if ordering & setup costs are made
negligible?
17
What if demand uncertainty and variability are
eliminated?
What if replenishment lead times are made
insignificant?
What if ordering & setup costs are made negligible?
What if production capacity is never a constraint?
18
Demand Constant Time varying Stochastic
Supply lead time Deterministic Stochastic Load-dependent
Review Continuous review Periodic review
Characteristics of Inventory Systems
19
Excess Demand Backordering Lost sales Impatient customers Item substitution
Capacity Unlimited Limited Deterministic Stochastic
Characteristics of Inventory Systems(continued…)
20
Number of items & customer classes Single item Multiple items Single customer class Multiple customer classes
Inventory quality Perishability Obsolescence Imperfect yield
Characteristics of Inventory Systems(continued…)
21
Holding cost (h) Capital cost Taxes and insurance Deterioration, spoilage, obsolescence
Ordering (setup) cost (A) Purchasing (production) costs (c) Shortage cost (p)
backordering cost lost sale cost
Cost Measures
22
h = ic (cost per unit per time period)
28% = cost of capital 2% = taxes and insurance6% = storage cost1% = breakage cost 37% = total interest charge (i) per year
If c = $100, then h = ic = $37
Example
23
The Economic Order Quantity (EOQ) Model
24
Assumptions of the Basic Model
Demand occurs continuously over time with a constant rate
Inventory can be replenished instantaneously There are no capacity limits or limits on the size of
replenishment orders A replenishment order incurs a fixed ordering (or setup)
cost Multiple products can be analyzed independently of each
other No backorders are allowed
25
Notation
D: demand rate (units per unit time)
c: unit purchase/production cost (dollars per unit)
A: fixed cost to place an order (dollars)
h: holding cost (dollars per unit per unit time); if the holding cost consists entirely of interest on money tied up in inventory, then h=ic where i is an interest rate.
Q: the size of the order (a decision variable)
26
Inventory versus Time
Q
Inven
tory
Time
27
Inventory versus Time
Q/D 2Q/D 3Q/D 4Q/D
Q
Inven
tory
Time
28
Costs
Holding cost:
average inventory2
Average holding cost per unit time2
Average unit holding cost2
Q
hQ
hQD
29
Costs
Holding cost:
Ordering/setup cost:
per order, so unit order cost
Average order cost per unit time=
AAQADQ
average inventory2
Average holding cost per unit time2
Average unit holding cost2
Q
hQ
hQD
30
Costs
Holding cost:
Ordering/setup cost:
Production cost: c per unit
per order, so unit order cost
Average order cost per unit time=
AAQADQ
average inventory2
Average holding cost per unit time2
Average unit holding cost2
Q
hQ
hQD
31
Total Cost
Total cost per unit time:
cDQ
DA
hQQY
2)(
32
Total Cost
Total cost per unit time:
Total cost per unit:'( )
2
hQ AY Q c
D Q
cDQ
DA
hQQY
2)(
33
Economic Order Quantity
hQ/2
AD/Q
Q
Y(Q
)
34
The Economic Order Quantity
2
( )0
2
dY Q h A
dQ D Q
35
The Economic Order Quantity
h
ADQ
Q
A
D
h
dQ
QdY
2
02
)(
*
2
36
Optimal Cost
Optimal average cost per unit:
Optimal average cost per unit time (e.g., per year):
**
*'( )
2
2
2 2
22 /
2
hQ AY Q c
D Q
h AD h Ac
D AD h
Ac Ah D c
AD h
*( ) 2Y Q ADh cD
37
Sensitivity to Order Quantity
Ordering and holding cost from using Q’:
Ratio
2
hQ AD
Q
*
* *
Cost( ) 2 1
Cost( ) 22
Q hQ AD Q Q Q
Q Q QADh
38
Sensitivity to Order Quantity
Ordering and holding cost from using Q’:
Ratio
Example Q' = 2Q*, then the ratio of the actual to optimal cost is (1/2)[2 + (1/2)] = 1.25
2
hQ AD
Q
*
* *
Cost( ) 2 1
Cost( ) 22
Q hQ AD Q Q Q
Q Q QADh
39
Sensitivity to Order Quantity
Large deviations from the optimal order quantity lead to relatively small deviations from the optimal cost.
40
Order Quantity versus Order Interval
Order Interval: Let T represent time between orders, then
Total cost:
Optimal Order Interval:
DQT
**
2A QT
hD D
cDT
AhDTcD
Q
DA
hQQY
22)(
41
Some Limitations of the EOQ Model
Demand is deterministic and constant
Instantaneous replenishments
Ordering costs are constant and independent of order size
No accounting for interactions among multiple items
No backordering
42
Extensions
Non-zero order replenishment lead times
Non-zero safety stocks
Finite supply capacity
Backordering
43
Non-Zero Replenishment Lead Times
44
Non-Zero Replenishment Lead Times
If L is the lead time and r is the reorder point, then r = DL
A non-zero lead time has no effect on Q* or Y(Q)
45
Non-Zero Safety Stocks
If ss is the safety stock, then
A non-zero safety stock affects Y(Q) but has no effect on Q*
cDQDAssQhQY )
2()(