Post on 22-Jan-2018
Help to decide
How much to order
When to order
Basic EOQ model
Receive an order
Use the inventory at a constant rate
Reorder same amount
Instantaneously receive the order
On
-han
d i
nve
nto
ry (
un
its)
Time
Averagecycleinventory
Q
Q—2
1 cycle
Receive order
Inventory depletion (demand rate)
Total Cost = Holding Cost + Order CostTotal Cost = Holding Cost + Order Cost
An
nu
al c
ost
(d
olla
rs)
Lot Size (Q)
Holding cost (HC)
An
nu
al c
ost
(d
olla
rs)
Lot Size (Q)
Holding cost (HC)
Ordering cost (OC)
HQ
ingCostAnnualHold
=2
)//)(( yearunittHoldingCosryAveInvento
ingCostAnnualHold =
| | | | | | | |50 100 150 200 250 300 350 400
Lot Size (Q)
3000 —
2000 —
1000 —
0 —
Holding cost = (H)Q2
An
nu
al c
ost
(d
oll
ars)
)(OrderCostityOrderQuant
ndAnnualDemarCostAnnualOrde =
SQ
DrCostAnnualOrde =
| | | | | | | |50 100 150 200 250 300 350 400
Lot Size (Q)
3000 —
2000 —
1000 —
0 —
Holding cost = (H)Q2
Ordering cost = (S)DQ
An
nu
al c
ost
(d
oll
ars)
| | | | | | | |50 100 150 200 250 300 350 400
Lot Size (Q)
3000 —
2000 —
1000 —
0 —
Total cost = (H) + (S)DQ
Q2
Holding cost = (H)Q2
Ordering cost = (S)DQ
An
nu
al c
ost
(d
oll
ars)
HQ
SQ
DTC
2+=
ngCostTotalHoldiCostTotalOrderTotalCost +=
HQ
SQ
DTC
2+=D – Total demand
Q – Order quantity
S – Setup/order cost
H – Holding cost
Reorder point (ROP)
Lead time – amount of time from order placement to
receipt of goods
Lead time demand – the demand the occurs during
the lead time
Abstract•In this paper, we study periodic inventory systems with long review periods.
•We develop dynamic programming models for these systems in which regular orders as well as emergency orders can be placed periodically. •We identify two cases depending on whether or not a fixed cost for placing an emergency order is present.
•We show that if the emergency supply mode can be used, there exists a critical inventory level such that if the inventory position at a review epoch falls below this critical level, an emergency order is placed.
•.
•We also develop simple procedures for computing the optimal policy parameters. In all cases, the optimal order-up-to level is obtained by solving a myopic cost function.
• •Thus, the proposed ordering policies are easy to implement
we develop dynamic programming models for an inventory system where regular orders as well as emergency orders can be placed periodically.
We identify two important cases depending on whether or not a fixed cost for placing an emergency order is present.
We show that if the emergency supply channel can be used, there exists a critical inventory level such that if the inventory position at a review epoch falls below this level, an emergency order is placed.
We also develop simple procedures for computing the optimal policy parameters. In all cases, the optimal order-up-to level is obtained by solving a myopic cost function.
Thus, the proposed ordering policies are easy to implement.