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.