Lecture 5 (2)

Question 1

single period inventory model

Answer 1

One time purchasing decision (e.g. vendor selling t-shirts at a football game)

Seeks to balance the costs of inventory overstock and understock

Question 2

Multi-period inventory models

Answer 2

Fixed-order quantity models
Event triggered (e.g. running out of stock)

Fixed-time period models
Time triggered (e.g. monthly sales by call sales representative)

Question 3

Surplus cost (overage cost)

Answer 3

C0 per unit remaining at the end of the season

C0 = purchase cost - salvage value

Question 4

Shortage cost (underage cost)

Answer 4

Cu per unit short at the end of the season

Cu = sales price - purchase cost

Question 5

Expected total mismatch cost:

Answer 5

TC = C0Expected overage inentory + CuExpected underage inventory

Question 6

Margin analysis: to optimally balance the cost of overstocking versus the cost of understocking

Answer 6

Increase the size of the order (Q) until

C0P(D<Q) = CuP(D>Q) –> C0P(D<Q) = Cu(1-p(D<Q))

The optimal probability that an additional unit will not be sold is:

P(D<Q) = Cu/Co + Cu

Question 7

Balancing the risk and benefit of ordering a unit

Ordering one more unit increases the change of overage

Answer 7

Expected loss on the Qth unit = Co x F(Q)
F(Q) = Prob(Demand <Q)

b

Question 8

The benefit/gain of ordering one more unit is the reduciton in the chance of underage

Answer 8

Expected gain on the Qth unit = Cu x(1-F(Q))

Question 9

Balancing the risk and benefit of ordering a unit

Answer 9

As more units are ordered the expected benefit from ordering one unit decreases, while the expected loss of ordering one more unit increases. –> we are now looking for the point where the two functions cross.

Question 10

Critical ratio formula

Answer 10

CR = Cu/Co+Cu

Let Q* be the optimal order quantity
F(Q*) =CR

where F is the cdf of demand

Question 11

When the demand –N(myu,omega)

Find the z that corresponds to the critical ratio

Calculate optimal order Q* = myu (mean?)+ z*omega

THis is the quantity that minimizes total cost(=maximize profit)

Question 12

ABC inventory classification

Answer 12

Classifying inventory according to some measure of importance and allocating control efforts accordingly (pareto principle)

A = very important (20% of the total items, about 80% of the total inventory costs)
B= mod. important (account for the other 80% of total items and only 20% of costs)
C = least important

Question 13

Classification into ABC is usually based on

Answer 13

Single criterion

Demand (sales) value or demand (sales) volume

Question 14

Classification into A-B-C is usually based on single criterion
* demand (sales) value or demand (sales) volume
* However, other factors should be taken into account as well

Answer 14

Item criticality
Required customer service

Question 15

Multi dimensional ABC analysis

Answer 15

E.g. 2Way classification on sales volume and criticality

Use of composite, single criterion

Typically 20% A, 30% B and 50% C and same product availability (service level) for all
products but…

Question 16

summary

Answer 16

Organizations rely on inventory to balance supply and demand and to buffer uncertainties in the supply chain

Inventory can be one of the most expensive assets

Too much inventory –> excessive holding costs, tied capital etc

Too little inventory –> low custoer service, hhigh ordering costs

Newspaper model: optimal balances the cost of overstocking versus the cost cost of understocking for a single order period

Offers the optimal service level (probability of no stockout)

Maximizsed the expected profit

ABC analysis to prioritize monitoring efforts, set adequate (service) levels