Item used or sold as they are completed, without waiting for a full lot to be completed
Usual case is where production rate, p , exceeds the demand rate, d , so there is a buildup rate of ( p – d ) units during time when both production and demand occur.
Both p and d expressed in same time interval.
Special Inventory Models Non-Instantaneous Replenishment
Buildup at a rate of ( p-d ) (units/day) during production phase until a lot size of Q is produced
Buildup continues for Q / p days (units/units/day)
I max = units per day, ( p-d ), x number of days ( Q / p )
where: p = production rate d = demand rate Q = lot size
Non-Instantaneous Replenishment Economic Lot Size (ELS)
5.
Total Cost = Annual holding costs + annual ordering costs
Setting up the total cost equation, where D is the annual demand:
Non-Instantaneous Replenishment Economic Lot Size (ELS)
6.
Differentiation of this equation with respect to Q , setting the result equal to zero, and solving for Q results in the Economic Production Lot Size, ELS :
Since p > d , the second term is greater than 1,
so the ELS is __________ than the EOQ
Non-Instantaneous Replenishment Economic Lot Size (ELS)
7.
Demand = 30 barrels/day Setup cost = $200 Production rate = 190 barrels/day Annual holding cost = $0.21/barrel Annual demand = 10,500 barrels Plant operates 350 days/year Non-Instantaneous Replenishment Example ELS = p p - d 2 DS H
13.
C for P = $4.00 C for P = $3.50 C for P = $3.00 Total annual cost, $ Purchase quantity, Q 0 100 200 (a) Total cost curves with purchased materials added Purchase Discounts Total Cost Curves First price break Second price break
14.
Step 1:
Beginning with the lowest price, calculate the EOQ for each price level until a feasible EOQ is found.
it is feasible if the quantity lies in the range corresponding to its price.
As subsequent prices are larger than the previous one, the holding cost, H , ( H = i·P ) gets larger.
Since H is in the denominator of the EOQ formula, the EOQ gets smaller .
Purchase Discounts Solution Procedure
15.
Purchase Discounts Example Annual demand = 936 units Ordering cost = $100.00 Holding cost = 25% of unit price Order Quantity Price per Unit 0 - 249 $60.00 250 - 499 $59.00 500 or more $58.00
19.
Purchase Discounts Example Annual demand = 936 units Ordering cost = $100.00 Holding cost = 25% of unit price Order Quantity Price per Unit 0 - 249 $60.00 250 - 499 $59.00 500 or more $58.00
20.
The best purchase quantity is 250 units, which does not correspond to the deepest discount price.
This is not always true - EOQ is affected by:
small discounts, quantity break points,
large holding cost, and
small demand.
Small lot sizes may be better even though the price is not the lowest
Quantity Discounts Example
21.
Single-Period Inventory Model
One time purchasing decision (Example: vendor selling t-shirts at a football game)
Seeks to balance the costs of inventory overstock and under stock
Multi-Period Inventory Models
Fixed-Order Quantity Models
Event triggered (Example: running out of stock)
Fixed-Time Period Models
Time triggered (Example: Monthly sales call by sales representative)
Special Inventory Models Inventory Models
22.
Problem for seasonal and high fashion goods.
Only allowed to order one time.
Short selling seasons and long lead times prohibit the possibility of placing a second order.
A balance between ordering enough to meet demand and not having any left over at the end of the season.
Sometimes referred to as the ”Newsvendor” problem
Special Inventory Models One-Period Decisions
23.
List different demand levels and probabilities
Develop a payoff table, where each new row represents a different order quantity and each column represents a different demand.
One-Period Decisions Selecting the Purchase Quantity
24.
The payoff is:
where: p = profit per unit sold during the season l = loss per unit disposed of after the season Q = purchase quantity D = demand level
One-Period Decisions Selecting the Purchase Quantity
25.
Calculate the expected payoff of each Q . For a specific Q , first multiply each payoff by its demand probability, and then add the products.
Choose the order quantity Q with the highest expected payoff.
One-Period Decisions Selecting the Purchase Quantity
26.
For one item, p = $10 and l = $5. The probability distribution for the season’s demand is:
Demand Demand ( D ) Probability 10 0.2 20 0.3 30 0.3 40 0.1 50 0.1
One-Period Decisions Example
27.
Complete the following payoff matrix, as well as the column on the right showing expected payoff.