2. LOT-SIZING
Deterministic model, where in reality the demand is uncertain and
subject to change.
Optimal solution to the deterministic model may actually yield higher
cost because of the changes in the demand.
Some heuristic methods (example : Least Unit Cost) give lower cost
in the long run.
If the demand and/or costs change, the optimal solution may change
significantly causing some managerial problems.
The heuristic methods may not require such changes in the
production plan.
3.
4.
Firms Objective : “Making Money:
Reduce Inventory – Lowers Cost – Enhances Profit
LUC is used to take the advantage of
economic purchase order discounts and also
to meet the variations in the product demand.
To find out lowest cost order quantity.
5. LEAST UNIT COST
A dynamic lot sizing technique that:
Includes ordering cost and inventory carrying cost
for each trial lot size.
Divides by the number of units in lot size.
Then picking the lot size with lowest unit cost.
6. LOT SIZING CALCULATION
As
it is discussed before, least unit cost heuristic
chooses a lot size that equals the demand of some K
periods in future, where K>0.
The
average holding and ordering cost per unit is
computed for each K=1, 2, 3, etc. starting from K=1
and increasing K by 1 until the average cost per unit
starts increasing. The best K is the last one up to which
the average cost per unit decreases.
The
only difference is that Silver-Meal heuristic chooses
K on the basis of average cost per period and least unit
cost on average cost per unit.
Unit cost = [(Ordering cost + Carrying cost + purchase
price) /
Order quantity ]
7. LOT-SIZING
Example: The MRP gross requirements for Item A are shown here for the next 10
weeks. Lead time for A is three weeks and setup cost is $10. There is a
carrying cost of $0.01 per unit per week. Beginning inventory is 90 units.
Week
1
2
3
4
5
Gross requirements Week
30
6
50
7
10
8
20
9
70
10
Determine the lot sizes.
Gross requirements
80
20
60
200
50
8. Lot-Sizing: Least Unit Cost
j
rj
Order for weeks
1 week, week 4
2 weeks, weeks 4 to 5
3 weeks, weeks 4 to 6
4 weeks, weeks 4 to 7
5 weeks, weeks 4 to 8
6 weeks, weeks 4 to 9
7 weeks, weeks 4 to 10
1
2
3
4
5
6
7
20 70 80 20
60 200 50
Units in the inventory at the end of Week
Q
4
5
6
7
8
9 10
H. Ord. Unit
Cost Cost Cost
The order is placed for K periods, for some K>0. Using the above table to find K.
9. Lot-Sizing: Least Unit Cost
Period
Gross
Requirements
Beginning
Inventory
Net
Requirements
Time-phased Net
Requirements
Planned order
Release
Planned
Deliveries
Ending
Inventory
1
2
3
4 5 6 7 8
9 10
30 50 10 20 70 80 20 60 200 50
90 60 10
0
0
0
0
20
20
60 10
0
Week 4 net requirement = 20 > 0. So, an order is required.
10. Lot-Sizing: Least Unit Cost
j
rj
Order for weeks
1 week, week 4
2 weeks, weeks 4 to 5
3 weeks, weeks 4 to 6
4 weeks, weeks 4 to 7
5 weeks, weeks 4 to 8
6 weeks, weeks 4 to 9
7 weeks, weeks 4 to 10
1
2
3
4
5
6
7
20 70 80 20
60 200 50
Units in the inventory at the end of Week
Q
4
5
6
7
8
9 10
20
If K=1, order is placed for 1 week and the order size = 20.
Then, the ending inventory = inventory holding cost =0.
The order cost = $10.
Average cost per unit = (0+10)/20=$0.50
H. Ord. Unit
Cost Cost Cost
0.00
10
.500
11. Lot-Sizing: Least Unit Cost
j
rj
Order for weeks
1 week, week 4
2 weeks, weeks 4 to 5
3 weeks, weeks 4 to 6
4 weeks, weeks 4 to 7
5 weeks, weeks 4 to 8
6 weeks, weeks 4 to 9
7 weeks, weeks 4 to 10
1
2
3
4
5
6
7
20 70 80 20
60 200 50
Units in the inventory at the end of Week
Q
4
5
6
7
8
9 10
H. Ord. Unit
Cost Cost Cost
20
0.00 10
.500
90 70
0.70 10
.119
If K=2, order is placed for 2 weeks and the order size = 20+70=90.
Then, inventory at the end of week 4 = 90-20=70 and
Holding cost =70 ×0.01. = 0.70.
Average cost per unit = (0.70+10)/90=$0.119.
