LOT SIZING:LEAST UNIT COST

BY:

RISHABH JAIN 311

UMANG AGARWAL 352

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.

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.

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.

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 ]

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 Gross requirements Week Gross requirements

1 30 6 80

2 50 7 20

3 10 8 60

4 20 9 200

5 70 10 50

Determine the lot sizes.

LOT-SIZING

j 1 2 3 4 5 6 7r j 20 70 80 20 60 200 50

H. Ord. UnitOrder for weeks Q 4 5 6 7 8 9 10 Cost Cost Cost1 week, week 4

2 weeks, weeks 4 to 53 weeks, weeks 4 to 64 weeks, weeks 4 to 75 weeks, weeks 4 to 86 weeks, weeks 4 to 9

7 weeks, weeks 4 to 10

Units in the inventory at the end of Week

Lot-Sizing: Least Unit Cost

The order is placed for K periods, for some K>0. Using the above table to find K.

Lot-Sizing: Least Unit Cost

Period 1 2 3 4 5 6 7 8 9 10GrossRequirements

30 50 10 20 70 80 20 60 200 50

BeginningInventory

90 60 10 0

NetRequirements

0 0 0 20

Time-phased NetRequirementsPlanned orderReleasePlannedDeliveriesEndingInventory

60 10 0

20

Week 4 net requirement = 20 > 0. So, an order is required.

j 1 2 3 4 5 6 7r j 20 70 80 20 60 200 50

H. Ord. UnitOrder for weeks Q 4 5 6 7 8 9 10 Cost Cost Cost1 week, week 4

2 weeks, weeks 4 to 53 weeks, weeks 4 to 64 weeks, weeks 4 to 75 weeks, weeks 4 to 86 weeks, weeks 4 to 9

7 weeks, weeks 4 to 10

Units in the inventory at the end of Week

Lot-Sizing: Least Unit Cost

20 0.00 10 .500

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

j 1 2 3 4 5 6 7r j 20 70 80 20 60 200 50

H. Ord. UnitOrder for weeks Q 4 5 6 7 8 9 10 Cost Cost Cost1 week, week 4

2 weeks, weeks 4 to 53 weeks, weeks 4 to 64 weeks, weeks 4 to 75 weeks, weeks 4 to 86 weeks, weeks 4 to 9

7 weeks, weeks 4 to 10

Units in the inventory at the end of Week

Lot-Sizing: Least Unit 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.

THANK YOU