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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...


Firms Objective : “Making Money:






Reduce Inventory – Lowers Cost – Enhances Profit

LUC is used to take the adv...
LEAST UNIT COST


A dynamic lot sizing technique that:


Includes ordering cost and inventory carrying cost
for each tri...
LOT SIZING CALCULATION
 As

it is discussed before, least unit cost heuristic
chooses a lot size that equals the demand o...
LOT-SIZING
Example: The MRP gross requirements for Item A are shown here for the next 10
weeks. Lead time for A is three w...
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...
Lot-Sizing: Least Unit Cost
Period
Gross
Requirements
Beginning
Inventory
Net
Requirements
Time-phased Net
Requirements
Pl...
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...
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...
THANK
YOU
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Opc least unit cost

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Transcript of "Opc least unit cost"

  1. 1. LOT SIZING: LEAST UNIT COST BY: RISHABH JAIN 311 UMANG AGARWAL 352
  2. 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. 3.  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.
  4. 4. 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.
  5. 5. 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 ]
  6. 6. 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
  7. 7. 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.
  8. 8. 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.
  9. 9. 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
  10. 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 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.
  11. 11. THANK YOU
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