Schedule Lot Size Rules & Cost Trade-offs

Schedule Lot Size Rules & Cost Trade-offs ISQA 459/559 Mellie Pullman

Homework A-Cat Corp • Note the holding cost should be $.50 per week • Case says: “Inventory carrying cost =0.5 per cent”

Lead Times • The time required to purchase, produce, or assemble an item • For purchased items – the time between the recognition of a need and the availability of the item for production • For production – the sum of the order, wait, move, setup, store, and run times

Must have D and E completed here so production can begin on B Start production of D 1 week 2 weeks to produce D B 2 weeks E A 2 weeks 1 week E 1 week 2 weeks G C 3 weeks F 1 week D | | | | | | | | 1 2 3 4 5 6 7 8 Time in weeks Time-Phased Product Structure

Set-up & Order Costs • Set-up: Cost to prepare a machine or process for an order • Order: cost of supplies, forms, order processing time, support. • Often combined together as S: set up and ordering cost

Lot-Sizing TechniquesL4L • Lot-for-lot techniques order just what is required for production based on net requirements • May not always be feasible • If setup costs are high, costs may be high as well

Lot-for-Lot Example (1 week lead time) Holding cost = $1/week; Setup cost = $100

Lot-for-Lot Example No on-hand inventory is carried through the system Total holding cost = $0 There are seven setups for this item in this plan Total setup cost = 7 x $100 = $700 Holding cost = $1/week; Setup cost = $100

Lot-Sizing Techniques • Economic order quantity (EOQ) • EOQ expects a known constant demand and MRP systems often deal with unknown and variable demand

Basic EOQ Model Important assumptions Demand is known, constant, and independent Lead time is known and constant Receipt of inventory is instantaneous and complete Quantity discounts are not possible Only variable costs are setup and holding Stockouts can be completely avoided

2DS H Q* = 2(27)(100) 1.00 Q* = = 5,400 = 73.48 units An EOQ Example Determine optimal number of items to order D = 27 units per week S = $100 per order H = $1.00 per unit per week

EOQ Lot Size Example Holding cost = $1/week; Setup cost = $100; 52 weeks Average weekly gross requirements = 27; EOQ = 73 units

EOQ Lot Size Example Annual demand = 1,404 Total cost = setup cost + holding cost Total cost = (1,404/73) x $100 + (73/2) x ($1 x 52 weeks) Total cost = $3,798 Cost for 10 weeks = $3,798 x (10 weeks/52 weeks) = $730 Or// 4*100 + 375*1 =775 Holding cost = $1/week; Setup cost = $100; Average weekly gross requirements = 27; EOQ = 73 units

Lot-Sizing TechniquesLeast Total Cost • LTC looks at batches of orders • Looking at total cost of placing orders & carrying inventory • You combine orders to the point where the holding/ carrying cost for an order is closest the order/setup cost.

Least Total Cost Holding cost = $1/week; Setup cost = $100;

Total Cost Approach3 grouped orders

Total Cost Approach with 3- Grouped orders Holding cost = $1/week; Setup cost = $100; Total inventory on hand = 190 *1=190 Orders 3 *100= 300

Least Unit Cost Approach

Least unit Cost Approach Holding cost = $1/week; Setup cost = $100; Total inventory on hand = 195 *1=195 Orders 3 *100= 300

Lot-Sizing Summary For these examples Lot-for-lot $700.00 EOQ $775.00 Total Cost $490.00 Unit Cost $495.00

You try it example: EOQ CostEOQ = 200 Holding cost = $1/week; Setup cost = $100;

Total Cost Example Holding cost = $1/week; Setup cost = $100;

You try it Total Cost Approach

L4L Example Holding cost = $1/week; Setup cost = $100;

Lot-Sizing Summary • In theory, all lot sizes should be recomputed whenever there is a requirement or order quantity change • In practice, this results in system nervousness and instability • Lot-for-lot should be used when economical • Lot sizes can be modified to allow for scrap, process constraints, and purchase lots

Lot-Sizing Summary • Use lot-sizing with care as it can cause considerable distortion of requirements at lower levels of the BOM • When setup costs are significant and demand is reasonably smooth, Total Cost or EOQ should give reasonable results

200 – 150 – 100 – 50 – – 200 – 150 – 100 – 50 – – Capacity exceeded in periods 4 & 6 Lot 6 “split” Lot 11 moved Available capacity Available capacity Lot 11 Lot 6 Lot 6 Lot 11 Standard labor hours Standard labor hours Lot 9 Lot 9 Lot 15 Lot 15 Lot 12 Lot 12 Lot 7 Lot 7 Lot 2 Lot 2 Lot 4 Lot 4 Lot 1 Lot 1 Lot 10 Lot 10 Lot 14 Lot 14 Lot 16 Lot 16 Lot 13 Lot 13 Lot 8 Lot 8 Lot 3 Lot 3 Lot 5 Lot 5 1 1 2 2 3 3 4 4 5 5 6 6 7 7 8 8 Period (a) Period (b) Resource Requirements Profile

Smoothing Tactics • Overlapping • Sends part of the work to following operations before the entire lot is complete • Reduces lead time • Operations splitting • Sends the lot to two different machines for the same operation • Shorter throughput time but increased setup costs • Lot splitting • Breaking up the order into smaller lots and running part ahead of schedule

Schedule Lot Size Rules & Cost Trade-offs