Inventory Stable Demand Dr Ron Lembke Economic Order

Inventory: Stable Demand Dr. Ron Lembke

Economic Order Quantity Assumptions Demand rate is known and constant No order lead time Shortages are not allowed Costs: S - setup cost per order H - holding cost per unit time

EOQ Inventory Level Q* Optimal Order Quantity Decrease Due to Constant Demand Instantaneous Average Receipt of Optimal Inventory Q/2 Order Quantity Time

Total Costs Average Inventory = Q/2 Annual Holding costs = H * Q/2 # Orders per year = D / Q Annual Ordering Costs = S * D/Q Annual Total Costs = Holding + Ordering

How Much to Order? Total Cost Annual Cost = Holding + Ordering Cost = S * D/Q Holding Cost = H * Q/2 Optimal Q Order Quantity

Optimal Quantity Total Costs = Take derivative with respect to Q = Solve for Q: Set equal to zero

EOQ Inventory Level Q* Reorder Point (R) Time Lead Time

Adding Lead Time Use same order size Order before inventory depleted Where: = demand rate (per day) L = lead time (in days) both in same time period (wks, months, etc. )

A Question: If the EOQ is based on so many horrible assumptions that are never really true, why is it the most commonly used ordering policy? Cost curve very flat around optimal Q, so a small change in Q means small increase in Total Costs If overestimate D by 10%, and S by 10%, and H by 20%, they pretty much cancel each other out Have to overestimate all in the wrong direction before Q affected

Sensitivity Suppose we do not order optimal Q*, but order Q instead. Percentage profit loss given by: Should order 100, order 150 (50% over): 0. 5*(0. 66 + 1. 5) =1. 08 an 8%cost increase

Quantity Discounts

Quantity Discounts- Price Break How does this all change if price changes depending on order size? Holding cost as function of cost: H=i*C Explicitly consider price:

Discount Example D = 10, 000 S = $20 Price C = 5. 00 4. 50 3. 90 Quantity Q < 500 -999 Q >= 1000 Must Include Cost of Goods: i = 20% EOQ 633 667 716

Discount Pricing Total Cost Price 1 Price 2 Price 3 X 633 X 667 X 716 500 1, 000 Order Size C=$5 C=$4. 5 C=$3. 9

Discount Example Order 667 at a time: Hold 667/2 * 4. 50 * 0. 2= Order 10, 000/667 * 20 = Mat’l 10, 000*4. 50 = $300. 15 $299. 85 $45, 000. 00 45, 600. 00 Order 1, 000 at a time: Hold 1, 000/2 * 3. 90 * 0. 2= $390. 00 Order 10, 000/1, 000 * 20 = $200. 00 Mat’l 10, 000*3. 90 = $39, 000. 00 39, 590. 00

Excel graph of costs

Discount Model 1. Compute EOQ for next cheapest price 2. Is EOQ feasible? (is EOQ in range? ) If EOQ is too small, use lowest possible Q to get price. 3. Compute total cost for this quantity 4. Repeat until EOQ is feasible or too big. 5. Select quantity/price with lowest total cost.

Laundry soap prices - 2012 $4. 99 51 oz. $/oz $0. 0978 savings $6. 99 77 oz. $8. 99 103 oz. $9. 99 129 oz. $0. 091 7% $0. 087 4. 4% $0. 077 11. 5%

Value Pack - 2015 Regular: $1. 88 for 10. 56 oz = $0. 178 per ounce Value Pack $2. 98 for 15. 85 oz = $0. 188 per ounce 5. 6% higher price!

Triscuits - 2015 $1. 98 8 oz. $/oz $0. 2475 $3. 88 12 oz. $0. 323 30% higher price!

Goldfish - 2015 $1. 97 6. 6 oz. $2. 97 11 oz. $6. 48 30 oz. $/oz $0. 298 savings $0. 270 9. 4% $0. 216 20%

Summary Economic Order Quantity Perfectly balances ordering and holding costs Very robust, errors in input quantities have small impact on correctness of results Discount Model Start with EOQ calculations, using H= i. C Compute EOQ for each price, Determine feasible quantity Compute Total Costs: Holding, Ordering, and Cost of Goods.