Reorder Level Additional assumption: Lead time is known and constant No need to carrying stock from one cycle to the next So each order should be scheduled to arrive as existing stock runs out Reorder level = demand during lead time = lead time x demand per unit time ROL = LT x D Revisit Ex 1: Carpet Sell. Given that product lead time is 5 days. Calculate reorder level (ROL) 1
Reorder Level with Longer Lead Time When lead time is longer than the stock cycle There is always one order outstanding. Example: when it is time to place order B, there is one order, A outstanding and due to arrive before B. The stock on hand plus the outstanding order must be enough to last until B arrive or equal the lead time demand ROL Stock on hand ROL = LT x D + Stock on order = LT x D - Stock on order 2
Reorder Level with Longer Lead Time When lead time is very long Several orders are outstanding at anytime When lead time is between n and n+1 cycle length n x T < LT < (n+1) x T There are n orders outstanding ROL = Lead time demand - Stock on order = LT x D - n x Q o 3
Ex 2 Demand for an item is steady at 1,200 units a year with an ordering cost of $16 and holding cost of $0.24 per unit per year. Describe a appropriate ordering policy if the lead time is constant at (a) (b) (c) 3 months 9 months 18 months 4
Discussion Questions What are the benefit of short lead times? How can these be achieved in practice? 5
IM 322 Inventory Management Chapter 4 Models for Known Demand -6- Textbook: Donald Waters, Inventory Control and Management, 2 nd ed
Chapter Outline Extension of EOQ by relaxing some assumptions 1. Discount in the unit cost / price from suppliers 2. Increasing cost with higher quantity 3. Finish replenishment rate 4. Back orders 7
Price Discount from Suppliers Costs vary with the quantity ordered (Q) 8
Price Discount from Suppliers Price discount for higher quantity orders P = Unit price of item Example: Quantity (Q) Unit Price 0-100 $10 101-200 $8 201 or more $6 Inventory cost ($) TC (P 1 = $10 ) TC (P 2 = $8 ) TC (P 3 = $6 ) holding cost Reordering cost Q(P 2 ) = 100 Q(P 3 ) = 200 Q opt 9
Start 1. Take the next lowest unit cost 4. Calculate the cost at the break point NO 2. Find the lowest point using EOQ equation 3. Is this point valid? Procedure for Finding Best Order Size YES 5. Calculate the cost at this valid minimum 6. Compare the costs of all the points considered 7. Find the lowest cost and corresponding Q 10 End
Price Discount from Suppliers: Finding the lowest valid cost Case 1: All costs are constant except the unit cost (or unit price from supplier) Q o will be calculated using EOQ formula RC Q o = 2 HC D Q o could be either Valid minimum: within the range of valid order quantities for this particular unit cost Invalid minimum: falls outside the valid order range for this particular unit cost 11
Ex 1a: Sweatshirt in Bookstore The university bookstore purchases sweatshirts with school logo from a vendor. The vendor sells the sweatshirts to the store for $38 a piece. The cost to bookstore for placing an order is $120, and the annual carrying cost is estimated as $9.5 per unit. 1700 sweatshirts are estimated to be sold during the year. The vendor has offered the bookstore the following volume discount: Order Size Discount 1-299 300-499 500-799 800 and up What is an optimal order quantity? 0% 2% 4% 5% 12
Price Discount from Suppliers: Finding the lowest valid cost Case 2: All costs are constant except the unit cost (or unit price from supplier) and holding cost Holding cost can be expressed a proportion of the unit cost (I) For each unit cost (UC i ), the minimum point of the cost curve comes with Q oi Q oi for each curve could be either Valid minimum: within the range of valid order quantities for this particular unit cost Invalid minimum: falls outside the valid order range for this particular unit cost 13 RC D Q o = 2 HC Q oi RC D = 2 I UC i
Ex 1b: Sweatshirt in Bookstore The university bookstore purchases sweatshirts with school logo from a vendor. The vendor sells the sweatshirts to the store for $38 a piece. The cost to bookstore for placing an order is $120, and the annual carrying cost is 25% of the cost of sweatshirt. 1700 sweatshirts are estimated to be sold during the year. The vendor has offered the bookstore the following volume discount: Order Size Discount 1-299 300-499 500-799 800 and up 0% 2% 4% 5% 14 What is an optimal order quantity?
Rising cost with larger quantity 15
Ex 2 Rising delivery cost Kwok Cheng Ho makes a range of high quality garden ornaments. On average day he uses 4 tons of fine grain sand. This sand costs $20 a ton to buy, and $1.90 a ton to store for a day. Deliveries are made by modified lorries that carry up to 15 tons, and each delivery of a load or part load costs $200. Find the cheapest way to ensure continuous supplies of sand 16
Finish replenishment rate Inventory Level Q I max Production quantity Demand during production interval Maximum inventory D P D 17 Production and demand (PT) T Demand only (DT) Time
CASE 1
CASE 3
CASE 3
CASE 3
CASE 1, CASE 2, CASE 3
EX 2