Supply Chain Management Lecture 18

Outline Today –Chapter 10 3e: Sections 1, 2 (up to page 273), 6 4e: Sections 1, 2, 3 (up to page 260) Thursday –Finish Chapter 10 –Start with Chapter 11

Staples Visit Date –Friday April 2 Location –Staples fulfillment Center –Brighton, CO Subject –Lunch and Learn

Guest Lecture Date –Tuesday April 20 Speaker –Paul Dodge (Senior Vice President – Supply Chain) Subject –Today’s Supply Chain

The Importance of Inventory Firms can reduce costs by reducing inventory, but customers become dissatisfied when an item is out of stock The objective of inventory management is to strike a balance between inventory investment and customer service

Inventory Decisions How much to order? –Order quantity or lot size (Q) When to order? –Order frequency (n) Find an inventory policy that is optimal with respect to some criteria (usually cost)

Inventory Profile Inventory Time Q Q/2 0 Cycle Lot size Q Average demand D Average inventory due to cycle inventory Q/2 Average inventory Average demand Average flow time = = Q/2D

The Role of Cycle Inventory in a Supply Chain What is cycle inventory? –Cycle inventory is the average inventory in a supply chain due to either production or purchases in lot sizes that are larger than those demanded by customers What is lot size or batch size? –Lot or batch size is the quantity that a stage of a supply chain either produces of purchases at a time

Inventory Profile Q/2 Inventory Time Q 0 Inventory Time Q 0

Why Order in Large/Small Lots? Fixed ordering cost: S (cost incurred per order/lot) –Increase the lot size to decrease the fixed ordering cost per unit Holding cost: H (cost of carrying one unit in inventory) –Decrease the lot size to decrease holding cost Material cost: C (cost per unit) Lot size Q is chosen by trading off holding costs against fixed ordering costs

Cost Influenced by Lot Size Order Quantity Annual Cost Holding Cost Ordering Cost Material Cost

Material Cost (C) Material cost ($/unit) –The average price paid per unit

Supply Chain Cost Influenced by Lot Size Order Quantity Annual Cost Material Cost CD

Holding Cost (H) Holding cost ($/unit/year) –Cost of carrying one unit in inventory for a specified period of time Warehousing/occupancy cost6% Handling costs3% Obsolescence cost 3% Cost of capital11% Miscellaneous cost3% Total holding cost26% % of Category Inventory Value

Supply Chain Cost Influenced by Lot Size Order Quantity Annual Cost Holding Cost Material Cost (Q/2)H

Ordering Cost (S) Ordering cost ($/lot) –Fixed cost incurred each time an order is placed (does not vary with the size of the order) Buyer time (order placement) Transportation cost Receiving cost Purchase Order DescriptionQty. Microwave1 Purchase Order DescriptionQty. Microwave1 Purchase Order DescriptionQty. Microwave1 Purchase Order DescriptionQty. Microwave1 1 Order = $ Orders = $400,000 Order quantity Purchase Order DescriptionQty. Microwave1000

Supply Chain Cost Influenced by Lot Size Order Quantity Annual Cost Holding Cost Ordering Cost Material Cost (D/Q)S

Supply Chain Cost Influenced by Lot Size Order Quantity Annual Cost Holding Cost Total Cost Curve Ordering Cost Material Cost Optimal Order Quantity (Q*) CD + (D/Q)S + (Q/2)H

Economic Order Quantity (EOQ) Optimal order quantity hC Q*

Example: Economic Order Quantity Example 10-1 –Demand for the Deskpro computer at Best Buy is 1,000 units per month. Best Buy incurs a fixed order placement, transportation, and receiving cost of $4,000 each time an order is placed. Each computer costs Best Buy $500 and the retailer has an annual holding cost of 20 percent. = 1,000 x 12 = 12,000DSChDSCh = $4,000 = $500 = 0.2

Example: Economic Order Quantity Example 10-1 D = 12,000 S = 4,000 C = 500 h = 0.2 Q*= sqrt((2DS)/(hC)) = sqrt((2 x 12,000 x 4,000)/(0.2 x 500)) = 980 hC Q*

Example: Economic Order Quantity Example 10-1 D = 12,000 S = 4,000 C = 500 h = 0.2 Q* = 980 Order frequency Cycle inventory Average flow time = D/Q = 12,000 / 980 = = Q/2 = 980 / 2 = 490 = Q/(2D) = 980 / (2 x 12,000) = 0.041

Example: Economic Order Quantity Example 10-1 D = 12,000 S = 4,000 C = 500 h = 0.2 Q* = 980 Annual ordering and holding cost = (D/Q*)S + (Q*/2)hC What if Q = 1,000 What if Q = 900 What if Q = 200 cost = $98,000 cost = $98,333 cost = $250,000 = $48,990 + $48,990 = $97,980

Summary DescriptionFormula Optimal order quantityQ*Q*sqrt((2DS)/H) Order frequencynD/QD/Q Cycle inventoryQ/2 Average flow time(Avg inventory)/(Avg demand) Order cost(D/Q)S(D/Q)S Holding cost(Q/2)H Material costCD

Key Points from EOQ Model 1.Total ordering and holding costs are relatively stable around the economic order quantity 2.If demand increases by a factor k, the optimal lot size increases by a factor  k 3.To reduce the optimal lot size by a factor of k, the fixed order cost S must be reduced by a factor k 2 hC Q*

Example: Economic Order Quantity Example 10-2 –The store manager at Best Buy would like to reduce the optimal lot size from 980 to 200. For this lot size reduction to be optimal, the store manager wants to evaluate how much the order cost per lot should be reduced (currently $4,000) Q* = sqrt((2DS)/(hC)) 200 = sqrt((2 x 12,000 x S)/(0.2 x 500)) S = (hC(Q*) 2 )/2D = (0.2 x 500 x )/(2 x 12,000) = $166.7

Example: Economic Order Quantity How can the store manager reduce the fixed ordering cost? –Aggregate multiple products in a single order Can possibly combine shipments of different products from the same supplier Can also have a single delivery coming from multiple suppliers

Aggregating Multiple Products in a Single Order Example 10-1 (continued) –Assume Best Buy sells 4 different models of Deskpro each with demand of 1,000 units per month (all costs are same) –4 single orders Q* for each model equals 980 Annual order and holding cost equal 97,980 x 4 = $391,920 –1 aggregate order D = 12,000 x 4 = 48,000 Q* = sqrt((2 x 48,000 x 4,000)/(0.2 x 500)) = 1,960 (= 490 for each model) Annual order and holding cost = (D/Q)S + (Q/2)hC = ((48,000/1,960) x 4,000) + (1,960/2) x 0.2 x 500 = $244,918

Lot Sizing with Multiple Products or Customers Ordering cost has two components –Common (to all products) –Individual (to each product) Example –It is cheaper for Wal-Mart to receive a truck containing a single product than a truck containing many different products Inventory and restocking effort is much less for a single product

Lot Sizing with Multiple Products or Customers Multiple products –Independent orders No aggregation: Each product ordered separately –Joint order of all products Complete aggregation: All products delivered on each truck –Joint order of a subset of products Tailored aggregation: Selected subsets of products on each truck Which option will likely have the lowest cost?