Reflections on Economic Order Quantity and Lean Processes Joseph E. (Gene) Justin, Ph.D. Ninth Southern California Aerospace Systems and Technology Conference Sponsored by AIAA Orange County Section 19 May 2012 Adjunct Assistant Professor Embry-Riddle Aeronautical University 5001 Airport Plaza Drive, Suite 150, Long Beach, CA 90815 Core Adjunct Faculty University of Redlands 1200 E. Colton Avenue, P.O. Box 3080, Redlands, CA 92374 genejustin01@aol.com (714) 896-1945 1
Summary Economic Order Quantity (EOQ) (from Harris, 1912) formulates the ordering quantity that minimizes the annual holding and ordering costs EOQ is a linear demand model but is surprising robust even with today s technologies, global complexities, and uncertainties, including disasters and threats, risks, issues, and opportunities Lean theory and Just-In-Time (JIT) focus on eliminating barriers to a pull supply chain system where an item arrives just it is needed Zero inventory and zero safety stock is a JIT goal, and lowering stock surfaces bottlenecks in the supply chain that need to be eliminated Lean and JIT claim to the first telltale indicator to see the unexpected -- Lean is more proactive, more adaptive, quicker, more innovative, more likely to improvise, and more likely to satisfy the customer in a crisis From these perspectives, this paper examines if EOQ and JIT are that much different in addressing reducing holding and ordering costs EOQ and JIT are similar in objective in reducing holding and ordering costs 2
Old School and Lean In the 1950s, ordering and holding costs were cheap, and Massive Big Marketing led to Large D (Demand) -- Detroit built the massive run of cars with little changes and created the marketing demand, and the customers came Now, Lean -- Toyota Way -- Only build when the customer orders that model, and products are pulled by JIT (Just in Time) order as needed The Toyota Way (Liker, 2003) The Machine that Changed the World (Womack, Jones, Roos) Lean Thinking (Womack and Jones) How to Fix Detroit (Taylor, 2005) Toyota, workers, and, the extended web of suppliers identify and overcome road blocks to increased performance Continuous improvement to overhaul the industry worldwide The Toyota way continuously reduces and removes supply chain roadblocks Then Lean works on the remaining roadblocks Lean forces one to cut inventories, and surface supply chain holding and ordering bottlenecks 3
Q EOQ and Q* D = Annual demand Ch = Cost of holding one item in inventory Co = Cost of ordering an order TC = Total Annual Cost Q = Order Quantity Average Inventory Level = 1/2 Q (Linear Demand) Number of Orders in a Year = D/Q Total Annual Cost = TC = 1/2 Q Ch + (D/Q) Co (Terms are ~equal) Optimum EOQ = Q* = SQRT ( 2 D Co / Ch ) Q* tells you how much to order given the cost of ordering and the cost of inventory 4 1/2 Q Time
Q JIT and Q* Half-Ordering 1/2 Q Lean asks rhetorically what happens if you cut your ordering in half, and then half again, and again, etc -- Forces you to eliminate bottlenecks and to cut ordering and holding costs, and speed up the whole supply chain process In this case, limit of Q when continuously cut, becoming smaller, and smaller, approach 1 Item arrives just-in-time when it absolutely needed at the last moment Time Lean leads to manage and custom Demand, and to eliminating costs in ordering 5 and holding to near-zero
JIT and Q*, Continued As items arrive just-in-time when absolutely needed at the last moment, then Q is reduced and reduced again, and again. Ideally, Q* approach ~ Q*=1, meaning SQRT ( 2 D Co / Ch ) approach 1 Therefore, ~ 2 D Co / Ch = 1 As Q goes to 1, Ch ~ = 2 D Co, and R approach lower custom levels And, as D goes to 1 (small custom orders), Ch = 2 Co, and go to near-zero This means by cutting Q below the optimum Q* order size, one will be order more and more often. Thus, one must quickly lower the ordering costs (otherwise total cost goes up) And, one must reduce the holding cost (since there is less to hold to avoid the total cost going up) Flexibility in Q allows Product to flexible allowing custom ordering Lean leads to Pull Order Sizes to eliminate costs in ordering and holding to near-zero, and allow custom orders 6
Conclusion Ordering Quantity Strategies Q* optimum to balance Product Demand, and the costs of ordering and holding is equal to Lean if one continuously cutting ordering and holding costs and ordering quantities Lean Ch and Co must be close to equal and approach zero Lean allows D to be set for custom orders Lean has zero holding safety stock and quicker orders Lean has to survive by being quick to see bottlenecks, unexpected Lean will be more innovative, more likely to improvise Lean is the closest to the product supply chain and the customer needs 7
References Anderson, Sweeney, Williams, and Martin An Introduction to Management Science: Quantitative Approaches to Decision Making, Twelfth Edition (12e), West Publishing Company, 2008 Deming Institute, (http://www.deming.org) Goldratt, A., The AGI Institute (http://www.goldratt.com) Juran Institute, (http://www.juran.com) Laurenzo, E., Learning on Lean Solutions, Aerospace America, June 2005. Lean Aerospace Initiative, (http://www.lean.mit.edu) Liker, Jeffrey. The Toyota Way: 14 Management Principles from the World s Greatest Manufacture. McGraw-Hill, New York, 2003 Taguchi, Genichi, Taguchi s Quality Engineering Handbook, 2004. Taylor, How to Fix Detroit, 2005 Womack, Jones, Roos, The Machine that Changed the World Womack and Jones Lean Thinking 8
Biography Joseph E. (Gene) Justin is an Adjunct Assistant Professor at Embry-Riddle Aeronautical University and an Adjunct Faculty at the University of Redlands, School of Business in Redlands, California. Gene is a USAF Academy graduate, a former USAF Astronautical Engineering Officer, and a former USAF Academy Assistant Professor of Astronautics. He was a HQ USAF Research Fellow at the Rand Corporation, and HQ AF Systems Command Exchange Officer to Strategic Air Command. His assignments included AF Avionics Laboratory, Wright Patterson AFB; ICBM SPO, Norton AFB; and the Pentagon, Washington DC. He is a retired USAF Major. Gene Justin completed military courses through Air War University, Naval War College. National Defense University. Gene has a MS in Astronautical and Aeronautical Engineering from Ohio State University, a MA in International Relations from the University of Southern California, an Executive MBA from the University of California Los Angeles, and Ph.D. in Management from Claremont Graduate University. He is a member of IEEE, and AIAA Associate Fellow (Life Member) He has over 30 published articles, and he has two Patents 9