OPSM 501: Operations Management Week 5: Batching EOQ Koç University Graduate School of Business MBA Program Zeynep Aksin

High-Inventory Manufacturing D : 3/4 hr/unit B : 1/10 hr/unit C : 1 hr/unit B : 1/10 hr/unit A : 1/2 hr/unit Time (hours) months (24 hrs a day, 7 days a week) inventory avg. inventory Order : 1000 units

Low-Inventory Manufacturing D : 3/4 hr/unit B : 1/10 hr/unit C : 1 hr/unit B : 1/10 hr/unit A : 1/2 hr/unit Time (hours) months avg. inventory Order : 1000 units inventory Move batches of 200 Release materials according to the bottleneck

When do you detect quality problems? D B C B A Damage done Quality control

How do you incorporate engineering changes? D B C B A Engineering change one month after start of order

Shorter Lead time - High margins D B C B A overtime No overtime Quoted lead time of the order is 3 months

Due-date performance D B C B A Forecast validity

SMED (Single minute exchange of die): reduce set-up times Batch Flow Operations Carry a Lot of Inventory

Things that influence flow time  Process control  Lotsize –Before I move from one product run to another, how much will I produce Physical constraints Customer order size Managerial decisions  Set-up time/production time

Batching in practice Common in low volume manufacturing (including a lot of high-tech) Also: transportation, education / training Example: mailing list development Creates an inherent mismatch between demand and supply

Lotsize decision  Three products: P1, P2, P3  Produce 100 units of each  Alternatives –100 P1 100 P2 100P3 –1P1 1P2 1P3 1P1 1P2 1P3 100 times  Set-up time –Cutting tools, cleaning, calibration, loading programs, etc.

Set-up times  Set-up time does not depend on lotsize and is the same for all lotsizes.  Production time depends on lotsize –Not always (baking, heat treat)  Long set-up times large lotsizes

Example  P1,P2,P3 example –Set-up time 60 min. –Production time 10 min/unit –Need 3 of each type  Try the alternatives –1P1, 1P2, 1P3, 1P1, 1P2, 1P3, 1P1, 1P2, 1P3 –3P1, 3P2, 3P3

Responsiveness Costs High Low High per unit costs Low per unit costs Now Smaller batches Larger batches Reduce set-up times Higher frontier Product Space, Efficient frontier

Capacity calculation changes: Note: Capacity increases with batch size: Note further: … and so does inventory (and thus flow time) Batch Size Set-up time + Batch-size*Time per unit Capacity given Batch Size= See chapter 5 Process Analysis with Batching

Example Milling S=120 min p= 2 min/unit Assembly S=0 p=3 min/unit B=12? B=300? Recommended B=?

Economies of Scale: Inventory Management for a Retailer The South Face retail shop in the SapphireTower has observed a stable monthly demand for its line of Gore-Tex jackets on the order of 100 jackets per month. The retail shop incurs a fixed cost of $2,000 every time it places an order to the Adana warehouse for stock replenishment. The marginal cost of a jacket is $200, and South Face’s cost of capital is approximately 25%. What order size would you recommend for The South Face? retailer warehouse

Economies of Scale: Inventory Build-Up Diagram R: Annual demand rate, Q: Number of jackets per replenishment order  Number of orders per year = R/Q.  Average number of jackets in inventory = Q/2. Q Time t Inventory Profile : # of jackets in inventory over time. R = Demand rate Inventory

Find most economical order quantity: Spreadsheet for The South Face

Total Annual Cost Total Annual Cost = Annual Purchasing Cost Annual Ordering Cost Annual Holding Cost ++  Using calculus, we can take the derivative of the total cost function and set the derivative (slope) equal to zero  We can also use economic intuition

Economies of Scale: Economic Order Quantity EOQ R :Demand per year, S :Setup or Order Cost ($/setup; $/order), H :Marginal annual holding cost ($/per unit per year), Q :Order quantity. C :Cost per unit ($/unit), r :Cost of capital (%/yr), h :Physical unit holding cost ($/unit,yr), H = (h + r) C. Batch Size Q Total annual costs H Q/2: Annual holding cost S R /Q:Annual setup cost EOQ

EOQ Model: if there is a lead time L ROP = Reorder point L = Lead time (constant) Q = Economic order quantity L L ROP Time # Units on hand Q EOQ

Economic Order Quantity (EOQ) Model  Economic Order Quantity (EOQ) Model –Robust, widely used –Insensitive to errors in estimating parameters ( Rule): 40% error in one of the parameters 20% error in Q < 2% of total cost penalty

Learning Objectives: Batching & Economies of Scale  Increasing batch size of production (or purchase) increases average inventories (and thus cycle times).  Average inventory for a batch size of Q is Q/2.  The optimal batch size trades off setup cost and holding cost.  To reduce batch size, one has to reduce setup cost (time).  Square-root relationship between Q and (R, S): –If demand increases by a factor of 4, it is optimal to increase batch size by a factor of 2 and produce (order) twice as often. –To reduce batch size by a factor of 2, setup cost has to be reduced by a factor of 4.

Announcements  HW 2 is due next time  The Goal is due next time  Have a nice break!