Koç University Graduate School of Business MBA Program OPSM 501: Operations Management Week 5: Batching EOQ Zeynep Aksin email@example.com
High-Inventory Manufacturing Order : 1000 units 4 months (24 hrs a day, 7 days a week) A : 1/2 hr/unit inventory B : 1/10 hr/unit avg. inventory C : 1 hr/unit B : 1/10 hr/unit D : 3/4 hr/unit 1000 2000 Time (hours)
Low-Inventory Manufacturing Order : 1000 units 2 months Move batches of 200 Release materials according to the bottleneck A : 1/2 hr/unit B : 1/10 hr/unit C : 1 hr/unit inventory B : 1/10 hr/unit avg. inventory D : 3/4 hr/unit 1000 2000 Time (hours)
When do you detect quality problems? Quality control A B C B D Damage done
How do you incorporate engineering changes? A B C B D Engineering change one month after start of order
Shorter Lead time - High margins Quoted lead time of the order is 3 months A B C B D overtime No overtime
Due-date performance A B C B D Forecast validity
Batch Flow Operations Carry a Lot of Inventory • SMED (Single minute exchange of die): reduce set-up times
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 timeslarge 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
Product Space, Efficient frontier Responsiveness High Reduce set-up times Smaller batches Now Larger batches Higher frontier Low High perunit costs Low perunit costs Costs
Process Analysis with Batching 0.5 1/p Capacity 0.45 0.4 0.35 0.3 0.25 0.2 0.15 Capacity given Batch Size= 0.1 0.05 0 Batch Size Batch Size 10 50 90 130 170 210 250 290 330 370 410 450 490 530 570 610 650 Set-up time + Batch-size*Time per unit • Capacity calculation changes: • Note: Capacity increases with batch size: • Note further: … and so does inventory (and thus flow time) See chapter 5
Example Milling S=120 min p= 2 min/unit Assembly S=0 p=3 min/unit B=12? B=300? Recommended B=?
warehouse retailer 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 $200, and South Face’s cost of capital is approximately 25%. What order size would you recommend for The South Face?
Inventory Profile: # of jackets in inventory over time. Inventory Q R = Demand rate Time t Economies of Scale: Inventory Build-Up Diagram R: Annual demand rate, Q: Number of jackets per replenishment order • Number of orders per year = R/Q. • Average number of jackets in inventory = Q/2 .
Annual Purchasing Cost Annual Ordering Cost Annual Holding Cost Total Annual Cost = + + Total Annual Cost • Using calculus, we can take the derivative of the total cost function and set the derivative (slope) equal to zero • We can also use economic intuition
Total annual costs H Q/2: Annual holding cost S R /Q:Annual setup cost EOQ Batch Size Q Economies of Scale: Economic Order Quantity EOQ R : Demand per year, S : Setup or Order Cost ($/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.
EOQ Model: if there is a lead time L QEOQ # Units on hand ROP Time L L ROP = Reorder point L = Lead time (constant) Q = Economic order quantity
Economic Order Quantity (EOQ) Model • Economic Order Quantity (EOQ) Model • Robust, widely used • Insensitive to errors in estimating parameters (40-20-2 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!