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Notes • Quiz This Friday • Covers 13 March through today MGTSC 352 Lecture 21: Inventory Management A&E Noise example Methods for finding good inventory policies: 1) simulation 2) EOQ + LTD models Using EOQ for the Distribution Game: Multi-Echelon Systems Why Keep Inventory? 1. Seasonality (anticipated variation) 2. Provide flexibility (unanticipated variation) a.k.a.: 3. Economies of scale 4. Price speculation (not an ops reason) 5. Something to work on 6. NDR,JP Inventory By Where it IS • • • • Raw Materials Finished Goods Work in Process Or, with apologies to PS, “One man’s ceiling is another man’s floor.” Inventory Approximation 1: constant demand Therefore: We let inventory drop to zero just before an order arrives Time Acquisition Costs (pg. 142) No matter what the inventory policy, acquisition costs = Demand X Cost They don’t change, So they don’t go in the model (Unless you get quantity discounts, then it matters.) Order Costs • Number of orders per year (3695 VCRs / year)/(80 VCRs / order) = 46.2 orders / year • Total order cost per year (46.2 orders / year)($30 / order) = $1385.63 / year • Total Order Costs = S * D/Q Holding Costs (pg. 143) • Minimum inventory 0 for now Later = Safety Stock • Maximum inventory = Q (+SS) • Average inventory Q/2 = (80)/2 = 40 VCRs • Total holding cost per year (40 VCR-years)($37.5 / VCR / year) = $1500 / year • Total Holding Costs = H*Q/2 pg. 144 EOQ = Economic Order Quantity Model • Given demand is constant • Find the Q that minimizes total cost Acquisition costs don’t depend on Q Total cost = acquisition cost + order cost + carrying cost + shortage cost No shortages, by assumption • Total relevant cost = order cost + carrying cost EOQ Derivation S = order cost ($/order) H = carrying cost ($/item/year) D = demand (units/year) Relevant cost RC RC(Q) = = = order cost SN SD/Q pg. 147 Q = order quantity N = number of orders per year Iavg = average inventory + + + carrying cost H Iavg HQ/2 Note: you can change year to day, week, or any other time unit, as long as you are consistent Common mistake: inconsistent time units To Excel EOQ Formula Relevant cost RC = RC(Q) = pg. 147 = ordering cost + carrying cost SN + H Iavg SD/Q + HQ/2 The magic part (optional) pg. 147 Using EOQ for A&E Noise YNOS XD D = 10.12 VCRs/day, S = $30/order, H = $0.10/VCR/day Q* = SQRT(210.1230/0.10) = 77.9 round to Q* = 78 N* = 10.12/78 = 0.13 orders/day = 47.4 orders/year Order every 365/47.4 = 8 days Relevant cost: RC(Q*) = S (D/Q*) + H (Q*/2) = 30 (10.12/78) + 0.10 (78/2) = 3.90 + 3.90 = $7.80 / day = $2,847 / year Common mistake: using inconsistent time units D = 10.12 VCRs/day, S = $30/order, H = $37.5/VCR/year Q* = SQRT(210.1230/37.5) = 4 • Off by (77.9 – 4)/77.9 = 95% • Will not be worth a lot of part marks Pg. 149 More on EOQ: Economies of Scale The Capital Health Region* operates four hospitals. Presently each hospital orders its own supplies and manages its inventory. A common item used is a sterile intravenous (IV) kit, with a weekly demand of 600 per week at each hospital. Each IV kit costs $5 and incurs a holding cost of 30% per year. Each order incurs a fixed cost of $150 regardless of order size. The supplier takes one week to deliver an order. Currently, each hospital orders 6,000 kits at a time. Question 1: Could costs be decreased by ordering more often? Question 2: Would it make sense to centralize inventory management for the four hospitals? * Fictional data Analysis for one Hospital • D = 600 / week = (600 / week) (52 weeks/year) = 31,200 / year • S = $150 / order • H = 0.3 5 = $1.50 / kit / year • Q = SQRT(2 D S / H) = 2,498 ≈ 2,500 • Costs: – Q = 6,000: S D / Q + H Q / 2 = $780 + $4,500 = $5,280 – Q = 2,500: S D / Q + H Q / 2 = $1,872 + $1,875 = $3,747 – 29% savings Analysis for one Hospital • D = 600 / week = (600 / week) (52 weeks/year) = 31,200 / year • S = $150 / order • H = 0.3 5 = $1.50 / kit / year • Q = SQRT(2 D S / H) = 2,498 ≈ 2,500 • Close your course pack • Active Learning: How do we change the analysis if inventory management were centralized for the four hospitals? Analysis for four hospitals managed together • • • • • D = 4 31,200 / year = 124,800 / year S = $150 / order H = $1.50 / kit / year Q = SQRT(2 124,800 150 / 1.5) = 4,996 ≈ 5,000 Costs: – Each hospital operated independently: 4 $3,747 = $14,988 / year – All four together: S D / Q + H Q / 2 = $3,744 + $3,750 = $7,494 / year – 50% savings • Quadrupling demand doubles the optimal order quantity and doubles the total relevant cost Four hospitals managed together • Costs: – Each hospital operated independently: 4 $3,747 = $14,988 / year – All four together: S D / Q + H Q / 2 = $3,744 + $3,750 = $7,494 / year – 50% savings • Quadrupling demand doubles the optimal order quantity and doubles the total relevant cost Determining ROP with EOQ model Lead time = 5 days Demand during lead time = (5 days) (10.12 VCRs / day) 51 VCRs Set ROP = 51 VCRs Inventory Problem: this calculation assumes constant demand. May lead to shortages too frequently ROP demand during lead time lead time Time Pg. 149 What happens to Holding Cost when we Increase ROP? • EOQ: constant demand, zero safety stock – ROP = avg. demand during lead time – Iavg = (min + max)/2 = (0+Q)/2 = Q/2 – Holding cost = H Q / 2 • If we add safety stock = SS, then: – ROP = avg. demand during lead time + SS – Iavg = Q/2 + min = SS + Q/2 – Holding cost = H (SS + Q / 2) Pg. 152 Inventory How Shortages Happen Active learning: How could we have avoided the shortage? ROP Demand during leadtime Leadtime Demand that was not met Time Inventory The demand during the lead time is uncertain. Here are 4 possibilities. ROP We’ll see how to pick ROP so as to provide a specified fill rate … to Excel Time LTD Recap • “LTD” worksheet in A&E Noise workbook – Purpose: vary ROP (and Q, if desired) and see what happens to the fill rate • “LTD-exotic version”: can vary the lead time – Useful for comparing suppliers that provide different lead times pg. 151 Simulation versus EOQ Dimension Simulation EOQ + LTD Ease of evaluating a policy Need to build model – time consuming Simple formula for RC – back of an envelope Finding the optimum Trial and error / data table Plug into formula for Q* Random demand fluctuations Taken into account Ignored in EOQ Seasonal demand fluctuations Can be taken into account Ignored Shortages Taken into account Ignored in EOQ Likely errors (common mistakes) Errors in formulas Inconsistent units Pg. 158 Back to the Distribution Game: Can we use EOQ here? A “multi-echelon” system Supplier Warehouse Retailer Retailer Retailer Using EOQ for a two-echelon system • Upper echelon: – Use warehouse holding cost rate • Ignore higher cost of holding inventory at retailers – Lead time = 15 (supplier warehouse) + 5 (warehouse retailer) = 20 days • Lower echelon: – Use incremental retailer holding cost rate – Lead time = 5 days • Coordination: warehouse order size should be a multiple of the sum of the retailer order sizes Data Assume open 250 days / year • • • • • • • • • Supplier to warehouse transit time: 15 days Warehouse to retailer transit time: 5 days Demand per retailer: 500 per year Selling price: $100/unit Purchase price: $70/unit Supplier to warehouse order cost: $200 Warehouse to retailer order cost: $2.75 Warehouse holding cost: $10/unit/year … To Excel Retailer holding cost: $12/unit/year Upper echelon: Use warehouse holding cost rate (Ignore higher cost of holding inventory at retailers) Lead time = 15 (supplier warehouse) + 5 (warehouse retailer) = 20 days Upper echelon Supplier Warehouse Retailer Retailer Retailer Lower echelon: Use incremental retailer holding cost rate = retailer holding cost rate – warehouse holding cost rate Lead time = 5 days Lower echelon Retailer Supplier Warehouse Retailer Retailer Coordination • Suppose each retailer uses QLower = 20. If all retailers order at once, the total is 60. • Active learning: you are the warehouse manager. Knowing the retailer order sizes, how would you pick the warehouse order size? Using EOQ for a 2-echelon system: the details • Upper echelon: – – – – – DUpper = 3 DRetailer SUpper = SWarehouse HUpper = HWarehouse LTUpper = LTSupplier Warehouse + LTWarehouse Retailer ROPUpper = DUpper LTUpper • Lower echelon – – – – – DLower = DRetailer SLower = SRetailer HLower = HRetailer - HWarehouse LTLower = LTWarehouse Retailer ROPLower = DLower LTLower • Coordination: QUpper = n SUM(QLower) • Choose n (an integer) and QLower to minimize total cost for the whole system Data Assume open 250 days / year • • • • • • • • • Supplier to warehouse transit time: 15 days Warehouse to retailer transit time: 5 days Demand per retailer: 500 per year Selling price: $100/unit Purchase price: $70/unit Supplier to warehouse order cost: $200 Warehouse to retailer order cost: $2.75 Warehouse holding cost: $10/unit/year … To Excel Retailer holding cost: $12/unit/year