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Rachmat A. Anggara PMBS, BOPR 5301, Session 5 O peration M anagement INVENTORY MANAGEMENT

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INVENTORY??

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INVENTORY is… One of the most expensive assets of many companies representing as much as 50% of total invested capital Operations managers must balance inventory investment and customer service

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Type of INVENTORY … Raw material Purchased but not processed Work-in-process Undergone some change but not completed A function of cycle time for a product Maintenance/repair/operating (MRO) Necessary to keep machinery and processes productive Finished goods Completed product awaiting shipment

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Material Flow Cycle.. InputWait forWait toMoveWait in queueSetupRunOutput inspectionbe movedtimefor operatortimetime Cycle time 95%5%

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INVENTORY Management.. How inventory items can be classified How accurate inventory records can be maintained How inventory cost can be minimized while keep customer order fulfilled

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INVENTORY Management.. Record Accuracy. –Manual. –Automate. Cycle Counting. –Reconciliation of inventory. –ABC analysis system. Control of Service Inventories. –Good personnel selection, training, and discipline –Tight control on incoming shipments –Effective control on all goods leaving facility

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ABC-Analysis B5.4%12, ,000#10500 B 23% 6.4%15, % #10867 B11.3%26, ,550 #12760 A33.2%77, #11526 A72%38.8% $ 90,000 $ ,00020%#10286Class Percent of Annual Dollar Volume Annual Dollar Volume = Unit Cost x Annual Volume (units) Percent of Number of Items Stocked Item Stock Number C.1% #10572 C.2% ,200#01307 C5%.4% %#01036 C.5%1, ,000#14075 C3.7%$ 8,502$ # % 33.9 % 48.5 %

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ABC-Analysis Pareto rule.. A Items B Items C Items Percent of annual dollar usage – – – – – – – – 0 0 – |||||||||| Percent of inventory items

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Control of Inventory Can be a critical component of profitability Losses may come from shrinkage or pilferage Applicable techniques include 1.Good personnel selection, training, and discipline 2.Tight control on incoming shipments 3.Effective control on all goods leaving facility

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Inventory Models INPUT MODEL (Independent) OUTPUT Demand Type: -Independent -Dependent Economic Order Quantity Order size Inventory Cost: -holding -order/setup -product Production Order Quantity Reorder point Forecasted Demand Quantity Discount Order time Probabilistic ModelTotal Inventory Cost

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1. Economic Order Quantity Order quantity = Q (maximum inventory level) Inventory level Time Usage rate Average inventory on hand Q2 Minimum inventory Inventory Usage overtime

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1. Economic Order Quantity Objective Minimise Cost Table 11.5 Annual cost Order quantity Curve for total cost of holding and setup Holding cost curve Setup (or order) cost curve Minimum total cost Optimal order quantity

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1. Economic Order Quantity Q= Number of pieces per order Q*= Optimal number of pieces per order (EOQ) D= Annual demand in units for the Inventory item S= Setup or ordering cost for each order H= Holding or carrying cost per unit per year Annual setup cost =(Number of orders placed per year) x (Setup or order cost per order) Annual demand Number of units in each order Setup or order cost per order = = (S) DQ Calculate Setup Cost

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1. Economic Order Quantity Q= Number of pieces per order Q*= Optimal number of pieces per order (EOQ) D= Annual demand in units for the Inventory item S= Setup or ordering cost for each order H= Holding or carrying cost per unit per year Calculate Holding Cost Annual holding cost =(Average inventory level) x (Holding cost per unit per year) Order quantity 2 = (Holding cost per unit per year) = (H) Q2

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1. Economic Order Quantity Optimal order quantity is found when annual setup cost equals annual holding cost DQ S = H Q2 Solving for Q* 2DS = Q 2 H Q 2 = 2DS/H Q* = 2DS/H Annual setup cost = S DQDQ Annual holding cost = H Q2Q2

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1. Economic Order Quantity (Example) Determine optimal number of needles to order D = 1,000 units S = $10 per order H = $.50 per unit per year Q* = 2DS H Q* = 2(1,000)(10)0.50 = 40,000 = 200 units

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1. Economic Order Quantity (Example) Determine optimal number of needles to order D = 1,000 units Q*= 200 units S = $10 per order H = $.50 per unit per year = N = = Expected number of orders Demand Order quantity DQ* N = = 5 orders per year 1,000200

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1. Economic Order Quantity (Example) Determine optimal number of needles to order D = 1,000 unitsQ*= 200 units S = $10 per orderN= 5 orders per year H = $.50 per unit per yearT= 50 days Total annual cost = Setup cost + Holding cost TC = S + H DQ Q2 TC = ($10) + ($.50) 1, TC = (5)($10) + (100)($.50) = $50 + $50 = $100

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1. Economic Order Quantity (Reorder Point) EOQ answers the “how much” question The reorder point (ROP) tells when to order ROP = Lead time for a new order in days Demand per day = d x L d = D Number of working days in a year

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1. Economic Order Quantity (Reorder Point) Demand = 8,000 DVDs per year 250 working day year Lead time for orders is 3 working days ROP = d x L d = D Number of working days in a year Number of working days in a year = 8,000/250 = 32 units = 32 units per day x 3 days = 96 units

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2. Production Order Quantity Used when inventory builds up over a period of time after an order is placed Used when units are produced and sold simultaneously

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2. Production Order Quantity Inventory level Time Demand part of cycle with no production Part of inventory cycle during which production (and usage) is taking place t Maximum inventory

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2. Production Order Quantity Q =Number of pieces per order p =Daily production rate H =Holding cost per unit per year d =Daily demand/usage rate t =Length of the production run in days = (Average inventory level) x Annual inventory holding cost Holding cost per unit per year = (Maximum inventory level)/2 Annual inventory level = – Maximum inventory level Total produced during the production run Total used during the production run = pt – dt

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2. Production Order Quantity Q =Number of pieces per order p =Daily production rate H =Holding cost per unit per year d =Daily demand/usage rate t =Length of the production run in days Setup cost =(D/Q)S Holding cost =1/2 HQ[1 - (d/p)] (D/Q)S = 1/2 HQ[1 - (d/p)] Q2 =Q2 =Q2 =Q2 = 2DS H[1 - (d/p)] Q* = 2DS H[1 - (d/p)]

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2. Production Order Quantity (example) D =1,000 units p =8 units per day S =$10 d =4 units per day H =$0.50 per unit per year Q* = 2DS H[1 - (d/p)] = or 283 hubcaps Q* = = 80,000 2(1,000)(10) 0.50[1 - (4/8)]

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3. Quantity Discount Model Reduced prices are often available when larger quantities are purchased Trade-off is between reduced product cost and increased holding cost Total cost = Setup cost + Holding cost + Product cost TC = S + + PD DQQH2

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3. Quantity Discount Model Discount Number Discount Quantity Discount (%) Discount Price (P) 1 0 to 999 no discount $ ,000 to 1,999 4$ ,000 and over 5$4.75 A typical quantity discount schedule

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3. Quantity Discount Model 1.For each discount, calculate Q*, I= holding cost, P= percentage 2.If Q* for a discount doesn’t qualify, choose the smallest possible order size to get the discount 3.Compute the total cost for each Q* or adjusted value from Step 2 4.Select the Q* that gives the lowest total cost Steps in analyzing a quantity discount

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3. Quantity Discount Model (example) Calculate Q* for every discount Example 9 Q 1 * = = 700 cars order 2(5,000)(49)(.2)(5.00) Q 2 * = = 714 cars order 2(5,000)(49)(.2)(4.80) Q 3 * = = 718 cars order 2(5,000)(49)(.2)(4.75)

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3. Quantity Discount Model (example) Adjusting Q* for every discount Q 1 * = = 700 cars order 2(5,000)(49)(.2)(5.00) Q 2 * = = 714 cars order 2(5,000)(49)(.2)(4.80) Q 3 * = = 718 cars order 2(5,000)(49)(.2)(4.75) 1,000 — adjusted 2,000 — adjusted

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3. Quantity Discount Model (example) Discount Number Unit Price Order Quantity Annual Product Cost Annual Ordering Cost Annual Holding Cost Total 1$ $25,000$350$350$25,700 2$4.801,000$24,000$245$480$24,725 3$4.752,000$23.750$122.50$950$24, Choose the price and quantity that gives the lowest total cost Buy 1,000 units at $4.80 per unit

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4. Probabilistic Model Used when demand is not constant or certain Use safety stock to achieve a desired service level and avoid stockouts ROP = d x L + ss Annual stockout costs = the sum of the units short x the probability x the stockout cost/unit x the number of orders per year

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4. Probabilistic Model Number of Units Probability ROP ROP = 50 unitsStockout cost = $40 per frame Orders per year = 6 Carrying cost = $5 per frame per year

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4. Probabilistic Model ROP = 50 unitsStockout cost = $40 per frame Orders per year = 6 Carrying cost = $5 per frame per year Safety Stock Additional Holding Cost Stockout Cost Total Cost 20 (20)($5) = $100 $0$ (10)($5) = $50 (10)(.1)($40)(6)=$240 $290 0$0 (10)(.2)($40)(6) + (20)(.1)($40)(6)=$960 $960 A safety stock of 20 frames gives the lowest total cost ROP = = 70 frames

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4. Probabilistic Model Another method for calculating safety stock.. ROP = demand during lead time + Z dlt whereZ =number of standard deviations dlt =standard deviation of demand during lead time Safety stock

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4. Probabilistic Model Example… Average demand = = 350 kits Standard deviation of demand during lead time = dlt = 10 kits 5% stockout policy (service level = 95%) Using Appendix I, for an area under the curve of 95%, the Z = 1.65 Safety stock = Z dlt = 1.65(10) = 16.5 kits Reorder point=expected demand during lead time + safety stock =350 kits kits of safety stock =366.5 or 367 kits

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Resume of Inventory Model MODELCONDITIONFORMULA Economic Order Quantity Demand is known, constant, and independent Lead time is known and constant Production Order Quantity units are produced and sold simultaneously Quantity Discount There is quantity discount Probabilistic Model demand is not constant or certain Q* = 2DS H Q* = 2DS H[1 - (d/p)] ROP = d x L + ss

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