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Adeyl Khan, Faculty, BBA, NSU

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Pencils, papers, clips, advertisements-flyer, visiting cards, nuts, bolts, trucks, needles, airplanes Raw materials, semi-finished goods, finished goods What is the worth? Let top management see the money withheld

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Adeyl Khan, Faculty, BBA, NSU Inventory- a stock or store of goods 12-3 Independent Demand B(4) E(1) D(2) C(2) F(2) D(3) A A Dependent Demand Independent demand is uncertain. Dependent demand is certain.

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Adeyl Khan, Faculty, BBA, NSU Inventory Models Independent demand – finished goods, items that are ready to be sold E.g. a computer Dependent demand – components of finished products E.g. parts that make up the computer 12-4

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Adeyl Khan, Faculty, BBA, NSU Types of Inventories Raw materials & purchased parts Partially completed goods called work in progress Finished-goods inventories manufacturing firms retail stores (merchandise ) Replacement parts, tools, & supplies Goods-in-transit to warehouses or customers 12-5

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Adeyl Khan, Faculty, BBA, NSU Functions of Inventory To meet anticipated demand Anticipation stock To smooth production requirements Seasonal demand (e.g. Potato case!) To decouple operations Buffer for continuous operation To protect against stock-outs Delayed delivery, abrupt demand Safety stocks 12-6

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Adeyl Khan, Faculty, BBA, NSU Functions of Inventory … To take advantage of order cycles Purchasing, Producing in Batches (Lots) Cycle stock for periodic To help hedge against price increases Oil price To permit operations Intermediate Stocks (WIP) Pipeline inventory To take advantage of quantity discounts 12-7

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Adeyl Khan, Faculty, BBA, NSU Objective of Inventory Control To achieve satisfactory levels of customer service while keeping inventory costs within reasonable bounds Level of customer service Costs of ordering and carrying inventory Inventory turnover Ratio of average cost of goods sold to average inventory investment. Days of inventory on hand 12-8

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Adeyl Khan, Faculty, BBA, NSU Effective Inventory Management A system to keep track of inventory (and S.O.) A reliable forecast of demand Knowledge of lead times (and variability) Reasonable estimates of Holding costs Ordering costs Shortage costs A classification system 12-9

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Adeyl Khan, Faculty, BBA, NSU Inventory Counting Systems Periodic System Physical count of items made at periodic intervals Small Retailers- checks and orders replenishment Perpetual Inventory System Keeps track of removals from inventory continuously, thus monitoring current levels of each item Reorder point Q Also requires periodic counting Errors, pilferage, spoliage 12-10 Cost?

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Adeyl Khan, Faculty, BBA, NSU Inventory Counting Systems … Two-Bin System - Two containers of inventory; reorder when the first is empty 2 nd cart has enough inventory for the lead time Order card Universal Bar Code - Bar code printed on a label that has information about the item to which it is attached 12-11

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Adeyl Khan, Faculty, BBA, NSU Key Inventory Terms Lead time: time interval between ordering and receiving the order Holding (carrying) costs: cost to carry an item in inventory for a length of time, usually a year Ordering costs: costs of ordering and receiving inventory Shortage costs: costs when demand exceeds supply 12-12

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Adeyl Khan, Faculty, BBA, NSU The Inventory Cycle- Figure 12.2 Profile of Inventory Level Over Time Quantity on hand Q Receive order Place order Receive order Place order Receive order Lead time Reorder point Usage rate Time

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Adeyl Khan, Faculty, BBA, NSU ABC Classification System Classifying inventory according to some measure of importance and allocating control efforts accordingly. A - very important B - mod. important C - least important 12-14 Annual $ value of items A B C High Low High Percentage of Items Example 1- P 549

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Adeyl Khan, Faculty, BBA, NSU Cycle Counting A physical count of items in inventory Cycle counting management How much accuracy is needed? When should cycle counting be performed? Who should do it? 12-15

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Adeyl Khan, Faculty, BBA, NSU Economic Order Quantity Models Economic order quantity (EOQ) model The order size that minimizes total annual cost Economic production model Quantity discount model 12-16

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Adeyl Khan, Faculty, BBA, NSU 12-17 Total Cost* Annual carrying cost Annual ordering cost Total cost* =+ TC = Q 2 H D Q S +

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Adeyl Khan, Faculty, BBA, NSU 12-18 Cost Minimization Goal- Figure 12.4C Order Quantity (Q) The Total-Cost Curve is U-Shaped Ordering Costs QOQO Annual Cost ( optimal order quantity) Minimum Total Cost

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Adeyl Khan, Faculty, BBA, NSU Only one product is involved Annual demand requirements known Demand is even throughout the year Lead time does not vary Each order is received in a single delivery There are no quantity discounts Assumptions of EOQ Model 12-19

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Adeyl Khan, Faculty, BBA, NSU Deriving the EOQ Using calculus, we take the derivative of the total cost function and set the derivative (slope) equal to zero and solve for Q. Minimum Total Cost The total cost curve reaches its minimum where the carrying and ordering costs are equal. 12-20 Q 2 H D Q S =

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Adeyl Khan, Faculty, BBA, NSU Economic Production Quantity (EPQ) Production done in batches or lots Capacity to produce a part exceeds the part’s usage or demand rate Similar to EOQ Orders are received incrementally during production 12-21 Assumptions Only one item is involved Annual demand is known Usage rate is constant Usage occurs continually Production rate is constant Lead time does not vary No quantity discounts

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Adeyl Khan, Faculty, BBA, NSU 12-22 Economic Run Size We do not buy the product. We produce it. Total demand / year is D Demand / day or consumption rate is u Production rate is p / day

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Adeyl Khan, Faculty, BBA, NSU Instantaneous Replenishment Incremental Replenishment

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Adeyl Khan, Faculty, BBA, NSU u p p-u u × ( number of working days ) = D = Total demand per year EPQ: Incremental Replenishment (Production and Consumption) Demand / day or consumption rate is u Production rate is p / day

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Adeyl Khan, Faculty, BBA, NSU State I max in terms of Q! EPQ: Ordering Cost and Carrying Cost

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Adeyl Khan, Faculty, BBA, NSU How much do we produce each time? Q How long does it take to produce Q? d 1 What is our production rate per day? p EPQ : Production & Consumption; rate & time p-u u I max d1d1 d2d2 How long does it take to consume Q? d 1 +d 2 What is our consumption rate per day ? u

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Adeyl Khan, Faculty, BBA, NSU Example- What is the optimal production size? A toy manufacturer Uses 48000 parts for one of its products. Consumption rate is uniform throughout the year. Working days are 240 / year. The firm can produce at a rate of 800 parts / day Carrying cost is $1 / part / year Setup cost for production run is $45 / setup

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Adeyl Khan, Faculty, BBA, NSU What is Run Time, What is Cycle Time Q 0 using formula = 2400 u = 48000 /240 = 200 units/day p-u u I max d1d1 d2d2

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Adeyl Khan, Faculty, BBA, NSU What is the Optimal Total Cost

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Adeyl Khan, Faculty, BBA, NSU EPQ : Optimal Q

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Adeyl Khan, Faculty, BBA, NSU Reorder Point- ROP Reorder Point When the quantity on hand of an item drops to this amount, the item is reordered If setup time takes 2 days, at which level of inventory we should start setup? 2(200) = 400 200 ?

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Adeyl Khan, Faculty, BBA, NSU Yet Another Example A company has a yearly demand of 120,000 boxes of its product. The product can be produced at a rate of 2000 boxes per day. The shop operates 240 days per year. Assume that demand is uniform throughout the year. Setup cost is $8000 for a run, and holding cost is $10 per box per year. a) What is the demand rate per day b) What is the Economic Production Quantity (EPQ) c) What is the run time d) What is the maximum inventory e) What is the total cost of the system

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Adeyl Khan, Faculty, BBA, NSU =16000 Yet Another Example … a) What is the demand rate per day Demand per year is 120,000 there are 240 days per year Demand per day = 120000/240 = 500 u = D/240 = 500 b) What is the Economic Production Quantity (EPQ)

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Adeyl Khan, Faculty, BBA, NSU Yet Another Example … c) What is the run time We produce 16000 units Our production rate is 2000 per day It takes 16000/2000 = 8 days d1 = EPQ/p = 8 days d) What is the maximum inventory We produce for 8 days. Each day we produce 2000 units and we consume 500 units of it. Therefore we add to our inventory at rate of 1500 per day for 8 days. That is Imax = 8(1500) = 12000 Imax = pd1 = 8(1500) = 12000

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Adeyl Khan, Faculty, BBA, NSU Yet Another Example … e) What is the total cost of the system

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Adeyl Khan, Faculty, BBA, NSU Including the Purchasing Cost 12-36 Annual carrying cost Purchasing cost TC =+ Q 2 H D Q S + + Annual ordering cost PD +

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Adeyl Khan, Faculty, BBA, NSU Total Costs with Vs. Quantity Ordered 12-37 Cost EOQ TC with PD TC without PD PD 0 Quantity Adding Purchasing cost doesn’t change EOQ

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Adeyl Khan, Faculty, BBA, NSU Total Cost with Constant Carrying Costs 12-38 OC EOQ Quantity Total Cost TC a TC c TC b Decreasing Price CC a,b,c

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Adeyl Khan, Faculty, BBA, NSU Total Cost with Variable Carrying Costs 12-39 Do the Math Ex 5, 6

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Adeyl Khan, Faculty, BBA, NSU ROP with EOQ Ordering Safety Stock Stock that is held in excess of expected demand due to variable demand rate and/or lead time. Service Level Probability that demand will not exceed supply during lead time. 12-40 When to Reorder

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Adeyl Khan, Faculty, BBA, NSU Determinants of the Reorder Point The rate of demand The lead time Demand and/or lead time variability Stockout risk (safety stock) 12-41

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Adeyl Khan, Faculty, BBA, NSU Safety Stock- Figure 12.12 12-42 LT Time Expected demand during lead time Maximum probable demand during lead time ROP Quantity Safety stock Safety stock reduces risk of stockout during lead time

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Adeyl Khan, Faculty, BBA, NSU Reorder Point- Figure 12.13 12-43 ROP Risk of a stockout Service level Probability of no stockout Expected demand Safety stock 0z Quantity z-scale The ROP based on a normal Distribution of lead time demand ROP s = Exp. Demand + z. σ dLT See also: Fig 11.14

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Adeyl Khan, Faculty, BBA, NSU Shortage and Service Level Service level determines ROP E(n) = E(z) z σ dLT E(n) = Expected number of short/cycle E(z) = Standardized number of units-short from table 11.3 σ dLT = Standard deviation of lead time Example 10 @ Page 568 44

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Adeyl Khan, Faculty, BBA, NSU Fixed-Order-Interval Model Orders are placed at fixed time intervals Order quantity for next interval? Suppliers might encourage fixed intervals May require only periodic checks of inventory levels Risk of stockout Fill rate – the percentage of demand filled by the stock on hand 12-45

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Adeyl Khan, Faculty, BBA, NSU Calculations 46 Ex 13

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Adeyl Khan, Faculty, BBA, NSU Fixed-Interval tradeoffs Benefits Tight control of inventory items Items from same supplier may yield savings in: Ordering Packing Shipping costs May be practical when inventories cannot be closely monitored Disadvantages Requires a larger safety stock Increases carrying cost Costs of periodic reviews 12-47

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Adeyl Khan, Faculty, BBA, NSU Single Period Model Model for ordering items with limited useful lives Perishables Shortage cost is generally the unrealized profits per unit Excess cost is the difference between purchase cost and salvage value of items left over at the end of a period Continuous stocking levels Identifies optimal stocking levels Optimal stocking level balances unit shortage and excess cost Discrete stocking levels Service levels are discrete rather than continuous Desired service level is equaled or exceeded 12-48

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Adeyl Khan, Faculty, BBA, NSU Optimal Stocking Level 12-49 Service Level So Quantity CeCs Balance point Service level = Cs Cs + Ce Cs = Shortage cost per unit Ce = Excess cost per unit

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Adeyl Khan, Faculty, BBA, NSU Example 15 Ce = $0.20 per unit Cs = $0.60 per unit Service level = Cs/(Cs+Ce) =.6/(.6+.2) Service level =.75 12-50 Service Level = 75% Quantity CeCs Stockout risk = 1.00 – 0.75 = 0.25

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Adeyl Khan, Faculty, BBA, NSU Operations Strategy Too much inventory Tends to hide problems Easier to live with problems than to eliminate them Costly to maintain Wise strategy Reduce lot sizes Reduce safety stock 12-51

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Adeyl Khan, Faculty, BBA, NSU Learning Objectives Define the term inventory and list the major reasons for holding inventories; and list the main requirements for effective inventory management. Discuss the nature and importance of service inventories Discuss periodic and perpetual review systems. Discuss the objectives of inventory management. Describe the A-B-C approach and explain how it is useful. 12-53

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Adeyl Khan, Faculty, BBA, NSU Learning Objectives Describe the basic EOQ model and its assumptions and solve typical problems. Describe the economic production quantity model and solve typical problems. Describe the quantity discount model and solve typical problems. Describe reorder point models and solve typical problems. Describe situations in which the single-period model would be appropriate, and solve typical problems. 12-54

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