Adeyl Khan, Faculty, BBA, NSU 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 Adeyl Khan, Faculty, BBA, NSU Inventory- a stock or store of goods Independent Demand Dependent Demand A B(4) D(2) C(2) E(1) D(3) F(2) Independent demand is uncertain. Dependent demand is certain. Adeyl Khan, Faculty, BBA, NSU 12-3 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 Adeyl Khan, Faculty, BBA, NSU 12-4 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 Adeyl Khan, Faculty, BBA, NSU 12-5 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 Adeyl Khan, Faculty, BBA, NSU 12-6 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 Adeyl Khan, Faculty, BBA, NSU 12-7 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 Adeyl Khan, Faculty, BBA, NSU 12-8 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 Adeyl Khan, Faculty, BBA, NSU 12-9 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 Adeyl Khan, Faculty, BBA, NSU Cost? 12-10 Inventory Counting Systems … Two-Bin System - Two containers of inventory; reorder when the first is empty 2nd 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 Adeyl Khan, Faculty, BBA, NSU 12-11 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 Adeyl Khan, Faculty, BBA, NSU 12-12 The Inventory Cycle- Figure 12.2 Profile of Inventory Level Over Time Q Quantity on hand Usage rate Reorder point Receive order Place Receive order order Lead time Adeyl Khan, Faculty, BBA, NSU Place Receive order order Time 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 High A Annual $ value of items Example 1- P 549 B C Low Low Adeyl Khan, Faculty, BBA, NSU High Percentage of12-14 Items 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? Adeyl Khan, Faculty, BBA, NSU 12-15 Economic Order Quantity Models Economic order quantity (EOQ) model The order size that minimizes total annual cost Economic production model Quantity discount model Adeyl Khan, Faculty, BBA, NSU 12-16 Total Cost* Annual Annual Total cost* = carrying + ordering cost cost TC = Adeyl Khan, Faculty, BBA, NSU Q H 2 + DS Q 12-17 Cost Minimization Goal- Figure 12.4C Annual Cost The Total-Cost Curve is U-Shaped Q D TC H S 2 Q Ordering Costs QO (optimal order quantity) Order Quantity (Q) Minimum Total Cost Adeyl Khan, Faculty, BBA, NSU 12-18 Assumptions of EOQ Model • • • • • 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 Adeyl Khan, Faculty, BBA, NSU 12-19 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. 2DS 2(Annual Demand)(Or der or Setup Cost) Q OPT = = H Annual Holding Cost Minimum Total Cost The total cost curve reaches its minimum where the carrying and ordering costs are equal. Q H 2 Adeyl Khan, Faculty, BBA, NSU = DS Q 12-20 Economic Production Quantity (EPQ) Production done in batches or lots Capacity to produce a part exceeds the part’s usage or demand rate Assumptions Similar to EOQ Orders are received incrementally during production Adeyl Khan, Faculty, BBA, NSU • • • • • • • 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 12-21 Economic Run Size Q0 2DS p H p u 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 Adeyl Khan, Faculty, BBA, NSU 12-22 Instantaneous Replenishment Incremental Replenishment Adeyl Khan, Faculty, BBA, NSU EPQ: Incremental Replenishment (Production and Consumption) Demand / day or consumption rate is u Production rate is p / day p-u p u u × ( number of working days ) = D = Total demand per year Adeyl Khan, Faculty, BBA, NSU EPQ: Ordering Cost and Carrying Cost D I max S TC H Q 2 State Imax in terms of Q! Adeyl Khan, Faculty, BBA, NSU EPQ : Production & Consumption; rate & time How much do we produce each time? Q How long does it take to produce Q? d1 What is our production rate per day? p Q pd1 How long does it take to consume Q? d1 +d2 What is our consumption rate per day ? u I max ud 2 Q u(d1 d 2 ) I max ( p u )d1 Adeyl Khan, Faculty, BBA, NSU I max p-u d1 d2 u 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 Adeyl Khan, Faculty, BBA, NSU What is Run Time, What is Cycle Time Q0 2DS H p p u Q u(d1 d 2 ) Q0 using formula = 2400 u = 48000 /240 = 200 units/day 2400 200(d1 d2 ) Q pd1 (d1 d2 ) 12 2400 800d1 d1 3 I max p-u d1 Adeyl Khan, Faculty, BBA, NSU u d2 What is the Optimal Total Cost I max ( p u )d1 I max (800 200)3 I max 1800 I Max D TC S H Q 2 48000 1800 TC 45 1 2400 2 TC 900 900 1800 Adeyl Khan, Faculty, BBA, NSU EPQ : Optimal Q EPQ 2 SDp H ( p u) 2 SD EPQ H Adeyl Khan, Faculty, BBA, NSU p p u 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 ? 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 Adeyl Khan, Faculty, BBA, NSU 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) 2 SD EPQ H p p u 2(8000)(120000) 2000 EPQ 10 2000 500 Adeyl Khan, Faculty, BBA, NSU =16000 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 Adeyl Khan, Faculty, BBA, NSU Yet Another Example … e) What is the total cost of the system I Max D TC S H Q 2 120000 12000 TC 8000 10 16000 2 TC 60000 60000 120000 Adeyl Khan, Faculty, BBA, NSU Annual Annual Purchasing + TC = carrying + ordering cost cost cost Q H TC = 2 + DS Q + PD Including the Purchasing Cost Adeyl Khan, Faculty, BBA, NSU 12-36 Cost Total Costs with Vs. Quantity Ordered Adding Purchasing cost doesn’t change EOQ TC with PD TC without PD PD 0 Adeyl Khan, Faculty, BBA, NSU EOQ Quantity 12-37 Total Cost with Constant Carrying Costs Total Cost TCa TCb Decreasing Price TCc CC a,b,c OC EOQ Adeyl Khan, Faculty, BBA, NSU Quantity 12-38 Do the Math Ex 5, 6 Total Cost with Variable Carrying Costs Adeyl Khan, Faculty, BBA, NSU 12-39 ROP with EOQ Ordering When to Reorder 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. Adeyl Khan, Faculty, BBA, NSU 12-40 Determinants of the Reorder Point The rate of demand The lead time Demand and/or lead time variability Stockout risk (safety stock) Adeyl Khan, Faculty, BBA, NSU 12-41 Quantity Safety Stock- Figure 12.12 Maximum probable demand during lead time Expected demand during lead time ROP Safety stock Safety stock reduces risk of stockout during lead time Adeyl Khan, Faculty, BBA, NSU LT Time 12-42 Reorder Point- Figure 12.13 See also: Fig 11.14 The ROP based on a normal Distribution of lead time demand Service level Risk of a stockout Probability of no stockout Expected demand 0 ROP Quantity Safety stock z z-scale ROPs = Exp. Demand + z. σdLT Adeyl Khan, Faculty, BBA, NSU 12-43 Shortage and Service Level Service level determines ROP E(n) = E(z) z σdLT E(n) = Expected number of short/cycle E(z) = Standardized number of units-short from table 11.3 σdLT = Standard deviation of lead time Example 10 @ Page 568 Adeyl Khan, Faculty, BBA, NSU 44 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 Adeyl Khan, Faculty, BBA, NSU 12-45 Calculations Ex 13 Adeyl Khan, Faculty, BBA, NSU 46 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 Adeyl Khan, Faculty, BBA, NSU Disadvantages • Requires a larger safety stock • Increases carrying cost • Costs of periodic reviews 12-47 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 Adeyl Khan, Faculty, BBA, NSU 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 Optimal Stocking Level Service level = Cs Cs + Ce Cs = Shortage cost per unit Ce = Excess cost per unit Ce Cs Service Level Quantity So Balance point Adeyl Khan, Faculty, BBA, NSU 12-49 Example 15 Ce = $0.20 per unit Cs = $0.60 per unit Service level = Cs/(Cs+Ce) = .6/(.6+.2) Service level = .75 Ce Cs Service Level = 75% Quantity Stockout risk = 1.00 – 0.75 = 0.25 Adeyl Khan, Faculty, BBA, NSU 12-50 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 Adeyl Khan, Faculty, BBA, NSU 12-51 Adeyl Khan, Faculty, BBA, NSU 52 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. Adeyl Khan, Faculty, BBA, NSU 12-53 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. Adeyl Khan, Faculty, BBA, NSU 12-54