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## Inventory

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**Inventory**Chapter 6**Inventory: is the set of the items that an organization**holds for later use by the organization.An Inventory System is a set of policies that monitors and controls inventory. It determines how much of each item should be kept, when low items should be replenished, and how many items should be ordered or made when replenishment is needed. Inventory System**The Functions of Inventory**• Provide a stock of goods to meet anticipated customer demand and provide a “selection” of goods • Decouple suppliers from production and production from distribution • Allow one to take advantage of quantity discounts • To provide a hedge against inflation • To protect against shortages due to delivery variation • To permit operations to continue smoothly with the use of “work-in-process”**Disadvantages of Inventory**• Higher costs • Item cost (if purchased) • Ordering (or setup) cost • Costs of forms, clerks’ wages etc. • Holding (or carrying) cost • Building lease, insurance, taxes etc. • Difficult to control • Uncertain demand • Uncertain lead time**Types of Inventory**• Raw materials • Purchased parts and supplies • Work-in-process • Component parts • Tools, machinery, and equipment • Finished goods**Component parts**and supplies Raw material Finished goods Work-in process In-process (partially completed) products Purchasing part Tools, machinery, and equipment Types of Inventory**Independent Demand: are those items that we sell to**customers. Ex. Ford Motor Company, their main independent demand will be the cars, trucks and van that they sell.A small part of the independent demand would the parts that they sell to customers.Finished productsBased on market demandRequires forecastingDependent Demand: are those items whose demand is determined by other items. When Ford Motors Company has demand for a car, that translates into demand for four tires, one engine, one transmission, and so on. The items used in the production of that car.Parts that go into the finished productsDependent demand is a known function of independent demandNo forecasting is required Two forms of Demands**Reasons To Hold Inventory**• Meet unexpected,seasonal, cyclical, and variations demand • Take advantage of price discounts • Hedge against price increases • Quantity discounts (To get a lower price) • To decouple work-centers • To allow flexible production schedule • As a safeguard against variations in delivery time (lead time)**Costs of Inventory**Visible Costs of Inventory. They are holding, shortage, reordering, and setup cost. Hidden Costs of Inventory Costs result from longer or uncertain lead-time, or by following bad inventory control system**The Visible Cost of Inventory**• Holding Cost: These are all the cost the organization incurs in the purchase and storing of the inventory. They include the cost of financing the purchase , storage costs, handling costs, taxes, obsolescence, pilferage, breakage, spoilage, reduced flexibility, and opportunity costs. They are also called Carriage cost. High holding cost favor low inventory levels and frequent replacements and vice versa. • Setup Cost: This is the cost of switching a production line from making one product to making a different product. Setup cost apply only to items the organization produces itself. High setup cost favors large production runs and the resulting larger inventory and vice versa.**The Visible Cost of Inventory**• Ordering Cost: This is the cost of placing an order for an item the organization purchases. It include placing the order, tracking the order, shipping costs, receiving and inspecting the order and handling the paperwork. High ordering costs favor fewer orders of larger size and resulting large inventory and vice versa. • Shortage Costs: This is the cost to the organization of not having an item when it is needed. These costs include loss of goodwill, loss of sale, loss of a customer, loss of profits and late penalties. Many of these costs are difficult or impossible to measure with any accuracy. High shortage cost favor large inventory and vice versa**Cyclic Inventory Control**Inventory control at Ware-Mart-Example The purchasing department is offering 7 alternative cycles and times (T): • Order every week, 52 times per year, T=1 week • Order every second week, 26 times per year, T=2 weeks • Order every month, 12 times per year, T=1 month • Order every second month, 6 times per year, T=2, months • Order quarterly, 4 times per year, T= 3 months • Order semiannually, twice per year, T=6 months • Order every year, once a year, T=1 year**Brent estimates :**Yearly demand rate = 12000 pots Quarterly demand = 3000 pots Average inventory = 1500 pots Every day demand = 100 pots Price/ pots = $6.75 Corporate holding cost = 20% of the purchasing cost for holding cost Unit Annual holding cost = 0.20 *6.75=$1.35 Forecast for the annual holding cost = 1500 * 1.35 = 2025 Ordering cost is between $25 and $30 Average Ordering cost = $28 Annual Ordering cost = 4*28 = $112 Annual Combined Cost = Annual Ordering Cost + Annual Holding cost = $2025+$112 = $2137**Purpose of the inventory system is to decide how much to**order and when • Objectives of inventory system • Keep enough inventory to meet customer demand • Control inventory costs • According to that there are different models for the inventory**Inventory Control Models**Parameters Ordering cost Holding costs Stock out costs Demand (Certainty,Uncertainties) Variables Time sequence of ordering Quantity sequence of ordering Model Performance measure Profit Cost Service level Influence Chart for selecting Inventory Controls Models**Inventory Control Models**Probabilistic Deterministic Continues review model Also known as a Fixed order quantity models • Economic order quantity EOQ • Production order quantity • Quantity discount • Periodic review model • Also known as a Fixed order period models • Single-period models • Multi-period models • Triggered policy • Quantity triggered model • Time triggered model**Inventory Controls Models**• Probabilistic Model: Where performance measures use expected values in realistic cases which involves uncertainty. • Deterministic Models: are sufficient by ignoring uncertainty , provided the decision maker takes both qualitative and quantitative factors into account. • Continuous Review Models: Assumes that inventory levels are monitored continuously and that orders are placed depending on the level of inventory. • Periodic Review Models: assume that the monitoring is performed only at a stated times, such as monthly or quarterly. • Fixed Order Quantity Models: assume that a constant quantity is order each time an order is placed.**Fixed Order Period Models: assume that a ordering cycle is**fixed, such as 1 week or 1 month • Multi period Models: assumes that the orders will be placed repeatedly. • Single Period Models: deals with situations in which only single orders is placed. • Quantity-Triggered Models: specify ordering when the inventory level sinks to a stated quantity. • Time-Triggered Models: specify ordering at specific time periods, such as weekly, monthly or quarterly.**Continuous inventory systems**• also known as fixed-order-quantity system • whenever inventory decreases to predetermined level known as a reorder point, new order is placed • order is for fixed amount (EOQ) that minimizes total inventory costs • Periodic inventory systems • also known as fixed-time-period system • inventory on hand is counted at specific time intervals • after inventory level determined, order is placed which will bring inventory back to desired level • new order quantity determined each time**Deterministic Model**Fixed Order Quantity Models Economic order quantity EOQ**The Economic Order Quantity Model (EOQ)**• EOQ model is a deterministic model with a fixed ordering cycle and fixed quantity ordered. • The model determines the EOQ that minimizes the combined total cost of ordering and holding inventory over a fixed time interval, often one year. • Excels what-if capabilities make the EOQ a potentially useful tool by allowing the decision maker to learn about inventory cost structure while performing the analysis. • The what-if scenario result can be useful inputs to decision making.**Economic Order Quantity (EOQ) Models**• EOQ – the optimal order quantity that will minimize total inventory carry costs • Basic EOQ model • determines optimal order size that minimizes the sum of carrying costs and ordering costs**EOQ Assumptions**• Known and constant demand • Known and constant lead time • Instantaneous receipt of material • No quantity discounts • Only order (setup) cost and holding cost • No stock outs Developing the EOQ Model Parameter Performance measure Annual Demand Unit Holding Cost Unit Ordering Cost EOQFormula Optimum order quantity Q* Minimum annual combined (holding and ordering) cost Quantity sequence of ordering Decision Variable**EOQ Model notations**D Annual Demand C Cost per unit I interest to hold the Inventory. H Expressed as a percentage of costs (C*I) O Ordering costs Q The Quantity to be ordered T Length of the Time N Number of annual order**Unit holding Cost (H)= c * i**EOQ or Qopt or Q*=squareroot((2*D*O)/H) No. of orders (N)=D/EOQ Annual Holding Cost (AHC)=H * EOQ/2 Annual ordering Cost (AOC)= O *N Combine Cost (CC)= AHC+ AOC Purchase Cost (PC)= D*C Total Cost= CC + PC Duration between Orders or Time between orders (T) = No of Working Days/N**EOQ Models**• Optimal order quantity (Qopt) = square root [(2OD) / H ] • Occurs where total cost is at a minimum • This happens where Holding cost curve intersects with Ordering cost curve • Is an approximate value • Round to nearest whole number • EOQ model is robust (resilient to errors)**EOQ ModelHow Much to Order?**Annual Cost Total (Combined) Cost Curve Holding Cost Curve Order (Setup) Cost Curve Order Quantity (Qopt) Optimal Order Quantity (Qopt)**[(H)(Q)] / 2**• [(O)(D)] / Q [(O)(D)] / Q + [(H)(Q)] / 2**The graphical figure shows the combined cost as a function**of the order quantity Q. The annual holding costs are a linear, straight-line function of Q. The ordering costs are represented by an inverse, diminishing curve.The combined cost is U-shaped, starting high, decreasing to minimum and then increasing again.The minimum cost is at the bottom of the U, (intersection of the Holding and Ordering cost) where the slope is zero.**Fundamental Assumptions of Traditional Manufacturing**• It is expensive to process orders for purchased items, and quantity discounts are available • as a result, orders for parts are placed infrequently, in large quantities • Setups are lengthy and expensive • as a result, large batches of each product are made**Production Lot Size**According to traditional thinking, • Setup costs decrease as production lot or batch size increases • Inventory levels and holding cost increases as batch size increases • The lot size that minimizes the net cost is called the Economic Production Lot (EPL)**Kinds of Lots**• Production or process lot • Purchase or order quantity • Transfer batch • Delivery quantity**Economic Production Lot Size**• The Economic Production Lot (EPL) size model is a variation of the basic EOQ model. • A replenishment order is not received in one lump sum as it is in the basic EOQ model. • Inventory is replenished gradually as the order is produced (which requires the production rate to be greater than the demand rate). • This model's variable costs are annual holding cost and annual set-up cost (equivalent to ordering cost). • For the optimal lot size, annual holding and set-up costs are equal.**Economic Production Lot SizeAssumptions**• Demand occurs at a constant rate of D items per year. • Production rate is P items per year (and P > D ). • Set-up cost O per run. • Holding cost H per item in inventory per year. • Purchase cost per unit C is constant (no quantity discount). • Set-up time (lead time) is constant. • Planned shortages are not permitted.**Production, Demand and Inventory**Economic Production Lot Fluctuating Inventory**EPL or EPQ**Unless you stop production, since you cannot sell the parts at the same or faster rate that you are making them, your inventory will grow. Note: P and D should be in same units Inv Slope=P-D Time**EPL**Slope=P-D Inv Slope=-D H Time T1 T2 Start Prod. Start Prod. Stop Prod.**Economic Production lot Size Model**O Ordering Cost P Production rate t time need to produce the lot Q = P x t t = Q/P Maximum inventory = ( P x t) – ( D x t ) = ( P – D ) x t = ( P – D) x Q/P =(1 – D/P) x Q Average inventory = (1 – D/P) x Q/2 F = 1 – D/P is critical in lot size calculations.**To Establish the model, we use the same EOQ formulas, but**when calculating the holding cost, we replace Q by Q x (1 – D/P) = QF Annual holding cost = [ Q x ( 1 – D/P)] x C x (i/2) = Q x F x (Ci/2) Annual setup cost = D/Q x O To minimize the total combined cost, we use the same EOQ formulas, but Q is Q x (1- D/P) for the holding cost.**The value of Q that minimizes the combined cost available**when: Q(1-D/P)H/2 + DO/Q = QFH/2 + DO/Q So the optimal value of the order quantity Q is The annual cost of holding and ordering (which are equal) is SO the minimum annual combined cost is**Economic Production Lot Size Model**• Production Build-up = (P-D) • Production Duration = Q/P • Maximum Inventory = (P-D)Q/P or (1-D/P)Q • Average Inventory = (1-D/P)Q/2 • Time between production starts = Q/D • Number of Production runs per year = D/Q • Total Annual Cost = Setups Holding Purchase**CASE1: Brent order 26 times a year, so each additional**dollar cost of ordering should increase annual cost by $26. CASE 2: If the ordering cost goes up by $1, the combined cost goes by 17 x $1= $17.**CASE 1: What-if the ordering cost goes up 10%? The ordering**cost is $28, so a 10% increase leads to an increase of $2.80. = 26x2.80=72.80 CC=$1039 + $72.80=$1112.80 means increase of 7%. A 10% increase in ordering cost leads to 7% increase in combined cost. What about CASE2 ?**CASE 1 : What if the interest rate charged as holding cost i**changes ? Only the holding cost changes, and the formula to use is CC= QCi/2 +DO/Q= 1557.6 x i + 728 If the percentages goes to 30%-50% increase, then CC= 1557.6 x .3 + 728= 467.3 +728= 1195 This is $155 higher than the base-case cost of $1039. To summarize, 50% increase in the percentage results in a 155/1039=14.9% increase in CC. What about CASE 2 ?