Inventory

Inventory Management

Inventory ManagementInventory is one of the most expensive assets of many companies.

It represents as much as 40% of total invested capital.

Inventory ManagementInventory is any stored resource that is used to satisfy a current or future need.Raw materials, work-in-process, and finished goods are examples of inventory.Two basic questions in inventory management are (1) how much to order (or produce), and (2) when to order (or produce).

Basic Functions of Inventory1. If product demand is high in summer, a firm might produce during winter. (Decoupling).2. Inventory can be a hedge against price changes and inflation.3. Another use of inventory is to take advantage of quantity discounts (when buying). (Many suppliers offer discounts for large orders)

Basic Function of inventory

4. To meet variation in product demand:- buffer or safety stock should be maintained5. Smooth Production

Just-in-Time InventoryJust in Time Inventory is the minimum inventory that is necessary to keep a system perfectly running.

Just-in-Time InventoryWith just in time (JIT) inventory, The exact amount of items arrive at the moment they are needed, Not a minute before OR not a minute after.

Just-in-Time InventoryTo achieve JIT inventory, Managers should Reduce the Variability Caused by some Internal and External Factors.

Holding, Ordering and Set-up CostsHolding Costs are the costs associated with holding or carrying inventory over time.It includes costs related to Storage; such as insurance, oppurtunity cost,rent, extra staffing, interest, and so on.

Holding, Ordering and Set-up CostsSome example holding costs are building rent or depreciation, building operating cost, taxes on building, insurance on building, material handling equipment leasing or depreciation, equipment operating cost, handling manpower cost, taxes on inventory, insurance, etc.

Holding, Ordering and Set-up CostsOrdering Costs include, cost of supplies, order processing, clerical cost, etc.The ordering cost is valid if the products are purchased NOT produced internally.

Holding, Ordering and Set-up CostsSet-up cost is the cost to prepare a machine for manufacturing an order.Set-up cost is highly correlated with set-up time.

Inventory ModelsBasically there are two inventory management systems:1.)Fixed order quantity system2.)Periodic review system

Fixed Order Quantity SystemAlso known as re order point systemIn this RE ORDER level is determined.As soon as the stock level reaches this point, an order for a predetermined no. of units is placed.

Periodic Review SystemIn this inventory is replenished at fixed interval of timeIn this, the time after which the supplies are ordered is fixed but not the quantity to be ordered.

Inventory ModelsIn this section, we will deal with the Fixed Order Quantity System.In this, we should be interested in answering:a) When to place an order for an item, andb) how much of an item to order.

Inventory ModelsThere are Four Basic Inventory Models:1) Economic Order Quantity (EOQ) Model (the most known model).2) Production Order Quantity Model.3) Back order inventory model.4) Quantity discount model.

Economic Order Quantity (EOQ) ModelEOQ model makes a number of assumptions:1-) Demand is known and constant.2-) Lead time (the time between placement of order and receipt of the order) is constant and known.

Economic Order Quantity (EOQ) Model3-) Orders arrive in one batch at a time, and they arrive in one point in time.4-) Quantity discounts are not possible.5-) The costs include only setup cost (or ordering cost when buying) and holding cost.6-) Orders are always placed at the right times. Therefore, stock outs (or shortages) can be completely avoided.

Economic Order Quantity (EOQ) ModelWith these assumptions, the graphic of inventory usage over time is as follows:

Economic Order Quantity (EOQ) Model

Economic Order Quantity (EOQ) ModelQ = order quantity (That is also equal to the Maximum Inventory)Minimum Inventory = 0When inventory level reaches 0, a new order is placed and received.

Economic Order Quantity (EOQ) ModelThe objective of inventory models is to minimize total cost.If we minimize the setup and holding costs, we will be able to minimize total cost:

Economic Order Quantity (EOQ) Model

Economic Order Quantity (EOQ) ModelAs the quantity ordered (Q) increases, holding cost increases, And setup cost decreases.In this graph, Optimal order quantity (Q*) occurs at a point where setup cost is equal to the total (annual) holding cost.

Economic Order Quantity (EOQ) ModelBy using this fact, we can write an equation for Q* as follows:D: Annual Demand in units for the inventory item.S: Setup cost (or the ordering cost) for each order.Note: (Setup cost for production, order cost for buying).H: Annual Holding cost of inventory per unit.

Economic Order Quantity (EOQ) ModelThere will be (D/Q) times of ordering in a whole year.Therefore,Annual ordering cost = (D/Q) . SAverage Annual Holding Cost = (Average Inventory) . H = (Q/2) . HAnnual Setup Cost = Annual Holding Cost(D/Q) . S=(Q/2) . H

Economic Order Quantity (EOQ) ModelTherefore, Q2 = 2DS / HQ* = [2DS / H]1/2Q* value is also called as EOQ.

ExampleAn Inventory model has the following characteristics:Annual Demand (D) = 1000 units Ordering (Setup) cost (S)= $10 per order; Holding cost per unit per year (H) = $.50Assume that there are 270 working days in a year (excluding holidays and weekends).

ExampleQuestions: a) Find the Economic Order Quantity (Q*) for this inventory model.b) How many orders should be placed during one year?c) What is the expected time between two consecutive orders?d) What is the total annual cost of this inventory model?

ExampleAnswers:a) Q* = [2(1000)10 / .50]1/2 = 200 unitsb) Expected number of orders placed during the year (N) = D / Q* = 1000 / 200 = 5 times.

Examplec) Expected time between orders (T) = (Working days in a year) / N = 270 / 5 = 54 days.d) Total Annual Cost = Annual Setup Cost + Annual Holding Cost = DS / Q*+ (Q*)H / 2= 1000 (10) / 200+(200) (.50) / 2= $100

Proof of Optimality by Using DerivationIf we take the derivative of Total Cost (TC) function, based on the order quantity (Q), we get the following:

TC = DS / Q+ (Q)H / 2dTC/dQ = (- DS / Q2) + (H / 2)

Proof of Optimality by Using DerivationAs a mathematic rule, if we set this derived equation equal to zero, we get the optimal (minimum) point of the total cost function:Therefore,

Proof of Optimality by Using Derivation

Proof of Optimality by Using DerivationOne more check is needed for the optimality of Q.That is we take the second derivative of the total cost function based on Q.If the second derivative is positive, the Q* value is a real optimum. (Rule)In fact, second derivative is equal to 2DS / Q3 which is a positive value (It is a real optimum).

Considering the Reorder PointSo far, we only decided how much to order (That is Q*).Now, we should find what time to order.We assumed that firm will wait until its inventory reaches to zero before placing an order.

Considering the Reorder PointAnd, we also assumed that the Orders will receive immediately.However, there is a time between placement and receipt of an order.This is called LEAD TIME or delivery time.

Considering the Reorder PointHere, we will use the term Reorder Point (ROP) for when to order.ROP (in units) = (Demand Per Day). (Lead time for a new order in days)

ROP = d. L

Considering the Reorder Point

Considering the Reorder PointWhen the inventory level reaches the ROP, a new order is required.

It will take a time that is equal to the Lead Time (L) to receive the new order.

Considering the Reorder PointHere, Demand per day (d) is found by the following equation:d = D / Number of working days in a yearThis ROP equation assumes that demand is uniform and constant.If this is not the case, an extra (safety) stock is added (because of uncertainty).

ExampleAnnual demand for an item is D = 8000/year. This year there will be 200 working days in a year.Delivery of an order for this item takes 3 working days (L = 3 days).

ExampleQuestions:

a) Find the demand per day for this item.b) What is the ROP for this item?

ExampleAnswers: a) Demand per day for this item (d) = 8000 / 200 = 40 units / day.b) ROP = d . L = 40 . 3 = 120 units.

When inventory level becomes 120 units, an Order should be placed.

SELECTIVE APPROACHES TO INVENTORY CONTROLABC ANALYSISFNS ANALYSIS- Fast moving,normal moving, slow movingVED ANALYSIS- Vital, Essential, Desirable

ABC AnalysisABC analysis divides on-hand inventory into three classifications on the basis of dollar (TL) volume.It is also known as Pareto analysis. (which is named after principles dictated by Pareto).

ABC AnalysisThe idea is to focus resources on the critical few and not on the trivial many.(Annual Dollar Volume of an Item) = (Its Annual Demand) x (Its Cost per unit)

ABC AnalysisClass A items are those on which the annual dollar volume is high.They represent 70-80% of total inventory costs, but they account for only 15% of total inventory items.

ABC AnalysisClass B items are those on which annual dollar volume is medium.They represent 15-25% of total dollar value, and they account for 30% of total inventory items on the average.

ABC AnalysisClass C items are low dollar volume items.They represent only the 5% of total dollar volume, but they include as many as 50-60% of total inventory items.

ABC Analysis

ABC AnalysisSome of the Inventory Management Policies that may be based on ABC analysis include:a) Class A items should have tighter inventory control.b) Class A items may be stored in a more secure area.c) Forecasting Class A items may warrant more care.