MEANING  Inventory-A physical resource that a firm holds in stock with the intent of selling it or transforming it into a more valuable state.  Inventory System- A set of policies and controls that monitors levels of inventory and determines what levels should be maintained, when stock should be replenished, and how large orders should be. It involves inventory planning and decision making with regard to the quantity and time of purchase, fixation of stock levels, maintenance of stores record and continuous stock taking.

THE INVENTORY DECISION  In an Inventory control situation, there are three basic questions to be answered. They are:- 1. How much to order? 2. When should the order be placed? 3. How much safety stock should be kept?

TYPES OF INVENTORIES Types of Inventories Direct Inventories Raw Material Work in Progress Finished Goods Indirect Inventories Transit Inventories Buffer Inventories Lot Size Inventories Decoupling Inventories Seasonal Inventories Fluctuation Inventories

Factors Affecting Inventory Control Policy A. Characteristics of the manufacturing system: 1. Degree of Specialization and differentiation of the products at various stages. 2. Process capability and flexibility. 3. Production capacity and storage facility. 4. Quality requirements. 5. Nature of production system. B. Amount of protection against storages: 1. Changes in size and frequency of orders. 2. Unpredictability of sales. 3. Physical and economic structure of distribution pattern. 4. Costs associated with failure to meet demand. 5. Accuracy, frequency and detail of demand forecasts. 6. Protection against breakdown or other interruptions in production.

Objectives of Inventory Control 1. A hedge against inflation. 2. Protection against fluctuation in demand. 3. Protection against fluctuation in supply. 4. To avoid stock outs and shortages. 5. Quantity discounts. 6. Optimum use of men, machines & materials. 7. Maintaining different level of stock. 8. Control of stock volume. 9. The decoupling function.

Scope of Inventory Control 1. Formulation of policy. 2. Organization structure. 3. Determination of economic order quantity. 4. Determination of safety stock. 5. Determination of lead time. 6. Minimum material handling & storage cost. 7. Effectiveness towards running of store.

TOOLS & TECHNIQUES OF INVENTORY MANAGEMENT 1. DETERMINATION OF STOCK LEVELS2.DETERMINATION OF SAFETY STOCKS3. INVENTORY CONTROL SYSTEMS4. ECONOMIC ORDER QUANTITY5. PRODUCTION QUANTITY MODEL6. QUANTITY DISCOUNTS7. ABC ANALYSIS8. JIT CONTROL SYSTEM9. VED ANALYSIS10. FNSD ANALYSIS11. PREPETUAL INVENTORY SYSTEM12. PRICE BREAKS APPROACH13. OTHER MODELS OF INVENTORY CONTROL

1. Determination Of Stock Levels Reorder Point Level of inventory at which a new order is placed. R = dL where d = demand rate per period L = lead time

Re-ordering level It is the level of stock quantity between minimum and maximum level and material order was sent for getting fresh stock. Formula : maximum usage of stock X maximum delivery period

Minimum level  It is the minimum balance, which must be maintained in hand at all times, so that there is no stoppage of production due to non availability of inventory. Remember You must need re-order level for getting it. Formula : Re-order level - ( Normal usage X average period )

Maximum level  It shows maximum quantity which should be in the stock, if we buy more, it means we are wasting money. Formula : re-order level X re-order quantity - ( minimum usage X minimum period )

Average Stock Level  This is the average of minimum and maximum level and it can be calculated by adding minimum level and maximum level and divided by 2. formula : minimum level + maximum level / 2

Danger level  It is the level at which normal issues of the raw material inventory are stopped and emergency issues are only made. formula : average consumption X lead time for emergency purchases

2. Determination of Safety Stocks Safety stock buffer added to on hand inventory during lead time Stockout an inventory shortage Service level probability that the inventory available during lead time will meet demand

Variable Demand with a Reorder Point Reorder point, R Q LT Time LT Inventory level 0

Reorder Point with a Safety Stock Reorder point, R Q LT Time LT Inventory level 0 Safety Stock

Reorder Point With Variable Demand R = dL + z  d L where d=average daily demand L=lead time  d =the standard deviation of daily demand z=number of standard deviations corresponding to the service level probability z  d L=safety stock

Reorder Point for a Service Level Probability of meeting demand during lead time = service level Probability of a stockout R Safety stock dL Demand z  d L

Reorder Point for Variable Demand The carpet store wants a reorder point with a 95% service level and a 5% stockout probability d= 30 yards per day L= 10 days  d = 5 yards per day For a 95% service level, z = 1.65 R= dL + z  d L = 30(10) + (1.65)(5)( 10) = yards Safety stock= z  d L = (1.65)(5)( 10) = 26.1 yards

3. Inventory Control Systems Continuous system (fixed- order-quantity or Q Systems) constant amount ordered when inventory declines to predetermined level Periodic system (fixed-time- period or P Systems) order placed for variable amount after fixed passage of time

 Fixed Order Quantity System or Q Systems – In reorder level system, a replenishment order fixed size (Q) is placed when the stock level falls to the fixed reorder level (R). Thus a fixed quantity is ordered at various interval of time.  Periodic Review System or P System – In periodic review system, the inventory levels are reviewed at fixed points of time, when the quantity to be ordered is decided. By this method variable quantities are ordered at fixed time intervals

4. ECONOMIC ORDER QUANTITY (EOQ)  Economic order quantity is the size of the lot to be purchased which is economically viable. This the quantity of materials which can be purchased at minimum costs.  ASSUMPTIONS  Demand rate D is constant, recurring, and known  Amount in inventory is known at all times  Ordering (setup) cost S per order is fixed  Lead time L is constant and known.  Unit cost C is constant (no quantity discounts)  Annual carrying cost is i time the average RUPEE value of the inventory  No stock outs allowed.  Material is ordered or produced in a lot or batch and the lot is received all at once

EOQ Inventory Order Cycle Demand rate 0Time Lead time Lead time Order Placed Order Placed Order Received Order Received Inventory Level Reorder point, R Order qty, Q As Q increases, average inventory level increases, but number of orders placed decreases ave = Q/2

EOQ Cost Model C o - cost of placing orderD - annual demand C c - annual per-unit carrying costQ - order quantity Annual ordering cost = CoDCoDQQCoDCoDQQQ Annual carrying cost = CcQCcQ22CcQCcQ222 Total cost = + CoDCoDQQCoDCoDQQQ CcQCcQ22CcQCcQ222

EOQ Cost Model TC = + CoDQCoDQ CcQ2CcQ2 = + CoDQ2CoDQ2 Cc2Cc2  TC  Q 0 = + C0DQ2C0DQ2 Cc2Cc2 Q opt = 2CoDCc2CoDCc Deriving Q opt Proving equality of costs at optimal point = CoDQCoDQ CcQ2CcQ2 Q 2 = 2CoDCc2CoDCc Q opt = 2CoDCc2CoDCc

EOQ Cost Model (cont.) Order Quantity, Q Annual cost ($) Total Cost Carrying Cost = CcQCcQ22CcQCcQ222 Slope = 0 Minimum total cost Optimal order Q opt Q opt Ordering Cost = CoDCoDQQCoDCoDQQQ

EOQ Example C c = $0.75 per yardC o = $150D = 10,000 yards Q opt = 2CoD2CoDCcCc2CoD2CoDCcCc 2(150)(10,000)(0.75) Q opt = 2,000 yards TC min = + CoDCoDQQCoDCoDQQQ CcQCcQ22CcQCcQ222 (150)(10,000)2,000(0.75)(2,000)2 TC min = $750 + $750 = $1,500 Orders per year =D/Q opt =10,000/2,000 =5 orders/year Order cycle time =311 days/(D/Q opt ) =311/5 =62.2 store days

5. Production Quantity Model  An inventory system in which an order is received gradually, as inventory is simultaneously being depleted  AKA non-instantaneous receipt model assumption that Q is received all at once is relaxed  p - daily rate at which an order is received over time, a.k.a. production rate  d - daily rate at which inventory is demanded

Production Quantity Model (cont.) Q(1-d/p) Inventorylevel (1-d/p) Q2 Time 0 Order receipt period BeginorderreceiptEndorderreceipt Maximum inventory level Average

Production Quantity Model (cont.) p = production rated = demand rate Maximum inventory level =Q - d =Q 1 - Qp dp Average inventory level = 1 - Q2 dp TC = dp CoDCoDQQCoDCoDQQQ CcQCcQ22CcQCcQ222 Q opt = 2C o D C c 1 - dp

Production Quantity Model: Example C c = $0.75 per yardC o = $150D = 10,000 yards d = 10,000/311 = 32.2 yards per dayp = 150 yards per day Q opt = = = 2,256.8 yards 2C o D C c 1 - dp 2(150)(10,000) TC = = $1,329 dp CoDCoDQQCoDCoDQQQ CcQCcQ22CcQCcQ222 Production run = = = days per order Qp2,

Production Quantity Model: Example (cont.) Number of production runs = = = 4.43 runs/year DQDQ 10,000 2,256.8 Maximum inventory level =Q 1 - = 2, =1,772 yards dpdp

6. QUANTITY DISCOUNTS Price per unit decreases as order quantity increases TC = + + PD CoDCoDQQCoDCoDQQQ CcQCcQ22CcQCcQ222 where P = per unit price of the item D = annual demand

Quantity Discount Model (cont.) Q opt Carrying cost Ordering cost Inventory cost ($) Q( d 1 ) = 100 Q( d 2 ) = 200 TC ( d 2 = $6 ) TC ( d 1 = $8 ) TC = ($10 ) ORDER SIZE PRICE $ – ( d 1 ) ( d 2 )

Quantity Discount: Example QUANTITYPRICE $1, , C o =$2,500 C c =$190 per computer D =200 Q opt = = = 72.5 PCs 2CoD2CoDCcCc2CoD2CoDCcCc2(2500)(200)190 TC = + + PD = $233,784 C o D Q opt C c Q opt 2 For Q = 72.5 TC = + + PD = $194,105 CoDCoDQQCoDCoDQQQ CcQCcQ22CcQCcQ222 For Q = 90

7. ABC ANALYSIS  The materials are divided in to a number of categories for adopting a selective approach for material control.  Classification of items as a, b, or c  Purpose: set priorities for management attention.  ‘A’ items: 20% of the items contributes, 80% value  ‘B’ items: 30 % of Items contributes, 15% Value  ‘C’ items: 50 % of Items contributes, 5% value  Three classes is arbitrary; could be any number.  Percents are approximate.

Percentage of items Percentage of dollar value — — — — — — — — — — 0 0 — +Class C Class A +Class B

ABC Classification  Class A 5 – 15 % of units 70 – 80 % of value  Class B 30 % of units 15 % of value  Class C 50 – 60 % of units 5 – 10 % of value

8. JIT CONTROL SYSTEM  Just in Time purchasing is the purchase of material in such a way that delivery of purchased items is assured before their use or demand.

9. VED Analysis  VED – Vital, Essential, Desirable – analysis is used primarily for control of spare parts. The spare, parts can be divided into three categories – vital, essential or desirable – keeping in view the critically to production.

10. FNSD Analysis  FNSD analysis divides the items into four categories in the descending order of their usage rate as follows:  ‘F’ means Fast moving items  ‘N’ means normal moving items  ‘S’ means slow moving items  ‘D’ means dead stock.

11. Perpetual Inventory System Perpetual Inventory is a system of records maintained by the controlling department, which reflects the physical movement of stocks and their current balance. It aims at devising the system of records by which the receipts and issues of stores may be recorded immediately at the time of each transaction and the balance may be brought out so as to show the up-to-date position. The records used for perpetual inventory are: (i) Bin Cards; (ii) Store Ledger Accounts or Stores Record cards; (iii) The forms and documents used for receipt, issue and transfer of materials.