Inventory • Inventory – A stock or store of goods • Independent demand items – Items that are ready to be sold or used
Types of Inventory • Raw materials and purchased parts • Work-in-process • Finished goods inventories or merchandise • Maintenance and repairs (MRO) inventory, tools and supplies • Goods-in-transit to warehouses or customers (pipeline inventory)
Inventory Functions • Inventories serve a number of functions such as: 1. To meet anticipated customer demand 2. To smooth production requirements 3. To decouple operations 4. To protect against stockouts 5. To take advantage of order cycles 6. To hedge against price increases 7. To permit operations 8. To take advantage of quantity discounts
Inventory Management • Management has two basic functions concerning inventory: 1. Establish a system for tracking items in inventory 2. Make decisions about • When to order • How much to order
Effective Inventory Management • Requires: 1. A system keep track of inventory 2. A reliable forecast of demand 3. Knowledge of lead time and lead time variability 4. Reasonable estimates of • holding costs • ordering costs • shortage costs 1. A classification system for inventory items
Inventory Counting Systems • Periodic System – Physical count of items in inventory made at periodic intervals • Perpetual Inventory System – System that keeps track of removals from inventory continuously, thus monitoring current levels of each item • Two-bin system – Two containers of inventory; reorder when the first is empty
Inventory Counting Technologies • Universal product code (UPC) – Bar code printed on a label that has information about the item to which it is attached • Radio frequency identification (RFID) tags – A technology that uses radio waves to identify objects, such as goods in supply chains
Demand Forecasts and Lead Time • Forecasts – Inventories are necessary to satisfy customer demands, so it is important to have a reliable estimates of the amount and timing of demand • Lead time – Time interval between ordering and receiving the order • Point-of-sale (POS) systems – A system that electronically records actual sales – Such demand information is very useful for enhancing forecasting and inventory management
ABC Classification System • A-B-C approach – Classifying inventory according to some measure of importance, and allocating control efforts accordingly – A items (very important) • 10 to 20 percent of the number of items in inventory and about 60 to 70 percent of the annual dollar value – B items (moderately important) High – C items (least important) • 50 to 60 percent of the number of items in inventory but only Annual A $ value about 10 to 15 percent of the of items annual dollar value B Low C Few Many Number of Items
Cycle Counting • Cycle counting – A physical count of items in inventory • Cycle counting management – How much accuracy is needed? • A items: ± 0.2 percent • B items: ± 1 percent • C items: ± 5 percent – When should cycle counting be performed? – Who should do it?
V-E-D Classification• Based on the critical nature of items.• Applicable to spare parts of equipment, as they do not follow a predictable demand pattern.• Very important in hospital pharmacy.
V-E-D Classification (Cont’d)• V-Vital : Items without which the activities will come to a halt.• E-Essential : Items which are likely to cause disruption of the normal activity.• D-Desirable : In the absence of which the work does not get hampered.
H-M-L Classification• Based on the unit value (in rupees) of items.• Similar to A-B-C analysis H-High M-Medium L -Low
F-S-N Classification• Takes into account the distribution and handling patterns of items from stores.• Important when obsolescence is to be controlled. F – Fast moving S – Slow moving N – Non moving
S-D-E Classification• Based on the lead-time analysis and availability. S – Scarce : longer lead time D – Difficult : long lead time E – Easy : reasonable lead time
S-O-S Classification• S-O-S :Seasonal- Off- Seasonal• Some items are seasonal in nature and hence require special purchasing and stocking strategies.• EOQ formula cannot be applied in these cases.• Inventories at the time of procurement will be extremely high.
G-O-L-F Classification• G-O-L-F stands for: G – Government O – Ordinary L – Local F – Foreign
X-Y-Z Classification• Based on the value of inventory stored.• If the values are high, special efforts should be made to reduce them.• This exercise can be done once a year.
Economic Order Quantity (EOQ):Determining How Much to Order• One of the oldest and most well known inventory control techniques• Easy to use• Based on a number of assumptions
Assumptions of the EOQ Model1. Demand is known and constant2. Lead time is known and constant3. Receipt of inventory is instantaneous4. Quantity discounts are not available5. Variable costs are limited to: ordering cost and carrying (or holding) cost6. If orders are placed at the right time, stock outs can be avoided
Minimizing EOQ Model Costs• Only ordering and carrying costs need to be minimized (all other costs are assumed constant)• As Q (order quantity) increases: –Carry cost increases –Ordering cost decreases (since the number of orders per year decreases)
The Inventory Cycle Profile of Inventory Level Over Time Q Usage Quantity rate on hand Reorder point Time Receive Place Receive Place Receive order order order order order Lead time
EOQ Model Total CostAt optimal order quantity (Q*): Carrying cost = Ordering cost
Finding the Optimal Order QuantityParameters: Q* = Optimal order quantity (the EOQ) D = Annual demand Co = Ordering cost per order Ch = Carrying (or holding) cost per unit per yr P = Purchase cost per unit
Two Methods for Carrying Cost Carry cost (Ch) can be expressed either: 1. As a fixed cost, such as Ch = $0.50 per unit per year 2. As a percentage of the item’s purchase cost (P) Ch = I x P I = a percentage of the purchase cost
EOQ Total Cost Total ordering cost = (D/Q) x Co Total carrying cost = (Q/2) x Ch Total purchase cost =PxD = Total cost Note: • (Q/2) is the average inventory level • Purchase cost does not depend on Q
Finding Q*Recall that at the optimal order quantity (Q*): Carry cost = Ordering cost (D/Q*) x Co = (Q*/2) x ChRearranging to solve for Q*: Q* = ( 2 DCo / Ch )
EOQ Example: Sumco Pump Co.Buys pump housing from a manufacturer and sells to retailers D = 1000 pumps annually Co = $10 per order Ch = $0.50 per pump per year P = $5 Q* = ?
Example• Zartex Co. produces fertilizer to sell to wholesalers. One raw material – calcium nitrate – is purchased from a nearby supplier at $22.50 per ton. Zartex estimates it will need 5,750,000 tons of calcium nitrate next year.• The annual carrying cost for this material is 40% of the acquisition cost, and the ordering cost is $595.
Examplea) What is the most economical order quantity?b) How many orders will be placed per year?
Example: Basic EOQ• Economical Order Quantity (EOQ) D = 5,750,000 tons/year Ch = .40(22.50) = $9.00/ton/year Co = $595/order• Q* = ( 2 DCo / Ch ) EOQ = 2(5,750,000)(595)/9.00 = 27,573.135 tons per order
Example: Basic EOQ• Number of Orders Per Year = D/Q = 5,750,000/27,573.135 = 208.5 orders/year
Economic Production Quantity (EPQ) • Assumptions – Only one product is involved – Annual demand requirements are known – Usage rate is constant – Usage occurs continually, but production occurs periodically – The production rate is constant – Lead time does not vary – There are no quantity discounts
When to Reorder • Reorder point – When the quantity on hand of an item drops to this amount, the item is reordered. – Determinants of the reorder point 1. The rate of demand 2. The lead time 3. The extent of demand and/or lead time variability 4. The degree of stockout risk acceptable to management
Reorder Point: Under Certainty ROP = d × LT where d = Demand rate (units per period, per day, per week) LT = Lead time (in same time units as d )
Reorder Point: Under Uncertainty • Demand or lead time uncertainty creates the possibility that demand will be greater than available supply • To reduce the likelihood of a stockout, it becomes necessary to carry safety stock – Safety stock • Stock that is held in excess of expected demand due to variable demand and/or lead time Expected demand ROP = + Safety Stock during lead time
Safety Stock Quantity Maximum probable demand during lead time Expected demand during lead timeROP Safety stock LT Time
Safety Stock? • As the amount of safety stock carried increases, the risk of stockout decreases. – This improves customer service level • Service level – The probability that demand will not exceed supply during lead time – Service level = 100% - Stockout risk
How Much Safety Stock? • The amount of safety stock that is appropriate for a given situation depends upon: 1. The average demand rate and average lead time 2. Demand and lead time variability 3. The desired service level Expected demand ROP = + zσ dLT during lead time where z = Number of standard deviations σ dLT = The standard deviation of lead time demand
Reorder Point: Demand UncertaintyROP = d + zσ d LTwhere z = Number of standard deviationsd = Average demand per period (per day, per week)σ d = The stddev. of demand per period (same time units as d )LT = Lead time (same time units as d )
Reorder Point: Lead Time UncertaintyROP = d × LT + zdσ LTwhere z = Number of standard deviations d = Demand per period (per day, per week)σ LT = The stddev. of lead time (same time units as d )LT = Average lead time (same time units as d )
How Much to Order: FOI • Fixed-order-interval (FOI) model – Orders are placed at fixed time intervals • Reasons for using the FOI model – Supplier’s policy may encourage its use – Grouping orders from the same supplier can produce savings in shipping costs – Some circumstances do not lend themselves to continuously monitoring inventory position