AMAZON.com • Jeff Bezos, in 1995, started AMAZON.com as a “virtual” retailer – no inventory, no warehouses, no overhead; just a bunch of computers. • Growth forced AMAZON.com to excel in inventory management! • AMAZON is now a worldwide leader in warehouse management and automation.
Order Fulfillment at AMAZON (1 of 2) • You order items; computer assigns your order to distribution center [closest facility that has the product(s)] • Lights indicate products ordered to workers who retrieve product and reset light. • Items placed in crate with items from other orders, and crate is placed on conveyor. Bar code on item is scanned 15 times – virtually eliminating error.
Order Fulfillment at AMAZON (2 of 2) • Crates arrive at a central point where items are boxed and labeled with new bar code. • Gift wrapping done by hand (30 packages per hour) • Box is packed, taped, weighed and labeled before leaving warehouse in a truck. • Order appears on your doorstep within a week
Inventory Defined • Inventory is the stock of any item or resource held to meet future demand and can include: raw materials, finished products, component parts, supplies, and work-in-process
Inventory Process stage Number & Value Demand Type Other Raw Material WIP Finished Goods A Items B Items C Items Maintenance Operating Independent Dependent Inventory Classifications
Independent Demand (Demand for the final end-product or demand not related to other items; demand created by external customers) Dependent Demand (Derived demand for component parts, subassemblies, raw materials, etc- used to produce final products) Independent vs. Dependent Demand Finished product Independent demand is uncertain Dependent demand is certain A B(4) C(2) D(1) E(1) E(2) B(1) E(3) Component parts
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
Types of Inventories (1 of 2) • Raw materials & purchased parts • Partially completed goods called work in progress • Finished-goods inventories (manufacturingfirms) or merchandise (retail stores)
Types of Inventories (2 of 2) • Replacement parts, tools, & supplies • Goods-in-transit to warehouses or customers
The Material Flow Cycle (2 of 2) Wait Time Queue Time Setup Time Run Time Move Time Input Output Cycle Time Run time: Job is at machine and being worked on Setup time: Job is at the work station, and the work station is being "setup." Queue time: Job is where it should be, but is not being processed because other work precedes it. Move time: The time a job spends in transit Wait time: When one process is finished, but the job is waiting to be moved to the next work area. Other:"Just-in-case" inventory.
Performance Measures • Inventory turnover (the ratio of annual cost of goods sold to average inventory investment) • Days of inventory on hand (expected number of days of sales that can be supplied from existing inventory)
Functions of Inventory (1 of 2) • To “decouple” or separate various parts of the production process, ie. to maintain independence of operations • To meet unexpected demand & to provide high levels of customer service • To smooth production requirements by meetingseasonal or cyclical variations in demand • To protect against stock-outs
Functions of Inventory (2 of 2) 5. To provide a safeguard for variation in raw material delivery time 6. To provide a stock of goods that will provide a “selection” for customers 7. To take advantage of economic purchase-order size 8. To take advantage of quantity discounts 9. To hedge against price increases
Disadvantages of Inventory • Higher costs • Item cost (if purchased) • Ordering (or setup) cost • Holding (or carrying) cost • Difficult to control • Hides production problems • May decrease flexibility
Inventory Costs • Holding (or carrying) costs • Costs for storage, handling, insurance, etc • Setup (or production change) costs • Costs to prepare a machine or process for manufacturing an order, eg. arranging specific equipment setups, etc • Ordering costs (costs of replenishing inventory) • Costs of placing an order and receiving goods • Shortage costs • Costs incurred when demand exceeds supply
Holding (Carrying) Costs • Obsolescence • Insurance • Extra staffing • Interest • Pilferage • Damage • Warehousing • Etc.
Inventory Holding Costs(Approximate Ranges) Cost as a % of Inventory Value 6% (3 - 10%) 3% (1 - 3.5%) 3% (3 -5%) 11% (6 - 24%) 3% (2 - 5%) 26% Category Housing costs (building rent, depreciation, operating cost, taxes, insurance) Material handling costs (equipment, lease or depreciation, power, operating cost) Labor cost from extra handling Investment costs (borrowing costs, taxes, and insurance on inventory) Pilferage, scrap, and obsolescence Overall carrying cost
Ordering Costs • Supplies • Forms • Order processing • Clerical support • etc.
Setup Costs • Clean-up costs • Re-tooling costs • Adjustment costs • etc.
Shortage Costs • Backordering cost • Cost of lost sales
Inventory Control System Defined • An inventory system is the set of policies and controls that monitor levels of inventory and determinewhat levels should be maintained, when stock should be replenished and how large orders should be • Answers questions as: • When to order? • How much to order?
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
Requirements of an Effective Inventory Management • A system to keep track of inventory • A reliable forecast of demand • Knowledge of lead times • Reasonable estimates of • Holding costs • Ordering costs • Shortage costs • A classification system
Inventory Counting (Control) Systems • Periodic System Physical count of items made at periodic intervals; order is placed for a variable amount after fixed passage of time • Perpetual (Continuous) Inventory System System that keeps track of removals from inventory continuously, thus monitoring current levels of each item (constant amount is ordered when inventory declines to a predetermined level)
Inventory Models • Single-Period Inventory Model • One time purchasing decision (Example: vendor selling t-shirts at a football game) • Seeks to balance the costs of inventory overstock and under stock • Multi-Period Inventory Models • Fixed-Order Quantity Models • Event triggered (Example: running out of stock) • Fixed-Time Period Models • Time triggered (Example: Monthly sales call by sales representative)
Single Period Model • Single period model: model for ordering of perishables and other items with limited useful lives • Shortage cost: generally the unrealized profits per unit • Excess cost: difference between purchase cost and salvage value of items left over at the end of a period
Single Period Model • 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
Single-Period Model This model states that we should continue to increase the size of the inventory so long as the probability of selling the last unit added is equal to or greater than the ratio of: Cu/Co+Cu
Ce Cs Service Level Quantity So Balance point Cs Cs + Ce Service level = Optimal Stocking Level Cs = Shortage cost per unitCe = Excess cost per unit
Ce Cs Service Level = 75% Quantity Single Period Example 1 • Ce = $0.20 per unit • Cs = $0.60 per unit • Service level = Cs/(Cs+Ce) = .6/(.6+.2) • Service level = .75 Stockout risk = 1.00 – 0.75 = 0.25
Single Period Model Example 2 Our college basketball team is playing in atournament game this weekend. Based on our past experience we sell on average 2,400 shirts with a standard deviation of 350. We make $10 on every shirt we sell at the game, but lose $5 on every shirt not sold. How many shirts should we make for the game? Cu = $10 and Co= $5; P≤ $10 / ($10 + $5) = .667 Z.667 = .432 therefore we need 2,400 + .432(350) = 2,551 shirts
Multi-Period Inventory Models • Fixed-Order Quantity Models (Types of) • Economic Order Quantity Model • Economic Production Order Quantity (Economic Lot Size) Model • Economic Order Quantity Model with Quantity Discounts • Fixed Time Period (Fixed Order Interval) Models
Economic Order Quantity Model Assumptions (1 of 2): • Demand for the product is known with certainty, is constant and uniform throughout the period • Lead time (time from ordering to receipt) is known and constant • Price per unit of product is constant (no quantity discounts) • Inventory holding cost is based on average inventory
Economic Order Quantity Model Assumptions (2 of 2): • Ordering or setup costs are constant • All demands for the product will be satisfied (no back orders are allowed) • No stockouts (shortages) are allowed • The order quantity is received all at once. (Instantaneous receipt of material in a single lot) The goal is to calculate the order quantitiy that minimizes total cost
4. The cycle then repeats. 1. You receive an order quantity Q. Number of units on hand (Inv. Level) Q Q Q R L L 2. You start using them up over time. 3. When you reach down to a level of inventory of R, you place your next Q sized order. Time R = Reorder point Q = Economic order quantity L = Lead time Basic Fixed-Order Quantity Model and Reorder Point Behavior
Inventory Level AverageInventory (Q/2) Order Quantity(Q) Reorder Point (ROP) Time Lead Time EOQ Model Demand rate Order placed Order received
Annual cost ($) Total Cost Slope = 0 Carrying Cost = Minimum total cost HQ 2 SD Q Ordering Cost = Optimal order Qopt Order Quantity, Q EOQ Cost Model: How Much to Order? By adding the holding and ordering costs together, we determine the total cost curve, which in turn is used to find the optimal order quantity that minimizes total costs
Purchase Order Description Qty. Microwave 1000 Order quantity Why Holding Costs Increase? • More units must be stored if more are ordered Purchase Order Description Qty. Microwave 1 Order quantity
1 Order (Postage $ 0.33) 1000 Orders (Postage $330) Purchase Order PurchaseOrder Purchase Order Purchase Order Description Qty. Purchase Order Description Qty. Description Qty. Description Qty. Microwave 1 Description Qty. Microwave 1000 Microwave 1 Microwave 1 Microwave 1 Order quantity Why Ordering Costs Decrease ? Cost is spread over more units Example: You need 1000 microwave ovens
Basic Fixed-Order Quantity (EOQ) Model Formula TC=Total annual cost D =Annual demand C =Cost per unit Q =Order quantity S =Cost of placing an order or setup cost R =Reorder point L =Lead time H=Annual holding and storage cost per unit of inventory Total Annual = Cost Annual Purchase Cost Annual Ordering Cost Annual Holding Cost + +
Deriving Qopt Proving equality of costs at optimal point SD Q H Q 2 TC = + SD Q2 Annual ordering cost = H 2 TC Q = + = S D Q S D Q SD Q2 H 2 Annualcarrying cost = 0 = + 2S D H S D Q H Q 2 H Q 2 HQ 2 Q2 = 2SD H Qopt = 2S D H Total cost = + Qopt = EOQ Cost Model Using calculus, we take the first derivative of the total cost function with respect to Q, and set the derivative (slope) equal to zero, solving for the optimized (cost minimized) value of Qopt
Deriving the EOQ How much to order?: When to order? We also need a reorder point to tell us when to place an order
× × 2 D S Optimal Order Quantity = = Q* H D = = Expected Number of Orders N Q* Working Days / Year Expected Time Between Orders = = T N D = d Working Days / Year = × ROP d L EOQ Model Equations
EOQ Example 1 (1 of 3) Given the information below, what are the EOQ and reorder point? Annual Demand = 1,000 units Days per year considered in averagedaily demand = 365 Cost to place an order = $10 Holding cost per unit per year = $2.50 Lead time = 7 days Cost per unit = $15
EOQ Example 1(2 of 3) In summary, you place an optimal order of 90 units. In the course of using the units to meet demand, when you only have 20 units left, place the next order of 90 units.
SD Q HQ 2 TCmin = (10)(1,000) 90 (2,5)(90) 2 TCmin = TCmin = $ 111 + $111 = 22 $ EOQ Example I(3 of 3) Orders per year = D/Qopt = 1000/90 = 11 orders/year Order cycle time=365/(D/Qopt)= 365/11 = 33.1days + +