C 11 Inventory Management Pencils, papers, clips, advertisements-flyer, visiting cards, nuts, bolts, trucks, needles, airplanes Raw materials, semi-finished goods, finished goods What is the worth? Let top management see the money withheld 

Inventory- a stock or store of goods Independent Demand B(4) E(1) D(2) C(2) F(2) D(3) A Dependent Demand Independent demand is uncertain. Dependent demand is certain.

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 Raw materials & purchased parts Partially completed goods called work in progress Finished-goods inventories manufacturing firms retail stores (merchandise ) Replacement parts, tools, & supplies Goods-in-transit to warehouses or customers

Functions of Inventory To meet anticipated demand Anticipation stock To smooth production requirements Seasonal demand (e.g. Potato case!) To decouple operations Buffer for continuous operation To protect against stock-outs Delayed delivery, abrupt demand Safety stocks

Functions of Inventory … To take advantage of order cycles Purchasing, Producing in Batches (Lots) Cycle stock for periodic To help hedge against price increases Oil price To permit operations Intermediate Stocks (WIP) Pipeline inventory To take advantage of quantity discounts

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 Inventory turnover Ratio of average cost of goods sold to average inventory investment. Days of inventory on hand

Effective Inventory Management A system to keep track of inventory (and S.O.) A reliable forecast of demand Knowledge of lead times (and variability) Reasonable estimates of Holding costs Ordering costs Shortage costs A classification system

Inventory Counting Systems Periodic System Physical count of items made at periodic intervals Small Retailers- checks and orders replenishment Perpetual Inventory System Keeps track of removals from inventory continuously, thus monitoring current levels of each item Reorder point Q Also requires periodic counting Errors, pilferage, spoliage Cost?

Inventory Counting Systems … Two-Bin System - Two containers of inventory; reorder when the first is empty 2nd cart has enough inventory for the lead time Order card Universal Bar Code - Bar code printed on a label that has information about the item to which it is attached

Key Inventory Terms Lead time: time interval between ordering and receiving the order Holding (carrying) costs: cost to carry an item in inventory for a length of time, usually a year Ordering costs: costs of ordering and receiving inventory Shortage costs: costs when demand exceeds supply

The Inventory Cycle- Figure 12.2 Profile of Inventory Level Over Time Q Usage rate Quantity on hand Reorder point Time Receive order Place order Receive order Place order Receive order Lead time

ABC Classification System Classifying inventory according to some measure of importance and allocating control efforts accordingly. A - very important B - mod. important C - least important Annual $ value of items A B C High Low Percentage of Items Example 1- P 549

Cycle Counting A physical count of items in inventory Cycle counting management How much accuracy is needed? When should cycle counting be performed? Who should do it?

Economic Order Quantity Models Economic order quantity (EOQ) model The order size that minimizes total annual cost Economic production model Quantity discount model

Total Cost* Annual carrying cost Annual ordering cost Total cost* = + Q 2 H D S + TC =

Cost Minimization Goal- Figure 12.4C The Total-Cost Curve is U-Shaped Annual Cost Ordering Costs Order Quantity (Q) QO (optimal order quantity) Minimum Total Cost

Only one product is involved Annual demand requirements known Demand is even throughout the year Lead time does not vary Each order is received in a single delivery There are no quantity discounts Assumptions of EOQ Model

Deriving the EOQ Using calculus, we take the derivative of the total cost function and set the derivative (slope) equal to zero and solve for Q. Minimum Total Cost The total cost curve reaches its minimum where the carrying and ordering costs are equal. Q 2 H D S =

Economic Production Quantity (EPQ) Production done in batches or lots Capacity to produce a part exceeds the part’s usage or demand rate Similar to EOQ Orders are received incrementally during production Assumptions Only one item is involved Annual demand is known Usage rate is constant Usage occurs continually Production rate is constant Lead time does not vary No quantity discounts

Economic Run Size We do not buy the product. We produce it. Total demand / year is D Demand / day or consumption rate is u Production rate is p / day

Instantaneous Replenishment Incremental Replenishment

EPQ: Incremental Replenishment (Production and Consumption) p-u Demand / day or consumption rate is u Production rate is p / day u × ( number of working days ) = D = Total demand per year

EPQ: Ordering Cost and Carrying Cost State Imax in terms of Q!

EPQ : Production & Consumption; rate & time How much do we produce each time? Q How long does it take to produce Q? d1 What is our production rate per day? p How long does it take to consume Q? d1 +d2 What is our consumption rate per day ? u p-u u I max d1 d2

Example- What is the optimal production size? A toy manufacturer Uses 48000 parts for one of its products. Consumption rate is uniform throughout the year. Working days are 240 / year. The firm can produce at a rate of 800 parts / day Carrying cost is $1 / part / year Setup cost for production run is $45 / setup

What is Run Time, What is Cycle Time Q0 using formula = 2400 u = 48000 /240 = 200 units/day p-u u I max d1 d2

What is the Optimal Total Cost

EPQ : Optimal Q

Reorder Point- ROP Reorder Point When the quantity on hand of an item drops to this amount, the item is reordered If setup time takes 2 days, at which level of inventory we should start setup? 2(200) = 400 200 ?

Yet Another Example A company has a yearly demand of 120,000 boxes of its product. The product can be produced at a rate of 2000 boxes per day. The shop operates 240 days per year. Assume that demand is uniform throughout the year. Setup cost is $8000 for a run, and holding cost is $10 per box per year. a) What is the demand rate per day b) What is the Economic Production Quantity (EPQ) c) What is the run time d) What is the maximum inventory e) What is the total cost of the system

Yet Another Example … =16000 What is the demand rate per day Demand per year is 120,000 there are 240 days per year Demand per day = 120000/240 = 500 u = D/240 = 500 b) What is the Economic Production Quantity (EPQ) =16000

Yet Another Example … c) What is the run time We produce 16000 units Our production rate is 2000 per day It takes 16000/2000 = 8 days d1 = EPQ/p = 8 days d) What is the maximum inventory We produce for 8 days. Each day we produce 2000 units and we consume 500 units of it. Therefore we add to our inventory at rate of 1500 per day for 8 days. That is Imax = 8(1500) = 12000 Imax = pd1 = 8(1500) = 12000

Yet Another Example … e) What is the total cost of the system

Including the Purchasing Cost Annual carrying cost Purchasing TC = + Q 2 H D S ordering PD Including the Purchasing Cost

Total Costs with Vs. Quantity Ordered EOQ TC with PD TC without PD PD Quantity Adding Purchasing cost doesn’t change EOQ

Total Cost with Constant Carrying Costs OC EOQ Quantity Total Cost TCa TCc TCb Decreasing Price CC a,b,c

Total Cost with Variable Carrying Costs Do the Math Ex 5, 6 Total Cost with Variable Carrying Costs

ROP with EOQ Ordering Safety Stock Service Level When to Reorder Safety Stock Stock that is held in excess of expected demand due to variable demand rate and/or lead time. Service Level Probability that demand will not exceed supply during lead time.

Determinants of the Reorder Point The rate of demand The lead time Demand and/or lead time variability Stockout risk (safety stock)

Safety Stock- Figure 12.12 Quantity Maximum probable demand LT Time Expected demand during lead time Maximum probable demand ROP Quantity Safety stock Safety stock reduces risk of stockout during lead time

Reorder Point- Figure 12.13 The ROP based on a normal See also: Fig 11.14 The ROP based on a normal Distribution of lead time demand Service level Risk of a stockout Probability of no stockout ROP Quantity Expected demand Safety stock z z-scale ROPs = Exp. Demand + z. σdLT

Shortage and Service Level Service level determines ROP E(n) = E(z) z σdLT E(n) = Expected number of short/cycle E(z) = Standardized number of units-short from table 11.3 σdLT = Standard deviation of lead time Example 10 @ Page 568

Fixed-Order-Interval Model Orders are placed at fixed time intervals Order quantity for next interval? Suppliers might encourage fixed intervals May require only periodic checks of inventory levels Risk of stockout Fill rate – the percentage of demand filled by the stock on hand

Calculations Ex 13

Fixed-Interval tradeoffs Benefits Tight control of inventory items Items from same supplier may yield savings in: Ordering Packing Shipping costs May be practical when inventories cannot be closely monitored Disadvantages Requires a larger safety stock Increases carrying cost Costs of periodic reviews

Single Period Model Model for ordering items with limited useful lives Perishables Shortage cost is generally the unrealized profits per unit Excess cost is the difference between purchase cost and salvage value of items left over at the end of a period 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

Optimal Stocking Level Service level = Cs Cs + Ce Cs = Shortage cost per unit Ce = Excess cost per unit Service Level So Quantity Ce Cs Balance point

Example 15 Stockout risk = 1.00 – 0.75 = 0.25 Ce = $0.20 per unit Cs = $0.60 per unit Service level = Cs/(Cs+Ce) = .6/(.6+.2) Service level = .75 Service Level = 75% Quantity Ce Cs Stockout risk = 1.00 – 0.75 = 0.25

Operations Strategy Too much inventory Wise strategy Tends to hide problems Easier to live with problems than to eliminate them Costly to maintain Wise strategy Reduce lot sizes Reduce safety stock

Learning Objectives Define the term inventory and list the major reasons for holding inventories; and list the main requirements for effective inventory management. Discuss the nature and importance of service inventories Discuss periodic and perpetual review systems. Discuss the objectives of inventory management. Describe the A-B-C approach and explain how it is useful.

Learning Objectives Describe the basic EOQ model and its assumptions and solve typical problems. Describe the economic production quantity model and solve typical problems. Describe the quantity discount model and solve typical problems. Describe reorder point models and solve typical problems. Describe situations in which the single-period model would be appropriate, and solve typical problems.