*Logistics and Supply Chain Management

Chapter 10Inventory ManagementLecturer: Ho Trung Thao (thao.hotrung@hoasen.edu.vn)

OutlineReasons for Holding StocksAggregate StockholdingsBuffering Supply and DemandTypes of Stock: Raw material, WIP, Finished goodsCost of Carrying Stock: Unit, Reorder, Holding, and Shortage CostEconomic Order Quantity (EOQ)Finding the order sizeFinding the time to place ordersSensitivity AnalysisWeakness of EOQ approachUncertain Demand and Safety StockPeriodic Review SystemsEffort of Stock ControlABC AnalysisVendor Manage Inventory*

REASONS FOR HOLDING STOCKQuestion: When and how much an organization should buy materials.

Ideally, materials move smoothly and continuously through a supply chain.

When materials stop moving they form stocks. All organizations hold stocks of some kind.

STOCKS: supplies of goods and materials that are held by an organization.

An INVENTORY: a list of things held in stock.*Aggregate Stockholdings

Buffering Supply and Demand Many organizations cannot reduce them. Ex: - Farmers grow one crop of hay a year, and then store it to feed animals throughout the year.

- A distiller stores whisky in barrels for at least three years before selling it.

- A video store buys copies of videos and keeps them in stock until people want to hire them.

These organizations do not want to eliminate stocks, but they want to control them properly.

Stocks give a buffer between variable and uncertain supply and demand.*

They allow operations to continue smoothly and avoid disruptions. To be more specific, stocks: act as a buffer between different parts of the supply chain allow for demands that are larger than expected, or at unexpected times allow for deliveries that are delayed or too small take advantage of price discounts on large orders allow the purchase of items when the price is low and expected to rise allow the purchase of items that are going out of production allow for seasonal operations make full loads and reduce transport costs give cover for emergencies can be profitable when inflation is high.*

Types of Stock Raw materials the materials, parts and components that have been delivered to an organization, but are not yet being used.

Work in process materials that have started, but not yet finished their journey through the production process. Finished goods goods that have finished the process and are waiting to be shipped out to customers.

Some stock items do not fall easily into these categories, and we can define two additional types:

Spare parts for machinery, equipment, and so on Consumables such as oil, fuel, paper, and so on.*

Types of stock (cont.)*

Independent Demand SystemDependent demand system: the demand for an item is found directly from a master schedule.

Independent demand system: the total demand for an item is made up of lots of separate demands that are not related to each other.

Ex: The overall demand for bread in a supermarket is made up of lots of demands from separate customers who act independently.

Independent demand systems control stocks by finding the best balance between various costs.*

Three basic questionsWhat items should we stock? When should we place an order? How much should we order? *

Unit Cost (U)Price charged by the suppliers for one unit of item, orTotal cost to organization of acquiring one unit$ / unitReorder cost (R)Cost of placing a routine order$ / order, $/setup

(Estimately, Reorder cost = the total annual cost of the purchasing dept. ) the number of orders it sends out

Holding cost (H)Cost of holding one unit of the item in stock for one period oftime$ / unit-periodShortage cost (SC)Cost of having a shortage and not being able to meet demandfrom stock$ / unit-periodNote: The total cost of holding stock is around 25% of its value a yearCosts of Carrying Stock

Example Janet is a purchasing clerk at Overton Travel Group. She earns 16,000 a year, with other employment costs of 3,000, and has a budget of 6,200 for telephone, communications, stationery and postage. In a typical month Janet places 100 orders. When goods arrive there is an inspection that costs about 15 an order. The cost of borrowing money is 9%, the obsolescence rate is 5% and insurance and other costs average 4%.

How can Overton estimate their reorder and holding costs?*

SolutionThe total number of orders a year:12mon.100order/mon.= 1200 orders/yr.

The reorder cost includes all costs that occur for an order: salary = 16,000/1200ord./yr = 13.33 an order employment costs = 3000/1200ord/yr = 2.50 an order expenses = 6200/1200ord./yr = 5.17 an order inspection = 15 an order So the reorder cost is 13.33 + 2.50 + 5.17 + 15 = 36 an order.

Holding costs include all costs that occur for holding stock: borrowing = 9% obsolescence = 5% insurance and taxes = 4% So the holding cost is 9 + 5 + 4 = 18% of inventory value a year.*

Costs of Carrying Stock (cont.)In practice, the most common costing is based on the amount paid and can use:

FIFO (first in, first out): assumes that stock is sold in the order it was bought, so the remaining stock is valued at the current replacement cost

LIFO (last in, first out): assumes that the latest stock is used first, so the remainder is valued at earlier acquisition costs

Average cost: uses a moving average cost over some periods.*Cost Flow Assumption

SolutionNo right answer to this, it depends on the conventions that we choose to use. FIFO assumes that the remaining units are the last that were bought, and the value of the last eight units is (226) + (324) + (322) = 190 LIFO assumes that the first units bought are still in stock, and the value of these first eight units is (621) + (219) = 164 Current replacement cost gives a value of (826) = 206 A three-month moving average gives a unit price of (22+24+26)/3 = 24, and a value of (824) = 192.*A company bought the following numbers of an item. In July it had 8 units in stock. What was the value of this stock?Month Jan Feb Mar Apr May Jun JulNumber bought 6 4 5 8 3 2 8Unit price 21 19 18 22 24 26

Example

ECONOMIC ORDER QUANTITY (EOQ)The EOQ: remains the best way of tackling a wide range of inventory problems.

Imagine a single item, held in stock to meet a constant demand of D per unit time. Assume that we know:unit cost (U)reorder cost (R)holding cost (H) no shortages are allowed.

The item is bought in batches from a supplier who delivers after a constant lead time (L).

Find the best order quantity (Q) and always place orders of this size. There is no point in carrying spare stock, so we time orders to arrive just as existing stock runs out. Then we get a series of stock cycles.*Finding the Order Size

Order quantity = Q (max. inventory level)Inventory (Stock) levelStock Cycle0Finding the Order Size (cont.)Time

Derivation of the EOQ

EOQ: the lot size or order size that minimizestotal annual inventory holding and ordering cost

Under basic EOQAmount enteringstock in cycle,QAmount leaving stockin cycle,DxT=Total cost per cycle=Unit costcomponentReorderCostcomponentHoldingCostcomponent++

At some point an order of size Q arrives. This is used at a constant rate, D, until no stock is left. We can find the total cost for the cycle (= unit cost + reorder cost + holding cost + shortage cost)No shortages are allowed, so we can ignore shortages cost, and the cost of buying the item is constant regardless of the ordering policy. The cost per unit time (Variable cost) isC = total reorder costs + total holding costs = RD/Q + HQ/2*Finding the Order Size (cont.)

Variation of Cost with Order SizesOptimal Order Quantity is when the Total Cost curve is at its lowest . This occurs when the Ordering Cost = Holding Cost

From the graph: the total holding cost rises linearly with order size the total reorder cost falls as the order quantity increases large infrequent orders give high total holding costs and low total reorder costs small frequent orders give low total holding costs and high total reorder costs adding the two costs gives a total cost curve that is an asymmetric U shape with a distinct minimum this minimum cost shows the optimal order size, the economic order quantity, EOQ.D = demandR = reorder costH = holding costEconomic order quantity Q: *Finding the Order Size (cont.)

ExampleJohn Pritchard buys stationery for Penwynn Motors. The demand for printed forms is constant at 20 boxes a month. Each box of forms costs 50, the cost of processing an order and arranging delivery is 60, and holding cost is 18 a box a year.

What are the economic order quantity, cycle length and costs?*

SolutionListing the values we know in consistent units:D = 20unit/mon. 12mon. = 240 units a yearU = 50 a unitR = 60 an orderH = 18 a unit a year. Substituting these values into the economic order quantity gives: = 40 units

Then the variable cost is:C = total reorder costs + total holding costs = RD/Q + HQ/2 = 60 240/40 + 18 40/2 = 360 + 360 = 720 a year

(You can see that the total reorder costs equal the total holding costs. This is always true if we order the economic order quantity, so we can simplify the calculation to twice the total holding cost or C = HQ = 18 40 = 720)

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Solution The fixed cost of buying boxes is the number of boxes bought a year, D, times the cost of each box, U. total cost = fixed cost + variable cost = UD + C = 50 240 + 720 = 12,720 a year

We buy 40 boxes at a time, and use 20 boxes a month, so the stock cycle length is 2 months. stock cycle length: T = Q/D T = Q/D = 40/240 = 1/6 years or 2 months

The best policy, with total costs of 12,720 a year, is to order 40 boxes of paper every 2 months.*

Finding the Time to Place Orders Lead time

When an organization buys materials, there is a lead time between placing the order and having the materials arrive in stock.

This is the time taken to prepare an order, send it to the supplier, allow the supplier to make or assemble the materials and prepare them for shipment, ship the goods back to the customer, allow the customer to receive and check the materials and put them into stock.

Depending on circumstances, this lead time can vary between a few minutes and months or even years.*

Suppose: the lead time, L: constant

the demand, D: constantPlace an order when the stock level falls to LD. This point is the reorder level (ROL).

Reorder level = lead time demand = lead time demand ROL = LD*Finding the Time to Place Orders (cont.)

SolutionListing the variables in consistent units:D= 20 units a weekR = 125 an orderH= 2 a unit a weekL = 2 weeksSubstituting these gives: = 50 units

Reorder level = lead time demand = LD = 2 20 = 40 unitsThe best policy is to place an order for 50 units whenever stock falls to 40 units.*Demand for an item is constant at 20 units a week, the reorder cost is 125 an order and holding cost is 2 an unit a week.

If suppliers guarantee delivery within 2 weeks, what is the best ordering policy for the item?Example

Reorder Level with Longer Lead Time

When lead time is longer than the stock cycleThere is always one order outstanding.Example:when it is time to place order B, there is one order, A outstanding and due to arrive before B.The stock on hand plus the outstanding order must be enough to last until B arrive or equal the lead time demandStock on handStock on order+=Lx DROLStock on order-=Lx D

n x T < L < (n+1) x TReorder Level with Longer Lead Time

When lead time is very long

Several orders are outstanding at anytime

When lead time is between n and n+1 cycle length

There are n ordersoutstandingROLStock on order

n x Qo-

-Lead time demand

Lx D=

=

ExampleDemand for an item is 5200 units a year and the EOQ is 250 units. If the lead time is 2 weeks, then ROL = (5200 / 52) 2 = 200 units.This means that as soon as the stock level falls to 200 units an order equal to EOQ = 250 units should be placed. This rule of ordering is applicable only if the lead time is shorter than the stock cycle. Here, the stock cycle is T = Q*/d = 250/100 = 2.5 weeks.

If the lead time is 3 weeks, then the ROL = 100 3 = 300 units. Since EOQ = 250 units, therefore stock level varies between zero and 250 units. Thus lead time demand of 300 units suggests that there should be one outstanding order. In such cases, an order is placed whenLead time demand = stock on hand + stock on order or ROL = Lead time demand stock on handIn general, an ordering policy is stated as: when lead time is between n T and (n+1) T, order an amount Q* whenever stock on hand falls to L D n Q*, where n is number of stock cycle and lead time exceeds cycle time T. In this example, lead time of 3 weeks is between 1 and 2 stock cycles, so n = 1, thenROL = L D n Q*= 3x100 1 250 = 50 units.i.e each time the stock on hand declines to 50 units, an order of 250 units is placed.*ROL= 50EOQ= 250ROL= 50EOQ= 250

Sensitivity Analysis Cheng Tau Hang notices that demand for an item his company supplies is constant at 500 units a month. Unit cost is $100 and shortage costs are known to be very high.

The purchasing department sends out an average of 3000 orders ayear, and their total operating costs are $180,000. Any stocks have financing charges of 15%, warehouse charges of 7% and other overheads of 8% a year.

The lead time is constant at one week.

Find a good ordering policy for the item.

What is the reorder level if the lead time increases to 3 weeks?

What range of order size keeps variable costs within 10% of optimal?

What is the variable cost if orders are placed for 200 units at a time?Solution:Text book : page 264 + 265*

Listing the values we know and making sure the units are consistent:D = 500units/ mon. 12mon./ yr. = 6000 units a yearU = $100 a unitR = annual cost of purchasing department = 180,000 = $60 an order number of orders a year 3000H = (15% + 7% + 8%) of unit cost a year = (0.3) U = $30 a unit a yearL = 1 week

Find the best ordering policy by substituting these values into the equations: order quantity, Q = 2RD/H = 2x60x600/30 = 154.9 units cycle length, T = Q/D = 154.9/6000 = 0.026 years or 1.3 weeks variable cost a year C = HQ = 30 154.9 = $4647 a year total cost a year = UD + C = 100 6000 + 4647 = $604,647 a year. The lead time is less than the stock cycle, so: Reorder level = LD = 1wk 6000unit a yr./52wk/yr. = 115.4 units The optimal policy is to order 154.9 units whenever stock falls to 115.4 units. The lead time is greater than the stock cycle (L = 3 weeks), there will be 2 orders outstanding when it is time to place another. Then:( nT < L < (n+1)T n =1 1x1.3 < 3 > 2 x 1.3n= 2 2x1.3 < 3 < 3x1.3. Hence n=2) Reorder level = lead time demand stock on order = LD 2Q = 3wk 6000units a yr. / 52wk/yr 2 154.9units = 36.4 units. To keep variable costs within 10% of optimal, the quantity ordered can vary between 64% and 156% of the economic order quantity, which is 99.1 units to 241.6 units. If fixed order sizes of 200 units are used the variable costs are: C = total reorder costs + total holding costs = RD / Q + HQ / 2 = 60 6000 / 200 + 30 200 / 2 = $4800 a yearWe are not using the economic order quantity, so the variable cost is higher and the total reorder costs no longer equal the total holding costs.

Advantages of this approach easy to understand and use giving good guidelines for order size finding other values (like costs and cycle lengths) easy to implement and automate encouraging stability easy to extend, allowing for different circumstances.

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Weaknesses takes a simplified view of inventory systems assumes demand is known and constant assumes all costs are known and fixed assumes a constant lead time and no uncertainty in supplies gives awkward order sizes at varying times assumes each item is independent of others does not encourage improvement, in the way that JIT does.

We can overcome some of these problems by developing more complicated models.*

UNCERTAIN DEMAND & SAFETY STOCKDemand varies more widely. We will illustrate one approach where the demand is normally distributed. Safety stocks: additional stocks to add a margin of safety. REORDER LEVEL = lead time demand + safety stock = LD + SS*

Service level: the probability that a demand is met directly from stock.

Cycle-service level: Service level as the probability of not running out of

stock in a stock cycle.

Suppose that:

Demand for an item is normally distributed with a mean of D per unit time

and standard deviation of . If the lead time is constant at L, the lead-time

demand is normally distributed with mean of LD.

The lead-time demand has a variance of 2L and standard deviation of L. demand in a single period has mean D and variance 2,

demand in L periods has mean LD and variance L2.

when lead-time demand is normally distributed the safety stock is:

SAFETY STOCK = Z standard deviation of lead-time demand = ZL*UNCERTAIN DEMAND & SAFETY STOCK

ExampleAssociated Kitchen Furnishings runs a retail shop to sell a range of kitchen cabinets.

The demand for cabinets is normally distributed with a mean of 200 units a week and a standard deviation of 40 units.

The reorder cost, including delivery, is 200, holding cost is 6 per unit a year and lead time is fixed at 3 weeks.

Describe an ordering policy that gives the shop a 95% cycle-service level. What is the cost of holding the safety stock in this case? How much does the cost rise if the service level is set at 97%?Solution:Text book, page 269*

Listing the values we know: D = 200 units a week = 10,400 units a year H = 6 a unit a year = 40 units L = 3 weeksR = 200 an order

Substituting these values gives: Q = (2RD/H) = (2 200 200 52/6) = 833 (to the nearest integer) Reorder level = LD + safety stock = 600 + safety stock

For a 95% service level Z = 1.64 standard deviations from the mean. Then: safety stock = ZL = 1.64 40 3 = 114 (to the nearest integer) The best policy is to order 833 units whenever stock falls to 600 + 114 = 714 units. On average orders will arrive when there are 114 units left. The holding cost of safety stock: = safety stock holding cost = 114 6 = 684 a year

If the service level is set at 97%, Z becomes 1.88 and: safety stock = ZL = 1.88 40 3 = 130The cost of holding this is:= safety stock holding cost = 130 6 = 780 a yearSolution

PERIODIC REVIEW SYSTEMSEOQ analysis uses a fixed order quantity for purchases, so an order of fixed size is placed whenever stock falls to a certain level.

Periodic review approach: orders varying amounts at regular intervals.

Question: How long should the interval between orders be?What is the target stock level?

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PERIODIC REVIEW SYSTEMS (cont.)Assume that the demand for each period is normally distributed with a mean D and standard deviation , and that both the order period (T) and lead time (L) are fixed.

target stock level = mean demand over (T+L) + safety stock = D(T+L) + Z(T+L)order quantity = target stock level stock on hand

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Computing Safety StockOrder-cycle service level is the probability that demand during lead time will not exceed on-hand inventoryA 95% service level means the stockout risk is 5%, and has a z-score Z95=1.645Area left of y-axis = .50

http://www.baskent.edu.tr/~kilterNormal distribution service levels and unit normal loss function

ExampleDemand for an item has a mean of 200 units a week and standard deviation of 40 units.Stock is checked every four weeks and lead time is constant at two weeks. Describe a policy that will give a 95% service level. If the holding cost is 2 a unit a week, what is the cost of the safety stock with this policy?

What is the effect of a 98% service level?Solution: Text book, page 273 *

Solution Listing the values given:D = 200 units; T = 4 weeks = 40 units; L = 2 weeksH = 2 a unit a week

For a 95% service level, Z is 1.64 (from a standard package or tables). Then:

safety stock = Z(T+L) = 1.64 40 6 = 161units (to the nearest integer) target stock level = D(T+L) + safety stock = 200 6 + 161 = 1361units.

When it is time to place an order, the policy is to find the stock on hand, and place an order for:

order size = target stock level stock on hand = 1361 stock on hand.If, for example, there are 200 units in stock, we place an order for 1361 200 = 1161 units. The safety stock is not normally used, so the holding cost: = safety stock holding cost = 161 2 = 322 a week.

Solution ( cont.)

If the service level is increased to 98%, Z = 2.05. Then: safety stock = Z(T+L) = 2.05 40 6 = 201 units target stock level = D(T+L) + safety stock = 2006 + 201 = 1401 units cost of the safety stock is safety stock holding cost = 201unit 2/unit/wk = 402 a week.

EFFORT OF STOCK CONTROLABC analysis

Vendor managed inventory

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ABC AnalysisAn ABC analysis puts items into categories that show the amount of effort worth spending on inventory control. This is a standard Pareto analysis or rule of 80/20, which suggests that 20% of inventory items need 80% of the attention, while the remaining 80% of items need only 20% of the attention. ABC analyses define:

A items as expensive and needing special care B items as ordinary ones needing standard care C items as cheap and needing little care.*Category % of items Cumulative % of use Cumulative % of % of items by value use by value A 10 10 70 70 B 30 40 20 90 C 60 100 10 100

ABC Analysis (cont.)*

ExampleSorting

ExampleSorting330/500330+50

Vendor Managed Inventory-Have another organization look after the stock control.

The most common arrangement of this kind is vendor managed inventory.

-With vendor managed inventory, the wholesaler controls the stocks, and

sends more along when they are needed. The benefits: the supplier can co-ordinate stocks over a wider area, use

optimal inventory policies, organize transport more efficiently, increase

integration in the supply chain, collect more information about demand

patterns, and give a consistent customer service*

Homework1,2,3,4,5,6,7,8 page 280

EOQ sensitivityComparing the minimum variable cost, VCo, from ordering batches of EOQ size Qo, with the variable cost, VC, of ordering any other quantity, Q.We know that:VCo = HQo and VC = RD/Q + HQ/2If we take the ratio of these we get:VC = RD + HQ VCo QHQo 2HQo = RDxQ0 + HQ QHQ2o 2HQo

Substitute We have

*Chapter 4 - Control MaterialINV. Counting systems:Periodic Review Sys.: Physical count of items made at periodic intervals

*In practice, there are always delays andStocks are formed whenever the organization's inputs or outputs are not used at the time they become available.In brief:Difference Between Inventory and Stock Stock and inventory are used interchangeably which is not correct Stock pertains to goods only, both in terms of quantity as well as its monetary value Inventory is the sum of stock and assets that include plant and machinery stock is what you have in the store inventory is when you count the stock

The terms stock and inventory are used interchangeably, but in actuality, the terms have two separate meanings. Although the difference is rather subtle, from an accounting standpoint, it's very important to your small business. In order to give an accurate accounting of items the business owns, learn the difference between the two terms and use them correctly.InventoryInventory includes a small business's finished products, as well as the raw materials used to make the products, the machinery used to produce the products and the building in which the products are made. In other words, anything that goes into producing the items sold by your business is part of its inventory.StockStock is the finished product that is sold by the business. In some cases, stock is also raw materials, if the business also sells those products to its customers. For example, a car dealership's stock includes cars, but also can include tires, engine parts or other car accessories.Differences Between Inventory and StockWhile stock deals with products that are sold as part of the business's daily operation, inventory includes sale products and the goods and materials used to produce them. For example, the cars, car parts and accessories are sold during normal business practices, but the machines that run diagnostic tests on cars or the car lot itself are not. Inventory takes in account all of the assets a business uses to produce the goods it sells and determines the sale price for the stock. The stock determines the amount of revenue a business generates. The more stock that is sold, the higher the revenues.*Despite the clear trend towards lower stocks,*****Fundamental Inventory Decision1.this questions is a matter of good housekeeping, simply avoiding stock that is not needed. 2.This depends on the inventory control system used, type of demand (high or low, steady or erratic, known exactly or estimated), value of the item, lead time between placing an order and receiving it into stock, supplier reliability, and a number of other factors.3. Large, infrequent orders give high average stock levels, but low costs for placing and administering orders: small, frequent orders give low average stocks, but high costs of placing and administering orders.

*****The economic order quantity (EOQ) model is one of the oldest and most commonly known inventory control techniquesIt dates from a 1915 publication by Ford W. HarrisIt is still used by a large number of organizations todayIt is easy to use but has a number of important assumptions

*The objective is to minimize total costsThe relevant costs are the ordering and carrying/holding costs, all other costs are constant. Thus, by minimizing the sum of the ordering and carrying costs, we are also minimizing the total costsThe annual ordering cost is the number of orders per year times the cost of placing each orderAs the inventory level changes daily, use the average inventory level to determine annual holding or carrying costThe annual carrying cost equals the average inventory times the inventory carrying cost per unit per yearThe maximum inventory is Q and the average inventory is Q/2.

************Higher safety stocks obviously give a greater cushion against unexpectedly high demand, and better customer service.**There are several ways of allocating reasonable effort to stock control. One uses an ABC analysis; another outsources part of the function, perhaps using vendor managed inventory.

The idea is to focus resources on the critical few and not on the trivial many.is a method for determining level of control and frequency of review of inventory items