CP3 Independent Demand Inventory

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MAN 3520 Fall 2012

CP3 Independent Demand Inventory: Page 1 of 30

FUNDAMENTALS OF INVENTORY

Within most organizations inventory exists in a variety of places, and in a variety of forms, and

for a variety of reasons. Although these inventories represent a substantial cost investment (insome cases as much as 50% of total capital invested), they are necessary to provide a desiredlevel of service to customers. The objective of inventory management is to strike a balancebetween inventory investment and customer service.


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FUNCTIONS OF INVENTORY

Inventory exists for a variety of reasons (i.e., serves several functions) within organizations.

1. Decoupling stages in the production process. Inventory between successive stages of atransformation process make each stage less dependent upon the output of the prior stage.If there is an interruption in output at one stage, succeeding stages may be able tocontinue operation by feeding off the inventory held between stages. This applies both tointernal operations and to external linkages with suppliers. This inventory is calledbuffering inventory.

2. Decoupling from demand fluctuations. This manifests itself in both seasonal inventoryand safety stock. When there is predictable variation in demand throughout the year, andwhen an organization does not have the capacity to produce peak demand when it isdemanded, the organization may have to produce and store finished products in advance

of that demand. This inventory is called seasonal inventory. When there is unpredictable(i.e. erratic and random) short term variation in demand, the organization may have tomaintain additional inventory to cover the unpredictable spikes in demand. Thisinventory is called safety stock.

3. Volume purchasing.Purchases in large quantities may result in reduced purchase priceand/or reduced delivery cost. Such incentives often lead organizations to acquire moreinventory than is immediately needed. This inventory is called volume discountinventory.

4. Hedge against possible future events. In many instances organizations perceive thatthere may be a disruptive economic or environmental event in the not too distant future.Inflation may suggest that there will soon be a price increase in some supply. Labor

negotiations may suggest that an impending trucker strike might affect delivery ofsupplies. Weather conditions indicate that a brewing tropical storm might affectshipments of supplies. In circumstances like these organizations may choose to ordermore inventory than is immediately needed to provide protection in the event that any ofthese situations actually occur. This inventory is called hedge inventory.


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TYPES OF INVENTORY

To better accommodate the functions of inventory, organizations maintain four types of

inventories.

1. Raw material inventory. Materials that are usually purchased and have not yet enteredthe transformation process.

2. Work-in-process (WIP) inventory. Materials and components that have undergone somechange but have not yet advanced to the stage of completed product.

3. Finished-goods inventory. Completed products awaiting shipment.4. Maintenance/repair/operating (MRO) inventory. Supplies necessary to keep machinery,

processes, facilities, and office operations running. These items do not get absorbed intothe products being made, but are crucial to the smooth operation of the organization.They range from such things as lubricating oil for machines and janitorial cleaning

products, to printer toner cartridges and other office supplies.


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BASIC INVENTORY DECISIONS

There are two basic decisions that must be made for every item that is maintained in inventory.

These decisions have to do with the timing of orders for the item and the size of orders for theitem. We will be examining several models and philosophies related to these two decisions. Asnoted on page 1, the objective of these inventory management models is to strike a balancebetween inventory investment and customer service.

How Much?

Lot sizing decision

Determination of thequantity to be ordered.

When?

Lot timing decision

Determination of thetiming for the orders

Basic Inventory Decisions


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INDEPENDENT VS. DEPENDENT DEMAND INVENTORY

Before examining specific inventory models, an important distinction must be made. Some

inventory items can be classified as independent demand items, and some can be classified asdependent demand items. We need to make the timing and sizing decisions for all inventoryitems, but we will find that the manner in which we make these decisions will differ dependingupon whether the item has independent demand or dependent demand.

Independent demand inventory item: Inventory item whose demand is not related to (ordependent upon) some higher level item. Demand for such items is usually thought of asforecasted demand. Independent demand inventory items are usually thought of as finishedproducts.

Dependent demand inventory item: Inventory item whose demand is related to (or dependent

upon) some higher level item. Demand for such items is usually thought of as derived demand.Dependent demand inventory items are usually thought of as the materials, parts, components,and assemblies that make up the finished product.


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RELEVANT INVENTORY COSTS

Relevant Inventory Costs

Item

Costs

Holding

Costs

Ordering/Setup

Costs

Shortage

CostsDirect cost forgetting an item.Purchase cost foroutside orders,manufacturing costfor internal orders.

Costs associatedwith carrying itemsin inventory. Storageand other relatedcosts.

Fixed costsassociated with

placing an order(either an orderingcost for outsideorders, or a setupcost for internalorders).

Costs associatedwith not havingenough inventory tomeet demand.


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BEHAVIOR OF COSTS FOR DIFFERENT INVENTORY DECISIONS

When assessing the cost effectiveness of an inventory policy, it is helpful to measure the total

inventory costs that will be incurred during some reference period of time. Most frequently, thattime interval used for comparing costs is one year. Over that span of time, there will be a certainneed, or demand, or requirement for each inventory item. In that context, the following describeshow the annual costs in each of the four categories will vary with changes in the inventory lotsizing decision.

Item costs: How the per unit item cost is measured depends upon whether the item is one that isobtained from an external source of supply, or is one that is manufactured internally. For itemsthat are ordered from external sources, the per unit item cost is predominantly the purchase pricepaid for the item. On some occasions this cost may also include some additional charges, likeinbound transportation cost, duties, or insurance. For items that are obtained from internal

sources, the per unit item cost is composed of the labor and material costs that went into itsproduction, and any factory overhead that might be allocated to the item. In many instances theitem cost is a constant, and is not affected by the lot sizing decision. In those cases, the totalannual item cost will be unaffected by the order size. Regardless of the order size (which impactshow many times we choose to order that item over the course of the year), our total annualacquisitions will equal the total annual need. Acquiring that total number of units at the constantcost per unit will yield the same total annual cost. (This situation would be somewhat different ifwe introduced the possibility of quantity discounts. We will consider that later.)

Cost

Lot Size (how much decision)

Total Annual Item Cost (assumesno quantity discounts)


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INVENTORY COST BEHAVIOR (CONTINUED)

Holding costs (also called carrying costs): Any items that are held in inventory will incur a

cost for their storage. This cost will be comprised of a variety of components. One obvious costwould be the cost of the storage facility (warehouse space charges and utility charges, cost ofmaterial handlers and material handling equipment in the warehouse). In addition to that, thereare some other, more subtle expenses that add to the holding cost. These include such things asinsurance on the held inventory; taxes on the held inventory; damage to, theft of, deterioration of,or obsolescence of the held items, and opportunity costs associated with having money tied up ininventory. The order size decision impacts the average level of inventory that must be carried. Ifsmaller quantities are ordered, on average there will be fewer units being held in inventory,resulting in lower annual inventory holding costs. If larger quantities are ordered, on averagethere will be more units being held in inventory, resulting in higher annual inventory holdingcosts.

Total Annual Holding Cost

Cost



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Ordering (or setup) costs: Any time inventory items are ordered, there is a fixed cost

associated with placing that order. When items are ordered from an outside source of supply, thatcost reflects the cost of the clerical work to prepare, release, monitor, and receive the order. Thiscost is considered to be constant regardless of the size of the order. When items are to bemanufactured internally, the order cost reflects the setup costs necessary to prepare theequipment for the manufacture of that order. Once again, this cost is constant regardless of howmany items are eventually manufactured in the batch. If one increases the size of the orders for aparticular inventory item, fewer of those orders will have to be placed during the course of theyear, hence the total annual cost of placing orders will decline.

Cost


Total Annual Ordering Cost


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Shortage costs: Companies incur shortage costs whenever demand for an item exceeds the

available inventory. These shortage costs can manifest themselves in the form of lost sales, lossof good will, customer irritation, backorder and expediting charges, etc. Companies are lesslikely to experience shortages if they have high levels of inventory, and are more likely toexperience shortages if they have low levels of inventory. The order size decision directlyimpacts the average level of inventory. Larger orders mean more items are being acquired thanare immediately needed, so the excess will go into inventory. Hence, smaller order quantitieslead to lower levels of inventory, and correspondingly a higher likelihood of shortages and theirassociated shortage costs. Larger order quantities lead to higher levels of inventory, andcorrespondingly a lower likelihood of shortages and their associated costs. The bottom line isthis: larger order sizes will lead to lower annual shortage costs.

Cost


Total Annual Shortage Cost


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All Four Cost Categories Combined: When all four inventory cost categories are

superimposed on the same graph, we obtain the following (somewhat cluttered) picture whichsuggests that there is one best answer to the how much decision. The quantity that should beordered is the lot size that corresponds to the lowest point on the total annual cost curve. Thisquantity is referred to as the economic order quantity, or EOQ.

AnnualShortage Cost

Annual Item Cost

AnnualHolding Cost

Total Annual Cost

AnnualOrdering Cost

Cost



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BASIC ECONOMIC ORDER QUANTITY (EOQ) MODEL

The EOQ model is a technique for determining the best answers to the how much and when

questions. It is based on the premise that there is an optimal order size that will yield the lowestpossible value of the total inventory cost. There are several assumptions regarding the behaviorof the inventory item that are central to the development of the model

EOQ assumptions:

1. Demand for the item is known and constant.2. Lead time is known and constant. (Lead time is the amount of time that elapses between

when the order is placed and when it is received.)3. When an order is received, all the items ordered arrive at once (instantaneous

replenishment).

4. The cost of all units ordered is the same, regardless of the quantity ordered (no quantitydiscounts).

5. Ordering costs are known and constant (the cost to place an order is always the same,regardless of the quantity ordered).

6. Since there is certainty with respect to the demand rate and the lead time, orders can betimed to arrive just when we would have run out. Consequently the model assumes thatthere will be no shortages.

Based on the above assumptions, there are only two costs that will vary with changes in the orderquantity, (1) the total annual ordering cost and (2) the total annual holding cost. Shortage costcan be ignored because of assumption 6. Furthermore, since the cost per unit of all items ordered

is the same, the total annual item cost will be a constant and will not be affected by the orderquantity. Inventory levels will fluctuate over time as in the following graph:

EOQ symbols:

D = annual demand (units per year)S = cost per order (dollars per order)H = holding cost per unit per year (dollars to carry one unit in inventory for one year)Q = order quantity

Q = Order SizeQ QQ

Time

Q/2

InventoryLevel


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CLASSIC ECONOMIC ORDER QUANTITY (EOQ) MODEL

We saw on the previous page that the only costs that need to be considered for the EOQ model

are the total annual ordering costs and the total annual holding costs. These can be quantified asfollows:

Annual Ordering Cost

The annual cost of ordering is simply the number of orders placed per year times the cost ofplacing an order. The number of orders placed per year is a function of the order size. Biggerorders means fewer orders per year, while smaller orders means more orders per year. In general,the number of orders placed per year will be the total annual demand divided by the size of theorders. In short,

Total Annual Ordering Cost = (D/Q)S

Annual Holding Cost

The annual cost of holding inventory is a bit trickier. If there was a constant level of inventory inthe warehouse throughout the year, we could simply multiply that constant inventory level by thecost to carry a unit in inventory for a year. Unfortunately the inventory level is not constantthroughout the year, but is instead constantly changing. It is at its maximum value (which is theorder quantity, Q) when a new batch arrives, then steadily declines to zero. Just when thatinventory is depleted, a new order is received, thereby immediately sending the inventory level

back to its maximum value (Q). This pattern continues throughout, with the inventory levelfluctuating between Q and zero. To get a handle on the holding cost we are incurring, we can usethe average inventory level throughout the year (which is Q/2). The cost of carrying thosefluctuating inventory levels is equivalent to the cost that would be incurred if we had maintainedthat average inventory level continuously and steadily throughout the year. That cost would havebeen equal to the average inventory level times the cost to carry a unit in inventory for a year. Inshort,

Total Annual Holding Cost = (Q/2)H

Total Annual Cost

The total annual relevant inventory cost would be the sum of the annual ordering cost and annualholding cost, or

TC = (D/Q)S + (Q/2)H

This is the annual inventory cost associated with any order size, Q.


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CLASSIC ECONOMIC ORDER QUANTITY (EOQ) MODEL

At this point we are not interested in any old Q value. We want to find the optimal Q (the EOQ,

which is the order size that results in the lowest annual cost). This can be found using a littlecalculus (take a derivative of the total cost equation with respect to Q, set this equal to zero, thensolve for Q). For those whose calculus is a little rusty, there is another option. The uniquecharacteristics of the ordering cost line and the holding cost line on a graph are such that theoptimal order size will occur where the annual ordering cost is equal to the annual holding cost.

EOQ occurs when:

(D/Q)S = (Q/2)H

a little algebra clean-up on this equation yields the following:Q2 = (2DS)/H

and finally______

Q* = 2DS/H

(Q* represents the optimal value for Q; this is what we call the EOQ)

Economic Order Quantity (EOQ)

AnnualHolding Cost

Total Annual Cost

AnnualOrdering Cost

Cost



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EOQ ILLUSTRATION

Given the following data for an inventory scenario whose characteristics fit the assumptions ofthe basic EOQ model:

D = 15,000 units per yearS = $3 per orderH = $1 per unit per yearLT = Replenishment lead time = 2 daysAssume we have 300 operating days per year

Find the following:1. Average daily demand2. EOQ3. Number of orders placed per year

4. Total annual ordering cost5. Total annual holding cost6. Time between orders7. Reorder point (in units)8. Average inventory level

Answers:1. Average daily demand

15,000 units/yr 300 days/yr = 50 units per day______ ______________

2. EOQ = 2DS/H = (2)(15,000)(3)/(1) = 300 units/order

3. Number of orders placed per yearD/Q = (15,000 units/yr)/(300 units/order) = 50 orders/yr

4. Total annual ordering cost(D/Q)(S) = [(15,000units/yr)/(300 units/order)]($3/order) = $150/yr

5. Total annual holding cost(Q/2)H = [(300 units/order/2)]($1/unit/yr) = $150/yr

6. Time between orders

(Q/d) = (300 units/order)/(50 units/day) = 6 days/order[or, 300days/yr50 orders/yr = 6 days/order]

7. Reorder point (in units)ROP = (daily demand)(Lead time) = (50 units/day)(2 days) = 100 units

8. Average inventory levelQ/2 = 300 units/2 = 150 units


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OBSERVATIONS ABOUT OUR EOQ ILLUSTRATION

Results of computations

EOQ = 300 unitsNumber of orders placed per year = 50Average inventory level = 150 unitsAnnual ordering cost = $150Annual holding cost = $150Time between the placement of orders = 6 days

Observation #1: Watch the inventory level instead of the calendar for when decision

We discovered that our order quantity of 300 units would lead to a replenishment every 6 days.We projected that we would run out on days 6, 12, 18, 24, 30, 36, etc. With a 2 day lead time,

we were smart enough to order 2 days in advance of when we would run out, which had usplacing orders on days 4, 10, 16, 22, 28, 34, etc. We only have to watch the calendar to keeptrack of when those order instants arise so that we can place the orders.

An alternative to watching the calendar would be to watch the inventory levels. Recall that theaverage daily demand for this item is 50 units per day. This means that at the moment we placean order, we have just enough inventory to cover the demand that will occur during the 2 daylead time. The demand during the 2 day lead time is 2 days x 50 units per day = 100 units. So, allwe have to do is keep our eyes on our inventory level, and when it reaches 100 units, that is thesignal that it is time to reorder. This level of inventory that triggers a reorder is called the reorderpoint (R).

EOQ = 300

100ROP

Inventory Level

Time


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OBSERVATIONS ABOUT OUR EOQ ILLUSTRATION

Observation #2: Model is robust (insensitive to errors in estimates for input data)

We estimated our holding cost to be $1/unit/yr when we made our EOQ calculation. Suppose thisestimate was in error, and the actual holding cost that will be incurred is $2/unit/yr (an error of100%!). If we had been aware of this true holding cost, and had used $2/unit/yr in our EQQcalculation, we would have determined the EOQ to be 212 units, and the ordering cost andholding cost would have each been $212, for a total annual cost of $424 (you can practice theapplication of the model to confirm these numbers on your own).

But, unfortunately we were not aware that the holding cost would be $2/unit/yr, so we made ourEOQ calculation using the incorrect $1/unit/yr. That calculation had us ordering 300 units eachtime we placed an order. With this order size, the true cost we will incur is as follows:

Ordering cost: (D/Q)S = (15,000 units/yr/300 units/order)($3/order) = $150Holding cost: (Q/2)H = (300 units/order/2)($2/unit/yr) = $300Total annual cost = $150 + $300 = $450

In summary, we could have been incurring an annual cost of $424 if we had better informationabout the holding cost, and were ordering the correct EOQ of 212 units. But, we used the wrongholding cost in our model (we were off by 100%), ended up ordering 300 units every time weordered, and incurred an annual cost of $450.

Notice that the cost we are incurring ($450) is a little more than 6% higher than the absolute

minimum cost ($424) that we might have incurred. Not bad. We made a 100% error on the inputside, but our results are only about 6% worse than they could have been. That is because the totalcost line on our cost graph is relatively flat in the vicinity of the EOQ. You can drift to the rightor left of the optimal order size and find that the resulting cost doesnt rise substantially. This iswhat is meant by the model being robust (or insensitive to errors).


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IMPACT OF CHANGING ASSUMPTIONS ON MODEL DEVELOPMENT

Our focus has been on the basic EOQ model. That is just one of dozens of inventory models for

independent demand items. The basic EOQ model was derived from a set of underlyingassumptions. If any of those assumptions do not fit a particular situation, then one must turn to adifferent model. Each of those available models is predicated upon a different set of underlyingassumptions. Some of the more popular ones (and ones described in the textbook) aresummarized below. We will not be expected to be knowledgeable about or work with any ofthese model extensions.

Economic Production Quantity (EPQ) Model: When replenishment items come from insidesources, the entire batch is usually not received all at once (instantaneous replenishment), butinstead is gradually received as a production batch is run (continuous replenishment). The patternof inventory level fluctuations over time changes, resulting in a slightly different quantitative

model for the optimal lot size.

Quantity Discount Model: When the supplier is willing to offer a lower price if large quantitiesof an item are ordered, the total annual purchase cost line will no longer be horizontal, but willinstead have step decreases in it. This will lead to a total cost curve that has breaks in itscontinuity (step changes) resulting in a slightly different model for determining the optimal ordersize.

Controlled Backorder Model (not mentioned in the book): In some instances it might bebeneficial to have shortages. If the backorder cost of a shortage is not very high, but the cost ofcarrying inventory is relative high, it may be more cost effective to incur some back orders on

each order cycle (the saw tooth graph dips below the horizontal axis on each order cycle). Thismeans that there will be less inventory being carried on average (resulting in lower holdingcosts) and some shortages that will incur some cost. How low below the horizontal axis thisgraph dips is a function of the relative values of the cost of holding inventory and the cost ofincurring a shortage.

Single-Period Inventory Model: Sometimes a unique situation that arises is one in which therewill be demand for an item in only one period, so the challenge is to determine the order size(stock size) that will best accommodate the anticipated (and uncertain) demand. Any itemsstocked in excess of demand will be scrapped. Any demand in excess of what has been stockedwill represent a missed opportunity for more profit. (This problem is sometimes referred to as the

newsboy problem, or the Christmas tree problem.)

These are but a few of the many variations to the basic EOQ model that are in existence. They allare designed to provide optimal answers to the how much and when questions. Choice of amodel should be dictated by the characteristics of the inventory situation that you are facing.


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DEMAND VARIABILITY AND UNCERTAINTY

The basic EOQ model assumes that demand rate is constant and predictable. As a result wealways knew when we were going to run out of inventory, so we could always reorder in a

timely fashion so that the new replenishment order would be received just when we ran out ofinventory.

In reality demand rates are rarely constant and rarely completely predictable. It is more likelythat demand rates will vary from day to day, and there will be uncertainty about what thosedemand rates will be at any one time. Consequently, there is a possibility that we may run out ofinventory before a replenishment order arrives. To prevent a shortage situation organizationsmust rely on safety stock.


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ILLUSTRATION OF SAFETY STOCK DETERMINATION

Data:

Average daily demand = 50 units per dayOperating year contains 300 days of operation (D = 15,000 units per year)Ordering cost S = $3 per orderHolding cost H = $1 per unit per yearLead time = 1 day

Computations:

EOQ (from EOQ formula) = 300 units per orderResulting number of orders per year = 50 orders per yearReorder point = 50 units (the average number of units demanded during the 1 day lead time)

Additional Data:Demand is not always a constant 50 units per day. There is variability in daily demand accordingto the following table of demands and probabilities:

Daily Demand 10 20 30 40 50 60 70 80 90Probability .01 .04 .05 .2 .4 .2 .05 .04 .01

Cumulative Probability .01 .05 .10 .30 .70 .90 .95 .99 1.00

LTLT

Time

ReorderPoint, 50

Inventory Level

300 300


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The graph above suggests that if you waited until you had 50 units left in inventory beforeplacing an order for 300 more units, you would be O.K. if the demand during the 1 day lead timewas 10, 20, 30, 40, or 50. However, if the demand during the 1 day lead time was 60, 70, 80, or90 you would have had a shortage. The size of the shortage would depend upon how many units

were demanded during the lead time, but the maximum possible shortage would have been 40units (if demand was the largest possible value of 90).

You can prevent shortages by providing safety stock when there is uncertainty in demand.(Safety stock can be viewed as a cushion placed at the bottom of the saw tooth graph ofinventory fluctuations over time.) If you wanted to guarantee that you would never have ashortage in this situation, you would need 40 units of safety stock at the bottom of the graph to"dip into" if demand spiked to higher than average values. But, adding 40 units of safety stockreally means that you have elevated your reorder point. You are not waiting until there are only50 units in inventory to place your order. You are ordering when there are 90 units in inventory.And, of course, 90 units are sufficient to cover the worst case scenario for this problem. Thegraph below illustrates the impact of 40 units of safety stock maintained in the system.

SafetyStock, 40 LTLT

Time

OriginalReorderPoint, 50

Inventory Level

300 300


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HOW MUCH SAFETY STOCK IS APPROPRIATE?

Service level: The probability that demand during lead time will not exceed the inventory on

hand when the order is placed.

In the previous illustration, it was suggested that you might provide 40 units of safety stock. Ifyou had done so, you would never experience a shortage. You would have achieved a servicelevel of 100%. This might not be a desirable solution for this problem. We are carrying arelatively high amount of safety stock, and there is a very low probability that lead time demandwill actually go as high as 90 units (only a 1% chance).

If you had chosen to carry only 30 units of safety stock (order when inventory drops to 80 units),you will be fine if lead time demand is anything up to and including 80 units. If lead timedemand turns out to be 90 (there is a 1% chance of that), you will come up 10 units short. But,

since you had enough inventory to cover 99% of the demands that might have occurred, youachieved a 99% service level. Many people might opt for this policy, for it will reduce theaverage annual level of inventory carried (i.e., reduce holding costs) and run only a slight risk ofincurring a shortage cost.

Others might be even more aggressive, and opt for an even lower service level. We could haveachieved a 95% service level with a reorder point of 70 (only 20 units of safety stock). We'velowered our inventory holding costs even further, but exposed ourselves to even more shortagecost risk.


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INVENTORY MONITORING APPROACHES

Fixed Quantity, or Q System: This approach maintains a constant order size, but allows the

time between the placement of orders to vary. This method of monitoring inventory is sometimesreferred to as aperpetual review method, a continuous review system, a reorder point system,and a two-bin system. The inventory level is continuously (perpetually) monitored, and when theinventory drops to the reorder point level, a replenishment order is placed. The size of the orderis constant (fixed quantity, typically the calculated economic order quantity for the item).Because demand continues to occur while we are waiting for the replenishment order to arrive(i.e., demand continues to occur during the lead time), the inventory level will generally bebelow the reorder point level when the replenishment arrives. This type of system providescloser control over inventory items since the inventory levels are under perpetual scrutiny.

How much decision: Order size is constant (fixed).

When decision: Time between the placement of orders can vary.

Time

ReorderPoint

LT

Q

Order#2

LT

Order#1 Q

LT

Q

Order#3

Inventory Level


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Periodic Review Systems: There are two, Fixed Period System (described in the textbook),

and a hybrid system (described below but not in the textbook)

Fixed Period System: This approach maintains a constant time between the placement of

orders, but allows the order size to vary. This method of monitoring inventory is sometimesreferred to as afixed interval system. It only requires that inventory levels be checked at fixedperiods of time. The amount that is ordered at a particular time point is the difference betweenthe current inventory level and a predetermined maximum inventory level (also called an orderup to level, or a target level). If demand has been low during the prior time interval, inventorylevels will be relatively high when the review time occurs, and the amount to be ordered will berelatively low. If demand has been high during the prior time interval, inventory levels will havebeen depleted to low levels when the review time occurs, and the amount to be ordered will behigher. Since demand continues to occur during the lead time, inventory levels will increasewhen the replenishment order arrives, but not all the way up to the maximum (i.e., target) level.

How much decision: Order size can vary.

When decision: Time between the placement of orders is constant (fixed).

LT

Q3

Order#3

Q2

LT

Q1

T1

Maximum (or order up to or target) inventory level

Time

LT

Order#2

Order#1

Inventory Level

T2

T3

Review time, T1

Review time, T2

Review time, T3


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Hybrid System: This approach allows both the order size and the time between the placementof orders to vary. This method of monitoring inventory is sometimes referred to as an optionalreplenishment system, or a min-max system. It is a hybrid system because it combines elementsof both the fixed quantity system and the fixed period system. It is similar to the periodic review

system in that it only checks inventory levels at fixed intervals of time, and it has a maximuminventory level (or order up to or target level). However, when one of those review periodsarises the system does not automatically place an order. An order is only placed if the size of theorder would be sufficient to warrant placing the order. This determination is made byincorporating the reorder point concept from the continuous review system. At the review periodthe inventory level on hand is compared to a minimum level for the item. If inventory has notfallen below this minimum level, no order is placed. However, if the inventory level has droppedbelow this minimum level, an order is placed. The size of the order is the difference between theinventory on hand and the maximum inventory level. Since demand continues to occur duringthe lead time, inventory levels will increase when the replenishment order arrives, but not all theway up to the maximum (i.e., target) level.

How much decision: Order size can vary.

When decision: Time between the placement of orders can vary.

Second order is placedat T

3since the inventory

has fallen blow theminimum LT

Q2

Order#2

LT

Q1

T1

Maximum (or order up to or target) inventory level

Time

MinimumLevel

Order#1

Inventory Level

T2

T3

First order is placedat T

1since the

inventory has fallenblow the minimum

No order at T2

since inventory isnot below theminimum


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POSITIVES AND NEGATIVES OF

INVENTORY MONITORING APPROACHES

ApproachAdvantages

(Positive aspects)Disadvantages

(Negative aspects)

Fixed Quantity

- provides tighter control overinventory items

- less safety stock needed

- requires constant monitoring(constant scrutiny)

- problems with multiple itemsfrom same source (many itemsarrive in separate shipments)

Fixed Period

- joint shipping advantage withmultiple items from same source

- does not require constant

monitoring

- requires more safety stock- occasional small nuisance

orders may result

- provides looser control overinventory items

Hybrid

- joint shipping advantage withmultiple items from same source

- does not require constantmonitoring

- no small nuisance orders

- requires more safety stock- provides looser control over

inventory items

COMPARISON OF INVENTORY MANAGEMENT SYSTEMS

System Order Size Time Between Orders

Fixed Quantity Constant (fixed) Varies

Fixed Period Varies Constant (fixed)

Hybrid Varies Varies


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ABC CLASSIFICATION OF ITEMS

It is not unusual for organizations to maintain many items in inventory (hundreds or eventhousands). Each of these items needs to be controlled. An important question is How much

scrutiny does each item deserve? Some of these items may have a high annual investment, andlogic would suggest that these items deserve very close scrutiny. On the other hand, some itemsmay have a low annual investment (these are often referred to as nuts and bolts items), andthey probably do not need as much attention. ABC analysis provides a mechanism to separate the"important few" from the "trivial many" so that the appropriate level of control can be assignedto each item. ABC analysis assigns all inventory items to one of these three classifications: Aitems need the tightest degree of control, while C items do not need very close scrutiny. Thegeneral graphical display for an ABC classification appears as follows:

This type of diagram is referred to as a Pareto graph, and is relevant to a variety of situations.

Cumulative % of Items 100%

A Items B Items C Items

Cumulative % of Value

100%


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ILLUSTRATION OF ABC ANALYSIS

The following table displays an organizations inventory items, their value per unit, and their

annual usage. (Note: To keep things manageable on the page, this illustration is greatly scaleddown from reality. Most organizations would be dealing with considerably more than the teninventory items displayed below.)

InventoryItem Number

AnnualUsage

ValuePer Unit

AnnualDollar Usage

1 10,000 $13 130,0002 14,000 $5 70,0003 2,000 $6 12,0004 10,000 $3 30,0005 5,000 $5 25,000

6 50,000 $8 400,0007 30,000 $10 300,0008 5,000 $1 5,0009 4,000 $5 20,00010 2,000 $4 8,000

Total $1,000,000Rearrange items in decreasing order of annual dollar usage:

ItemNumber

Annual$ Usage

% ofLine Items

Cumulative% of Items

% ofValue

Cumulative% of Value

ABCClass*

6 $400,000 10% 10% 40 40 A7 $300,000 10% 20% 30 70 A1 $130,000 10% 30% 13 83 B2 $70,000 10% 40% 7 90 B4 $30,000 10% 50% 3 93 C5 $25,000 10% 60% 2.5 95.5 C9 $20,000 10% 70% 2 97.5 C3 $12,000 10% 80% 1.2 98.7 C10 $8,000 10% 90% .8 99.5 C8 $5,000 10% 100% .5 100 C

Total $1,000,000

*Note: When classifying the items as A, B, or C items, it can be somewhat subjective as towhere the lines are drawn. With the unrealistically small demonstration above, the first 20% ofthe inventory items constitute 70% of the inventory value, so these items (Items 6 and 7) will bedesignated as A items. On the other extreme, 60% of the items constitute only 10% of theinventory value, so these items (Items 4, 5, 9, 3, 10, and 8) will be designated as C items. In themiddle, 20% of the items constitute 20 % of the inventory value, so these items (Items 1 and 2)will be designated as a B item.


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DEVELOPMENT OF THE ABC INVENTORY PARETO GRAPH

Cumulative percentages extracted from previous table (and rotated 90 degrees)

Items (rearranged order)1st

11st

21st

31st

41st

51st

61st

71st

81st

9All10

Cumulative % of items 10 20 30 40 50 60 70 80 90 100Cumulative % of value 40 70 82 90 93 95.5 97.5 98.7 99.5 100


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ALTERNATE REPRESENTATION OF OUR ABC ANALYSIS

The data reflected in the Pareto graph could also be displayed in a bar chart, as illustrated in the

textbook. The following is such a representation for our simple ABC illustration.

10 20 30 40 50 60 70

A items

B items

C items

Documents

CP3 Independent Demand Inventory