inventory extra notes

8/13/2019 Inventory Extra Notes

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current or future need".What isInventory(StockControl)? Inventoryisdefinedas: "the stored resource that is used to satisfy

I U Why InventoryisImportant* Operationsmanagersaround theglobehaverecognizedthat gooinventorycontroliscrucial* On onehand thefirmcantry toreduce'costsbyreducingon-haninventorylevels.On theotherhand,customersbecomedissatisfiewhenanitemisfrequentlyoutof stock.* Thus,companiesmuststrikeabalancebetweeninventory

investmentand customersservicelevels. * Costoptimizationisamajor factorinobtainingthisdelicate balance.

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Functions of InventorySix functions of inventory include:1- Meeting anticipated customers dem nd by providing good stocks.2- Separating production nd distribution process. For e g.building stock in summer for use in winter time as it is more cheeaperfor the company.3- Taking advantage of quantity discounts. Purchasing largequantities reduce cost of goods.4- Hedging against inflation nd price changes.5- Protecting against stock outs that can occur due to bad weather,supplier shortages, quality problems or improper deliveries.6- Permitting operations to continue smoothly with the use of"work-in-process" inventory.

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Just-in-Case[JIC]VersusJust-in-Time[JIT] Inventory JIC:Thisrequires stockingquantitieso resources and thenreordering whenthe inventoryfinishes. JIT:i weorder the quantity wegetthem directlybecauaewehavenoproblemo ordering and transporting. ThisisaJapanese method. The bestsolutionisinbetweenboth methods. Defectso bothmethods:

JIC: 1- highcostat the beginningo the project. 2- bigstoragearea3- the obsolesceor theftisliable

JIT: costishighfor ordering everyday

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Just in Case Inventory Models [JIC] There are two types of demand models: Independent and Dependent Both models stress two main issues in inventory analysis:

How much quantity to order? When to order the quantity?

All models share the following parameters regarding costs:1- Holding or arrying Costs: are the costs associated with holding (storing) orcarrying inventory over time. They also include cots related to storage such as insuran

i extra staffing and interest payments.II 2- a) Ordering Costs: are the costs associated with ordering and receivinginventory.They include costs of supplies, forms and order processing.b) Setup Costs: are the costs associated with preparing a machine or process formanufacturing an order.Operations managers can lower ordering costs by reducing setup costs and by usingefficient procedures as electronic ordering and payment.

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6/19

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IIInventory Models for Independent Demand:[Three types ofmodels are included:I 1- The basic Economic Order Quantity [EOQ]

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2- Production Order Quantity Model3- Quantity Discount Model

1 The basic Economic Order Quantity [EOQ]1.1 Assumptions:1- Demand is known and constant.2- Lead time, that is the time between the placement of the order and the receipt of theorder, is known and constant.3- Receipt of inventory is instantaneous. In other words, the inventory from an orderarrives in one batch at one time.4- Quantity discounts are not possible.5- The only variable costs are the ordering and holding costs. 8

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7/19

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+The graph of the inventory usage over time has a saw-tooth shape as in Figure 13.7shown in the following slide.

I +Q represents the amount that is ordered.+Because demand is constant over time, inventory drops at a uniform rate over time,

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represented by the slopped line in the previous figure.+When inventory level reaches 0, the new order is placed and received and theinventory level again jumps to Q units, represented by the vertical lines as in the f i g , .1 2 Minimizing Costs:eThe objective ofmost inventory models is to minimize total costs.eFor EOQ model, the significant coats are the setup (or ordering) cost and the holdin(carrying) coat.eIfwe minimize those costs the total cost will be minimized as the cost relations is asfollows:

TC = carrying cost ordering cost+ Q is the minimum quantity that satisfies the minimum cost I+ i u r ~ shows this relationship between the cost and the minimum q u r t t t ~ .. m mm.. .. .. .. m m mmm .m m . m ... . . .mm .mmmm.mmmmmmmmmmmmmmmm . . . . .m. . . . . .m m . . . . .mm .. m.m.mmm , I


8/19

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With the EOQ model, the optimal order quantity will occur at a pointwhere the total setup cost is equal to the total holding cost. Using the following variables, we can determine setup (order) andholding costs and solve for optimum Q:I Q= number of pieces per order, Q == optimum number of pieces per order (EOQ)D == annual demand in units for the inventory itemS == setup or ordering cost for each orderH == holding or carrying cost per unit per yearSteps for solving for Q = EOQ

See next slides for detail.

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2. develop an expression for holding cost3. set setup cost equal to holding cost4. solve the equation for the best order quantity.

Using the following variables, we can determine setup and holding costs andsolve for Q :Q = number of pieces per order

Q* = optimum number of pieces per order (EOQ)D =annual demand in units for the inventory itemS =setup or ordering cost for each order

H = holding or carrying cost per unit per year1. Annual setup cost = (no. of orders placed/yr)(setup or order cost/order)I\ annual demand )= ( h d (setup or order cost/order)no. uruts In eac or erD= SQ

2. Annual holding cost = (average inventory level)(holding cost/unit/yr)order qUantity)= ( 2 (holding cost/unit/yr) : 11i

_ Q- 2 i3. Optimal order quantity is found when annual setup cost = annual holding cost,'

namely, tt)1,D S= Q H *Q 2 J

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11/19

INVENTORY MODELS

4. To solve for Q , simply cross-multiply terms and isolate Q on the left of the- --equalssign.- - - - - - - - - - - - - - - -- - - - - - - -

20S 2HQ2 = 20SH

Q = ~ 2 0 S (13.1)HNow that 'we have derived equations for the optimal order quantity, Q , it is possibleto solve inventory problems directly, as is done in Example 3.

EX MPLE 3

Squirt! Inc., a c-offipany that markets hypodermic needles to hospitals, would liketo reduce its inventory cost by determining the optimal number of hypodermicneedles to obtain per order. The annual demand is 1,000 units, the setup or order'ing cost is 10 per order, and the holding cost per unit per year is $0.50. Usingthese figures, we can calculate the optimal number of units per order:

1. Q = ~ 2 0 S H 3. Q* = v'40,0002(1,000)( 10)2 Q = 4. Q* = 200 units0.50

We can also determine the expected number of orders placed during the yearN) and the expected time between orders T) as follows:

demand 0Expected number of orders = N = =order quantity Q (13.2)Expected time between orders = T = number of working days in a year (13.3)expected no. of ordersExample 4 illustrates this concept.

EX MPLE 4Using the data from Squirt, lnc., in Example 3, and a 250,day working year, wefind the number of orders N) and the expected time between orders T) as:

N= demand 1,000 = 5 orders per yearorder quantityT = number of working days /year

expected number of orders250 working days/year = 50 days between orders= 5 orders

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CHAPTER 13 INVENTORY MANAGEMENT ANDJUST IN TIME TACTICS

As mentioned earlier in this section, the total annual inventory cost is the sumof the setup and holding costs:

Total annual cost = setup cost + holding cost (13,4)

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In terms of the variables in the model, we can express the total cost asD QTotal cost =Q S+ '2 H

Example 5 shows how to use this formula.(13.5)

EX MPLE

Again using the Squirt, Inc., data (Examples 3 and 4), we determine that the totalannual inventory costs are

otal ost = S + ~ H= 1,000 ( 10) + 200 050)200 2= (5)( 10) + (100)( 0.50)= 50+ 50 = 100

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EX MPLE 6

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If management in the Squirt, Inc., example underestimated total annual demandby 50% (say it is actually 1,500 needles rather than 1,000 needles) while using the--sarne-f.Z0he-annnaHnventoqr-ee>st-itKl'efrSeS-0flly$l-3.GG-t$-l-OQ-vefsus -1 2 ~ - ) , or .25(}{J. Similarly, if management cuts its order size by 50% from 200 to 100, cost in;creases by $25 ($100 versus $125), or 25%.(a) If demand in Example 5 is actually 1,500 needles rather than 1,000, but man;agernent uses an EOQ of Q = 200 (when it should be Q = 244.9 based on D =1,500), total costs increase 25%:, .

Annual cost = gS + ~ HO

= 1,500 ($10)+ 200 ($050)200 2=$75.00 + $50.00 = $125.00

(b) If the order size is reduced from 2QO to 1.90 needles, but other parameters re;main the same, cost also increases 25%:

1 000 100Annual cost = 100 (10) + 2 ($0.50)=$100.00 + $25.00 =$125.00

Inventorylevel(units)Q* ~

Slope = units/day =d

Reorderpoint, ROP(units)

- - < - - Time (days)Lead time =

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14/19

CHAPTER 13 INVENTORY MANAGEMENT AND JUST-IN-TIME TACTICS

The reorder point ROP) is given as:ROP = (demand per day)(lead time for a new order in days) (13.6)

dxLThis equation for ROP assumes that demand is uniform and constant When this is notthe case, extra stock, often called safety stock should be added.

The demand per day, d, is found by dividing the annual demand D, by the number of working days in a year:Dd= .number of working days in a year

Computing the reorder point is demonstrated in Example 7.

EX MPLE

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Electronic Assembler, Inc., has a demand for TX512 VCRs of 8,000 per year. Thefirm operates a 200.day working year. On the average, delivery of an order takes 3working days. We calculate the reorder point as follows: .

D _ 8,000d = daily demand = number of working days - 200=40

ROP = reorder point = d x L = 40 units/day x 3 days= 120 units

Hence when the inventory stock drops to 120, an order should be placed.The order will arrive 3 days later, just the firm s stock is depleted.


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Production Order Quantity odel We previously assumed that the entire whole) inventory order wasreceived at one time in the EOQ model. However, there are some times when the firm may receive itsinventory over a period of time.

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I Under these circumstances the daily production or inventory flotrate and the daily demand rate usage rate)are taken into account. shows inventory level as function of time. This model is suitable for production environment. It is commonly called the Production Order Quantity Model. It is useful when inventory builds up over time. The same process is used to get the optimum Q which yields theminimum coat by equating holding cost and setup ordering) cost.

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number ofpieces per orderoptimum number of pieces per order (EOQ)

annual demand in units for the inventory itemS == setup or ordering cost for each orderH == holding or carrying cost per unit per yearp == daily production rate.d == daily demand rate or usage rate.t == length of the production run in days.Steps for solving for Q*

see details on page 5!2. see also example on page . 12

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FIGUR 13.10 Change in Inventory Levels over Time for the Production Model

Inventory levelPart of inventory cycleduring which productionis taking place

Maximum j ~ ./ Demand part of cycleinventoryTime- t - l

d = daily demand rate, or usage ratet = length of the production run in days

1 Annual inventory). ( , 1 1 ( holding cost ) ( h ldi = average inventory eve x ito ing cost per uru per year: .. = (average inventory level) x H\

( Average inventory) = max imum inventory level)/22. level .3 ( Maximum ) _ total produced during) _ ( total used dur ing ). inventory level - the production run the production run

= pt dtBut Q = total produced = pt, and thus t = Qlp. Therefore,Maximum 'inventory level =p d ~e

d Q Q\ P= Q I - ~

4. Annual inventory holding cost or simply holding cost)= maximum inventory level H) = [1 _ ~ ] H

Using the expression for holding cost above and the expression for setup costdeveloped in the basic EOQ model, we solve for the optimal number of pieces perorder by equating setup cost and holding cost:

Setup cost = D/Q)SHolding cost = l/z HQ [ dIp)]

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CHAPTER 13 INVENTORY MANAGEMENT AND JUST-IN-TIME TACfrCS

Set ordering cost equal to holding cost to obtain Q :';''(Os = Y2 HQ - dIp)] t.rQ T('

20S .Q = H [1 - dIp)] .to,I 20S (13:1 1:Q = -V H[1 - dll)] T

Example 8 shows how to use the above equation, Q; to solve for the optimumliorder or production quantity when inventory is consumed as it is produced. 'EX M PL E

Nathan Manufacturing, Inc., makes and sells specialty hubcaps for the retail automobile aftermarket. Nathan's forecast for its wire-wheel hubcap is 1,000 units next'year, with an average daily demand of 6 units. However, the production process ismost efficient at 8 units per day. So the company produces 8 per day but uses only 6per day. Given the following values, solve for the optimum number of units per order.Annual demand = p = 1,000 units

Setup cost = S = 10Holding cost = H = 0.50per unit per year

Daily production rate = p = 8 units dailyDaily demand rate = d =6 units daily

1. I 20SQ = -V H[l - dIp)]2(1,000)(10)2. Q = .J 0.50[1 - 6/8)]20,000 = Y160,000=

= 400 hubcaps

Also note that we can compute daily demand:od = : -number of days the plant is open

andNumber of days the plant is open = d

Therefore, Nathan Manufacturing, Inc., in Example 8, is open only 167 days eachyear because1,000Number of days the plant is open =-6- = 167

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mVEl'JTORYlVfODECS - - - - - - - - - - - You may want to compare the solution in Example 8 with the answer in Exam

ple 3. Eliminating the instantaneous receipt assumption, where p=8 and d = 6, hasresulted in an increase in Q* from 200 in Example 3 to 400 in Example 8.We can also calculate t when annual data are available. When annual dataare used, we can express t asI 2DS (13.8) t= 1/ H[l - DIP)]

where 0 = annual demand rateP =annual production rate

FIGURE 13 11 Total Cost Curve for the Quantity Discount Model

Total I I Total cost curve for Discount 2Cost Total cost I IIcurve for :'

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