inventory control for construction

Construction Materials

Management

(COTM 5202)

5. Inventory Controlby

Tadesse Ayalew

Lecturer , EiABC, AAU

BSc. IN CONSTRUCTION TECH. & MANAGEMENT, EiABC, MARCH 2014

1

5. 1 Inventory cost Components

The general objective of inventory control is to minimize the

total cost of keeping the inventory while making tradeoffs

among the major categories of costs:

(A) purchase costs,

(B) order cost,

(C) holding costs, and

(D) unavailable cost.

These cost categories are interrelated since reducing cost in

one category may increase cost in others.

The costs in all categories generally are subject to

considerable uncertainty.

A) Purchase Costs

The purchase cost of an item is the unit purchase price

from an external source including transportation and

freight costs.

For construction materials, it is common to receive

discounts for bulk purchases, so the unit purchase cost

declines as quantity increases.

Because of this, organizations may consolidate small orders

from a number of different projects to capture such bulk

discounts, in some cases; this is a basic saving to be

derived from a central purchasing office

B) Order Cost

The order cost reflects the administrative expense of

issuing a purchase order to an outside supplier.

Order costs are usually only a small portion of total costs

for material management in construction projects,

although ordering may require substantial time.

C) Holding Costs

The holding costs or carrying costs are primarily the

result of capital costs, handling, storage, obsolescence,

shrinkage and deterioration.

Capital cost results from the opportunity cost or

financial expense of capital tied up in inventory.

Handling and storage represent the movement and

protection charges incurred for materials.

C) Holding Costs (Cont….)

Storage costs also include the disruption caused to other

project activities by large inventories of materials that

get in the way. Obsolescence is the risk that an item will

lose value because of changes in specifications.

Shrinkage is the decrease in inventory over time due to

theft or loss. Deterioration reflects a change in material

quality due to age or environmental degradation.

D) Unavailability Cost

The unavailability cost is incurred when a desired

material is not available at the desired time.

In manufacturing industries, this cost is often called the

stock out or depletion cost.

Shortages may delay work, thereby wasting labor

resources or delaying the completion of the entire

project.

5.2 Tradeoffs of Costs in Materials Management.

To illustrate the type of trade-offs encountered in materials

management, suppose that a particular item is to be ordered

for a project. The amount of time required for processing the

order and shipping the item is uncertain.

Consequently, the project manager must decide how much

lead time to provide in ordering the item. Ordering early and

thereby providing a long lead time will increase the chance

that the item is available when needed but it increases the

cost of inventory and chance of spoilage on site.

5.3 Inventory Model

There are two types of inventory models

Deterministic inventory Model (Constant Demand)

Inventory Model with Probabilistic Demand

The objectives of this model is to determine an optimum order quantity (EOQ) denoted by Q* such that total inventory cost is minimized.

TVC= Ordering cost + carrying (holding cost)

ChQ

CoQ

D

2TVC =

5.3.1 Deterministic inventory models

Economic order quantity (EOQ) model with constant rate of demand

Minimizing CostsMinimizing Costs

Objective is to minimize total costsObjective is to minimize total costs

Table 11.5Table 11.5

Ann

ual c

ost

Ann

ual c

ost

Order quantityOrder quantity

Curve for total Curve for total cost of holding cost of holding

and setupand setup

Holding cost Holding cost curvecurve

Setup (or order) Setup (or order) cost curvecost curve

Minimum Minimum total costtotal cost

Optimal Optimal order order

quantityquantity

Economic order quantity (EOQ) model with constant rate of

demand( Cont…)

Since for maximum or minimum value of TVC its first derivatives should be zero

02

12

ChCoQ

D

Q* =Ch

DCo2 = Economic order quantity (EOQ)

Optimal length of the inventory replenishment cycles time (t*), optimal inventory between successive orders.

Q*= Annual demand * Reorder cycle time = D*t

Optimal No of order quantity to be placed in the given time period (which is assumed to be one year)

Important formulas

D

Q *Ch

DCo

D

2*

1 t* = =

*Q

D

Ch

DCo2

1

N*= D * =Co

DCh

2

Important formulas (cont…) Optimal (minimum) total variable inventory

cost (TVC*)TVC = Ch

QCo

Q

D

2

CoD.ChDCo2

1

Ch

DCoCh 2

2= * +

Optimal total inventory cost is the sum of variable costs

and fixed costs, so TC = D.C+TVC*

DCoCh2=

Economic order quantity (EOQ) model with ware house space

constraint

Steps Step1: for =1, compute EOQ for each

item separately by using the formula

Where fi = the storage space required per unit item i and is a non negative Lagrange multiplier

Q*= fiChi

DiCoi

22

; i =1, 2, 3….n

Step 2: if Qi* (i=1, 2, 3…n) is satisfied the condition,

(Total warehouse space available) then

stops, otherwise go to step three,Step 3: Increase the value of if value of left hand

side of fiQi = W is More than available storage space other wise decrease the value of .

Continue iteration until the condition is satisfied

WfiQi

Economic order quantity (EOQ) model with ware house space

constraint (cont…)

Economic order quantity (EOQ) model with quantity discount

EOQ model with one price break Suppose the following price discount

schedule is quoted by the suppliers in which a price (quantity discount) occurs at b1 this means,

Quantity Price per unit

0<Q1<b1 C1

b1<Q2 C2


(cont…) The optimal purchase quantity can be determined

by the procedure given below Step1: consider the lowest price (i.e. C2 )

and determine Q2* by the basic EOQ formula

Q2*=

If Q2* lies with in the prescribed range b1<Q2*, then Q2* is EOQ i.e. Q*= Q2*

rC

DCo

*

2

2


(cont…) And the optimal cost TC* associated with Q2* is

calculated as follows:

TC* (=TC2*) = D.C2+

Step2: If Q2* is not equal to or more than b1, then

Calculate Q1*

with C1 and corresponding total cost at Q1*. Compare

TC(b1) and TC (Q1*), If TC(b1)>TC(Q1*),then EOQ is

Q*= Q1*.Otherwise Q*= b1 is the required EOQ

)*(2 21

1

rCb

Cob

D


(cont…)

EOQ model with two price break Suppose the following price discount

schedule is quoted by the suppliers in which a price (quantity discount) occurs at b1 this means,

Quantity Price per unit

0<Q1< b1 C1

b1<Q2< b2 C2

b2< Q3 C3


(cont…)

Notice that C3< C2 < C1

The optimal purchase quantity can be determined by the procedure given below

Step1: a) Consider the lowest price (i.e. C3) and

determine Q3* by the basic EOQ formula

b) If Q3* > b2 , then EOQ (Q*) = Q3* and the optimal

cost TC (Q3*) is the cost associated with Q3*

c) If Q3*< b2, then go to step 2

Economic order quantity (EOQ) model with quantity discount (cont…)

Step2: a) Calculate Q2* is based on price C2.

b) Compare Q2* with b1 and if b1 < Q2* < b2 then compare TC

(Q2*) and TC (b2). If TC (Q2*)> TC (b2), then EOQ= b2. Otherwise

EOQ = (Q2*)

c) If Q3*< b1 as well as b2 then go to step three.

Step3: Calculate Q1* is based on price C1 and compare, TC (b1),

TC (b2) and

TC (Q1*) to find EOQ the quantity with lowest cost will

naturally

be the required EOQ

An EOQ ExampleAn EOQ Example

Determine optimal number of units to orderDetermine optimal number of units to orderD = 1,000 unitsD = 1,000 unitsCo = $10 per orderCo = $10 per orderH = $.50 per unit per yearH = $.50 per unit per year

Q* =Q* =2DCo2DCo

HH

Q* =Q* =2(1,000)(10)2(1,000)(10)

0.500.50= 40,000 = 200 units= 40,000 = 200 units


Determine optimal number of needles to orderDetermine optimal number of needles to orderD = 1,000 unitsD = 1,000 units Q* Q* = 200 units= 200 unitsCo = $10 per orderCo = $10 per orderH = $.50 per unit per yearH = $.50 per unit per year

= N = == N = =Expected Expected number of number of

ordersordersDemandDemand

Order quantityOrder quantity

DDQ*Q*

N = = 5 orders per year N = = 5 orders per year 1,0001,000200200


Determine optimal number of needles to orderDetermine optimal number of needles to orderD = 1,000 unitsD = 1,000 units Q*Q* = 200 units= 200 unitsS = $10 per orderS = $10 per order NN = 5 orders per year= 5 orders per yearH = $.50 per unit per yearH = $.50 per unit per year

= T == T =Expected time Expected time between ordersbetween orders

Number of working Number of working days per yeardays per year

NN

T = = 50 days between ordersT = = 50 days between orders25025055


Determine optimal number of needles to orderDetermine optimal number of needles to orderD = 1,000 unitsD = 1,000 units Q*Q* = 200 units= 200 unitsS = $10 per orderS = $10 per order NN = 5 orders per year= 5 orders per yearH = $.50 per unit per yearH = $.50 per unit per year TT = 50 days= 50 days

Total annual cost = Setup cost + Holding costTotal annual cost = Setup cost + Holding cost

TC = S + HTC = S + HDDQQ

QQ22

TC = ($10) + ($.50)TC = ($10) + ($.50)1,0001,000200200

20020022

TC = (5)($10) + (100)($.50) = $50 + $50 = $100TC = (5)($10) + (100)($.50) = $50 + $50 = $100

Reorder PointsReorder Points

EOQ answers the “how much” questionEOQ answers the “how much” question

The reorder point (ROP) tells when to orderThe reorder point (ROP) tells when to order

ROP =ROP =Lead time for a new Lead time for a new

order in daysorder in daysDemandDemand per dayper day

= d x L= d x L

d = d = DD

Number of working days in a yearNumber of working days in a year

Reorder Point CurveReorder Point Curve

Q*Q*

ROP ROP (units)(units)

Inve

ntor

y le

vel (

units

)In

vent

ory

leve

l (un

its)

Time (days)Time (days)Figure 12.5Figure 12.5 Lead time = LLead time = L

Slope = units/day = dSlope = units/day = d

Reorder Point ExampleReorder Point Example

Demand = 8,000 DVDs per yearDemand = 8,000 DVDs per year250 working day year250 working day yearLead time for orders is 3 working daysLead time for orders is 3 working days

ROP = d x LROP = d x L

d =d = DD

Number of working days in a yearNumber of working days in a year

= 8,000/250 = 32 units= 8,000/250 = 32 units

= 32 units per day x 3 days = 96 units= 32 units per day x 3 days = 96 units

Quantity Discount ModelsQuantity Discount Models

Discount Discount NumberNumber Discount QuantityDiscount Quantity Discount (%)Discount (%)

Discount Discount Price (P)Price (P)

11 00 to to 999999 no discountno discount $5.00$5.00

22 1,0001,000 to to 1,9991,999 44 $4.80$4.80

33 2,0002,000 and over and over 55 $4.75$4.75


A typical quantity discount scheduleA typical quantity discount schedule

Quantity Discount ExampleQuantity Discount ExampleCalculate Q* for every discountCalculate Q* for every discount Q* =

2DSIP

QQ11* = = 700 cars order* = = 700 cars order2(5,000)(49)2(5,000)(49)

(.2)(5.00)(.2)(5.00)


(.2)(4.80)(.2)(4.80)


(.2)(4.75)(.2)(4.75)

1,000 — adjusted1,000 — adjusted

2,000 — adjusted2,000 — adjusted

Quantity Discount ExampleQuantity Discount Example

Discount Discount NumberNumber

Unit Unit PricePrice

Order Order QuantityQuantity

Annual Annual Product Product

CostCost

Annual Annual Ordering Ordering

CostCost

Annual Annual Holding Holding

CostCost TotalTotal

11 $5.00$5.00 700700 $25,000$25,000 $350$350 $350$350 $25,700$25,700

22 $4.80$4.80 1,0001,000 $24,000$24,000 $245$245 $480$480 $24,725$24,725

33 $4.75$4.75 2,0002,000 $23.750$23.750 $122.50$122.50 $950$950 $24,822.50$24,822.50


Choose the price and quantity that gives the lowest total Choose the price and quantity that gives the lowest total costcost

Buy 1,000 units at $4.80 per unitBuy 1,000 units at $4.80 per unit

Try the following Exercises

Exercise 1

The production department of a company requires

3600kg of raw materials for manufacturing of particular

item per year. It has been estimated that cost of placing

an order is 36 birr and the cost of carrying inventories is

25% of the investment in the inventories. The price is

10 birr per kg. The purchase manager whishes to

determine an ordering policy for raw materials.

Exercise 2

A small shop produces three machines part I,II and III in lots. The shop has only 650m2 of storage space the appropriate data for three items are given in the following table

Item I II IIIDemand (unit per year) 5000 2000 10000

Procurement cost per order 100 200 75

Cost per unit 10 15 5Floor space requirements 0.7 0.8 0.4

The shop uses an inventory charge of 20% of average inventories valuation per year. If no stock out is allowed, determine the optimal lot size for each item under a given storage constraints.

Exercise 3

A shopkeeper estimates annual requirement of an item

as 2000 units.He buys from supplier 10 per item and the

cost of ordering is 50 birr each time. If the stock holding

costs are 25% per year of stock value how frequently

should replenish his stock? Further, suppose the supplier

offer 10% discount on order between 400 and 699 item,

a 20% discount on order exceeding or equal to 700 can

the shopkeeper reduce his cost by taking advantages

from either of the discount ?

Thank You

inventory control for construction

Engineering

cost of inventory

purchase costs

order costs

cost categories

inventory cost components

unavailability cost

opportunity cost

depletion cost