Upload
i-bee-general-construction
View
34
Download
5
Tags:
Embed Size (px)
Citation preview
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
Economic order quantity (EOQ) model with quantity discount
(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
Economic order quantity (EOQ) model with quantity discount
(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
Economic order quantity (EOQ) model with quantity discount
(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
Economic order quantity (EOQ) model with quantity discount
(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
An EOQ ExampleAn EOQ Example
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
An EOQ ExampleAn EOQ Example
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
An EOQ ExampleAn EOQ Example
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
Table 12.2Table 12.2
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)
QQ22* = = 714 cars order* = = 714 cars order2(5,000)(49)2(5,000)(49)
(.2)(4.80)(.2)(4.80)
QQ33* = = 718 cars order* = = 718 cars order2(5,000)(49)2(5,000)(49)
(.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
Table 12.3Table 12.3
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