Modelling just in time purchasing in the ready mixed concrete industry 3

Hence, the total annual cost under the JIT purchasing system for the JPTV models is proposed to be the product of the unit price under the JIT purchasing system P and the annual demand

Chapter 6 JIT purchasing threshold value models for the RMC industry

6.1 Introduction

The objective of this chapter is to develop JIT Purchasing Threshold Value (JPTV) models These models consider the inventory physical storage cost, together with the additional costs and benefits resulting from JIT purchasing, which have not been

considered by the models of Fazel (1997), Fazel et al (1998) and Schniederjans and Cao

(2000, 2001) or the models in the previous chapters These JPTV models are developed particularly for the Ready Mixed Concrete (RMC) industry and are applicable for boundary condition 2 (see Section 1.6 for its definition)

Section 6.2 expands the annual cost of carrying one unit of inventory in the classical

EOQ model ( h ) to include all the components of inventory physical storage cost The

features of the expanded EOQ models are also discussed Section 6.3 and Section 6.4 develop the EOQ-JIT cost indifference points under the revised EOQ models These EOQ-JIT cost indifference point models are the JPTV models

6.2 Revised EOQ model

Chapter 3 argued that there were reasons to include the physical storage cost into the

annual cost of carrying one unit of inventory in the classical EOQ model ( h ) However,

to empirically examine the capability of an inventory facility to carry the EOQ-JIT cost indifference point’s amount of inventories on the platform created by Fazel (1997), Fazel (1998) and Schniederjans and Cao (2000, 2001), the physical plant space was treated as a

indifference point in the previous chapters To accurately capture the impact of inventory purchasing policies on the selection of the inventory purchasing method and to develop the JPTV models, the physical plant space, which is a component of the physical storage

costs, needs be included into h This is to expand “ h ” to “ H ” which is the “expanded

annual cost of carrying one unit of inventory” The classical EOQ model is thus to be revised The features of the revised EOQ model are discussed below

6.2.1 Total annual cost under the revised EOQ model

When “ h ” is expanded to become “ H ”, the total costs under the revised EOQ model are

given by:

D P

HQ

Q

kD

TC Er = + 2 + E (6.1)

where: TC is total costs under the revised EOQ model Er

“ H ”, which includes all the components of the inventory carrying costs, is greater than

“ h ” in Eq (3.1) Accordingly, TC is also greater than Er TC in Eq (3.1) in the classical E

EOQ model

6.2.2 Optimal economic order quantity under the revised EOQ model

The optimum order quantity of the revised EOQ model derived from Eq (6.1) is:

The optimum order quantity of the revised EOQ model is significantly less than that of

the classical EOQ model, as H is substantially greater than h , assuming the values of the other parameters, namely, D and k remain unchanged

6.2.3 Total annual optimal cost under the revised EOQ model

The total annual optimal cost under the revised EOQ model derived based on Eq (6.1) and Eq (6.2) is:

D P kDH D

P kDH kDH

TC Er =21 2 +12 2 + E = 2 + E (6.3)

Eq (6.3) is valid only when the inventory is ordered at its economic order quantity This

means that the annual inventory ordering cost item ( Q kD ) equals the annual inventory

carrying cost item ( 2QH ) as shown in Eq (6.3)

To sum up, the revised EOQ model is different from the classical EOQ model on three counts First, the so called “fixed costs”, such as rental, utilities, personnel salaries, etc, are considered in the inventory carrying cost item in the revised EOQ model Hence, the annual cost of holding one unit of inventory in the revised EOQ model is greater than that

in the classical EOQ model The total annual cost under the revised EOQ model is also greater than that under the classical EOQ model Second, the revised EOQ model prefers small lot sizes and frequent deliveries Last, but not the least, the revised EOQ model aims to reduce the actual total inventory ordering and carrying cost, while the classical EOQ model aims to reduce the sum of the inventory ordering cost and a part of the inventory carrying cost The last point makes it very clear that the revised EOQ model is

more suitable than the classical EOQ model in representing the total annual cost under the EOQ system when comparing the EOQ system with the JIT purchasing system

The JPTV models are developed for two scenarios The first scenario does not consider a price discount The second scenario considers a price discount

6.3 EOQ-JIT cost indifference point under the revised EOQ model

6.3.1 EOQ-JIT cost difference function under the revised EOQ model

Based on assumption No 8 in Table 1.1, Fazel (1997) and Fazel et al (1998) suggested

that the total annual cost under the JIT purchasing system was the product of the unit price under the JIT purchasing system and the annual demand As suggested earlier, this proposition did not consider the additional costs and benefits resulting from JIT purchasing Hence, the total annual cost under the JIT purchasing system for the JPTV models is proposed to be the product of the unit price under the JIT purchasing system (P ) and the annual demand ( D ) plus the additional costs and benefits resulting from JIT J

purchasing, given by:

ξ+

= D P

TC Jr J (6.4) where: TC is the total annual cost under the JIT purchasing system for the JPTV Jr

flexibility of production, reduced waste and increased organizational

competitiveness under the JIT purchasing system The additional benefits of JIT purchasing contribute negatively to ξ

It is essential to highlight that the cost of the inventory physical plant space reduction in the JIT purchasing system has been assumed to take its maximum value and is considered

in the total annual optimal cost under the revised EOQ system This is because (a) the maximum value of the inventory physical plant space reduction under the JIT purchasing system is the inventory physical plant space under the EOQ system; and (b) the inventory physical plant space under the EOQ system has been considered as a component of

inventory carrying costs and included in “ H ” in Eq (6.3) The inventory physical plant

space reduction was proposed by Schniederjans and Olsen (1999) and Schniederjans and Cao (2000, 2001)

The total annual optimal cost under the revised EOQ model where the price discount is not considered (TC ) has been presented in Eq (6.3) The cost difference between the Er

revised EOQ system and the JIT purchasing system is thus given by:

ξ

−

−+

Z r 2 E J (6.5) where: Z is the cost difference between the revised EOQ system and the JIT purchasing r

J E

Note that 2kH is always positive 4 D− 3 / 2 is also always positive, as D is above zero

Hence d dD2Z2r, the second order derivative of Z with respect to D , is always negative r

According to the theorem of the second derivative test for maxima and minima of functions, two counts for the cost difference function can be concluded First, the curve

of the cost difference function Z is concave downwards Second, the cost difference r

between the EOQ and the JIT system is maximized at the demand level, at which 0

where: D is the maximum cost advantage point max

The maximum cost advantage of using a JIT purchasing system over an EOQ system can

be derived by substituting D for D in Eq (6.5) and its value is given by: max

( − )−ξ

=

E J

Zmax 2 (6.9)

where: Zmaxr is maximum cost advantage of using a JIT purchasing system over an EOQ

system

It should be noted that Eq (6.9) is applicable for computing the maximum cost advantage

of using the JIT purchasing system over the EOQ system only if the order size in the EOQ system equals the optimal economic order quantity Should the order quantity in the EOQ system not follow the optimal economic order quantity, the cost advantage of using the JIT purchasing system over the EOQ system would be given by:

ξ

−

−++

P P kH kH

422

1

ξ (6.11)

where: D indr1 is the lower EOQ-JIT cost indifference point under the revised EOQ

2

E J

E J E

J indr

P P

P P kH H

k P

P P kH kH

422

2

ξ (6.13)

where: D indr2 is the upper EOQ-JIT cost indifference point under the revised EOQ

system

The value of D indr2 is given by:

2 2 2

2

E J

E J E

J indr

P P

P P kH H

k P

When the sum of the additional costs and benefits of JIT purchasing equals zero, the upper EOQ-JIT cost indifference point (D indr2) equals

P −kH Fazel’s (1997) and Schniederjans and Cao’s (2001) studies were also focused

on the scenarios where ξ was equal to zero It is thus essential to compare the present study with that of Fazel’s (1997) and Schniederjans and Cao’s (2001) models

A comparison of the present study with that of Fazel’s (1997) model

other parameters, namely, k , P and J P remain unchanged This is because some of the E

inventory physical storage costs were not accounted for in D indF It should be noted that the EOQ-JIT cost indifference point proposed by Fazel (1997) is even less than D indF This has been explained in the explanation notes for Eq (3.7) in Section 3.3.1 Hence, the revised EOQ-JIT cost indifference point (D indr2) is substantially greater than the EOQ-JIT cost indifference point proposed by Fazel (1997) Again, this finding suggests that the JIT system can still remain cost effective even at a high level of annual demand, thus invalidating Fazel’s (1997) conclusion that JIT was cost effective only at low level of annual demand (Schniederjans and Cao, 2001) This conclusion is in line with what was reached in Chapter 3

A comparison of the present study with that of Schniederjans and Cao’s (2001) model

The concept of the carrying capacity of an inventory facility, which has been developed

in Chapter 3, can assist to compare the present study with that of Schniederjans and Cao’s (2001) model Eq (3.12) suggests that the carrying capacity of an inventory facility is governed by αE

h

N

Q = When selecting an inventory purchasing approach, it is possible

to design the size of the inventory facility proportionate to the optimal economic order quantity amount of inventory, orQ h =bQ r∗, where b is the stock flexibility parameter

and has been explained in Chapter 3 and Chapter 4 Substituting Q h =bQ r∗ into N =αE Q h, would result in N E =αbQ r∗ This is the formula of the floor area of an inventory facility determined by the inventory optimal economic order quantity Substituting

( 2 )2

E J

= into Eq (6.2), the optimal economic order quantity at the revised

EOQ-JIT cost indifference point ( ∗

rind

Q ) can be derived as

E J rind P k P

EOQ system can accommodate the EOQ-JIT cost indifference point’s amount of inventory The cost of the inventory physical plant space under the revised EOQ system

can be balanced by the JIT purchasing system For example, if F represents the annual

cost to own and maintain a square meter of physical inventory plant space, 2αbF is then

a component of H This again suggests that Schniederjans and Cao (2001) overlooked

that it was possible for an inventory facility to hold the EOQ-JIT cost indifference point’s amount of inventory when the floor area of an inventory facility reached N Eind : the minimum area of the inventory facility to house the EOQ-JIT cost indifference point’s amount of inventory This conclusion is in line with what was reached in Chapter 3 Another expression of this finding is that an EOQ based system can be more cost effective than a JIT purchasing system when the floor area of the inventory facility is above N Eind and the magnitude of the annual demand is above the EOQ-JIT cost indifference point, which equals

( 2 )2

E

P −kH

6.3.3.2 ξ is greater than zero

Eqs (6.11) to (6.14) can have three implications when the additional costs resulting from

JIT purchasing are greater than the additional benefits resulting from JIT purchasing First, Eqs (6.11) and (6.12) suggest that the JIT purchasing approach may not be a cost effective alternative for inventory purchasing, provided the annual demand of the inventory is less than the lower EOQ-JIT cost indifference point Second, Eqs (6.13) and (6.14) suggest that the additional costs resulting from JIT purchasing shift the upper EOQ-JIT cost indifference point (D ) to be less than

( 2kH ) Third, the EOQ

approach can always be preferred to the JIT purchasing approach, provided that the additional costs resulting from JIT purchasing are substantially high The analysis of the third implication is presented below

Eq (6.5) can be rewritten as:

J E

6.3.3.3 ξ is less than zero

Eq (6.11) suggests that D indr1 is not a feasible cost indifference point, when the sum of the additional costs and benefits resulting from JIT purchasing (ξ) is less than zero This

is because D indr1 is negative when ξ is less than zero However, D indr2 , which is given

by Eq (6.14), is still a feasible EOQ-JIT cost indifference point Eqs (6.13) and (6.14) suggest that the additional benefits resulting from JIT purchasing shift D indr2 to be a

value that is greater than

6.4 EOQ-JIT cost indifference point under the revised EOQ with a price discount model for the RMC industry

6.4.1 Existing EOQ with a price discount models

The cost incurred by suppliers is usually a decreasing function of the size of the delivery lot; the delivery price of an inventory is thus usually a decreasing function of the order

quantity (Fazel et al., 1998) Goyal and Gupta (1989) concluded that there were three basic types of price discount models, namely, Two-Part Tariff, Two-Block Tariff and All

Unit Quantity Discount In the Two-Part Tariff price discount model, “the buyer is required to pay a fixed charge and a uniform price p for all units purchased Although

the buyer pays the same marginal unit price for all quantities, the average price paid is a monotonically decreasing function of quantity purchased” (Goyal and Gupta, 1989,

p.263) In the Two-Block Tariff price discount model, “the price of a unit, p1, is

maintained up to a quantity x , the per unit price p2 is charged for all units in excess of quantity (p >1 p )” (Goyal and Gupta, 1989, p.263) In the All Unit Quantity Discount 2

model, when “a buyer buys less than a quantity x , the price of all units is decreased” (Goyal and Gupta, 1989, p.263) Britney et al (1983a, b), Dolan (1987) and Wilcox et al

discount models The price discount scheme proposed by Fazel et al (1998) was one variation of the All Unit Quantity Discount model, as the buyer paid the same unit price for every unit purchased (Fazel et al., 1998)

6.4.2 Critics on the price discount scheme of Fazel et al (1998)

As stated in Chapter 4, the EOQ-JIT cost difference functions of Schniederjans and Cao

(2000) and the EOQ-JIT cost difference functions Fazel et al (1998) were both based on

a price discount scheme proposed by Fazel et al (1998) The price discount scheme had

two assumptions a) For quantities below a certain level (Qmax) the delivery price was a decreasing, continuous and linear function of the order quantity b) Beyond Qmax , however, the price stayed at its minimum ( min

E

P ), which was the lowest price the supplier would charge, no matter how large the order quantity was The discount functions are mathematically defined as:

≤

−

=

−

=

=

max min

max 0

0

0

Q Q P

Q Q dQ

dP or

Q P

Q P

P

E

E

E E

E

E

E π π (6.16)

where 0

E

P , Q and πE were explained in Chapter 4

It seems that the price discount scheme proposed by Fazel et al (1998) may not fit well

into the reality in the RMC industry on at least two counts Firstly, the initial condition

for the first-order differential equation dQ dP E =−πE in the price discount model ( 0

E

P ), may

not even be a feasible price, as there may be a minimum order size so that an

infinitesimally small order size is not possible in RMC industry The lowest order quantity (Qmin) which one can order must be one with an unit price of 1

E

P , if the inventory is not divisible, for example, one truck of bulk Portland cement Secondly, the intensive site studies by the author and the in-depth discussion with the general manager

of RMC supplier L in Chongqing, China and the production manger of I S in Singapore suggested that a greater price discount can usually be offered by the raw materials suppliers, if the order quantity was to be increased There is no such things as min

E

P Nevertheless, there was a maximum order quantity limit for an individual RMC supplier The maximum order quantity limit for each individual RMC suppliers was usually governed by either the inventory carrying capacity of the inventory facility in the RMC batching plant or the production capacity of the raw material supplier, whichever was less The general manager of RMC supplier L and the production manager of I S made their suggestions based on their work experience in the RMC industry

6.4.3 A price discount scheme for the RMC industry

Based on the above analysis, to fit the RMC industry, a new price discount scheme that incorporate the reality in the RMC industry is suggested based on the price discount

scheme proposed by Fazel et al (1998) and is given below The delivery price per unit

starts from Qmin

E

P , where Qminis the lowest order quantity that can be placed The delivery price is then a decreasing, continuous, and linear function of the order quantity for the rest of the order quantity that is below a certain level (Qmax) Qmax is determined by the inventory carrying capacity of the RMC supplier and the production capacity of the raw

material supplier, whichever is less This discount scheme is shown graphically in Figure 6.1

Figure 6.1 The EOQ price discount scheme proposed for the RMC industry

The discount function can be mathematically presented as:

6.4.4 Revised EOQ with a price discount model for the RMC industry

The revised EOQ with a price discount model for the RMC industry is developed by incorporating the price discount scheme of the RMC industry in Eq (6.17) into the

revised EOQ model in Eq (6.1) The total annual cost under the revised EOQ with a price discount model is the sum of the inventory ordering cost, the expanded inventory carrying cost and the cost of the actual purchased units, and is thus given by:

QH Q

kD

E Erd = + 2 + min +π min −π for Qmin ≤Q≤Qmax (6.18) where: TC is the total annual cost under the revised EOQ with a price discount model Erd

Q is the optimum order quantity which minimizes the total cost under the

revised EOQ with a price discount system

It should be highlighted that the optimum order quantity of the revised EOQ with a price discount model ( ∗

rd

Q ) in Eq (6.19) is significantly less than the optimum order quantity

of the EOQ with a price discount model ( ∗

r

Q ) in Eq (4.3), which was proposed by Fazel

et al (1998) This is because the annual cost of carrying one unit of inventory in the revised EOQ with a price discount model is substantially greater than that in the models

of Fazel et al (1998), provided the values of the other parameters, namely, D , k and πE remain unchanged

6.4.5 EOQ-JIT cost indifference point under the revised EOQ with a price discount model for the RMC industry

Eq (6.19) results in the total annual optimal cost under the revised EOQ with a price discount system as:

D D

Q P

E

Q E E

E

for Qmin ≤Q≤Qmax (6.20)

Eq (6.20) is valid only when the inventory is ordered at its optimal economic order quantity The total annual cost under the JIT system (TC Jr) is still the same as given in

Eq (6.4) The difference between the total annual optimal cost under the revised EOQ with a price discount system in Eq (6.20) and the total annual cost under the JIT purchasing system in Eq (6.4) is thus:

ξπ

ππ

π

−

−+

+

−+

−

E E

E

Q E E

P P kH H

k Q

P P kH

D

E E

Q E J

E E

Q E J E

Q E J indrd

ππ

ξππ

ξπ

ξ

4

42

2 min

2 min

2 2 min 1

min

min min

for Qmin ≤Q≤Qmax (6.22) where: D indrd1 is the lower EOQ-JIT cost indifference point under the revised EOQ with a

price discount system for the RMC industry

k Q

P P kH H

k Q

P P kH

D

E E

Q E J

E E

Q E J E

Q E J indrd

ππ

ξππ

ξπ

ξ

4

42

2 min

2 min

2 2 min 2

min

min min

a price discount system for the RMC industry

The models in Eq (6.12), Eq (6.14), Eq (6.22) and Eq (6.23) are the JIT purchasing threshold value (JPTV) models suggested in this study

6.4.6 Discussion

Eq (6.22) and Eq (6.23) also indicate that the sum of the additional costs and benefits resulting from JIT purchasing (ξ) is an important factor that affects the lower and upper EOQ-JIT cost indifference points under the revised EOQ with a price discount system

As suggested earlier, ξ is not a constant and may have three scenarios: 1) ξ is equal to zero; 2) ξ is greater than zero; and 3) ξ is less than zero The lower and upper EOQ-JIT cost indifference points under the revised EOQ system are thus also discussed below for the three scenarios

It can be proved that the EOQ system is more cost effective than the JIT purchasing system when the annual demand is above the upper EOQ-JIT cost indifference point (D indrd2) and if the price discount rate (πE) is small It can also be proved that the JIT purchasing system is more cost effective than the EOQ system when the annual demand

is below D indrd2 and if the price discount rate (πE) is small

When ξequals zero, D indrd2 can be simplified as

kH

E E

Q E

2

2 min

E = +π The cases where both ξ and Q are equal to zero was the scenario min

that had been studied by Fazel et al (1998) and Schniederjans and Cao (2000) Hence, it

is essential to compare this present study with the studies of Fazel et al (1998) and

Schniederjans and Cao (2000)

A comparison of this present study with the study of Fazel et al (1998)

JIT cost indifference point proposed by Fazel et al (1998) Again, this finding suggests

that the JIT purchasing system can still be cost effective even at a high level of annual

demand, thus modifying the conclusion of Fazel et al (1998) that JIT purchasing was

cost effective only at a low level of annual demand, when a price discount was available This conclusion is in line with what was reached in Chapter 4

A comparison of this present study with the study of Schniederjans and Cao (2000)

Again, the concept of the carrying capacity of an inventory facility can assist to compare the present study with the study of Schniederjans and Cao (2000) As stated earlier, when selecting an inventory purchasing approach, it is possible to design the size of the inventory facility proportionate to the optimal economic order quantity of the inventory,

or Q =bQ∗ b is the stock flexibility parameter Q is the optimal economic order ∗

quantity under the revised EOQ with a price discount model which is given in Eq (6.19),

N is the floor area of an inventory facility under an EOQ system

Substituting Q h =bQ rd∗ into N =αE Q h, would result in N E =αbQ rd∗ , namely, the formula

of the area of an inventory facility governed by its optimal economic order quantity under the revised EOQ with a price discount system Substituting the simplified formula of

Q the optimal economic order

quantity at the revised EOQ-JIT cost indifference point (D indrd2) can be derived as

Q in N E =αbQ rd∗ , would result in the

minimum area of the inventory facility under the revised EOQ with a price discount system that can accommodate the EOQ-JIT cost indifference point’s amount of inventory

E J Edind P bk P

N = α− Hence, the total cost under the revised EOQ with a price

discount system will be equal to the total cost under the JIT purchasing system, provided

that (1) the inventory space reaches 2 0

be balanced by the JIT purchasing system by including 2αbF as a component of H

This again suggests that Schniederjans and Cao (2000) overlooked that it was possible for

an inventory facility to hold the EOQ-JIT cost indifference point’s amount of inventory when the floor area of an inventory facility reached N Edind Hence, another expression of this finding is that an EOQ based system can be more cost effective than a JIT purchasing system when a) the size of the inventory facility is above N Edind, and b) the magnitude of the annual demand is above the EOQ-JIT cost indifference point D indrd2, and c) the optimal economic order quantity is below Qmax As suggested earlier, N Edind is the minimum area of the inventory facility that can accommodate the EOQ-JIT cost indifference point’s amount of inventory under the revised EOQ with a price discount system This conclusion is in line with what was reached in Chapter 4

6.4.6.2 ξ is greater than zero

When the additional costs of JIT purchasing are greater than the benefits of JIT

purchasing, Eqs (6.22) to (6.23) have three implications First, Eq (6.22) suggests that the JIT purchasing approach may not be cost effective when the annual demand is low Second, Eqs (6.23) suggests that the upper EOQ-JIT cost indifference point (D indrd2) shifts to a lower value that is less than

kH

E E

Comparing Eq (6.22) and Eq (6.23), it can be found that the condition, under which the lower cost indifference point (D indrd1) and the upper cost indifference point (D indrd2) are real, is that the sum of the additional costs and benefits resulting from JIT purchasing (ξ)

is below a specific value This value is given by:

k

Q P

P kH H k Q

P P H k

E

E

Q E J E

E

Q E J

ξ

2 min 2

2 lim

When ξ the sum of the additional costs and benefits resulting from JIT purchasing are

greater than ( )ξ limit, D indrd1 and D indrd2 are not feasible cost indifference points

In such a scenario, an EOQ system is always preferred to a JIT system

6.4.6.3 ξ is less than zero

Setting Z in Eq (6.21) to zero, Eq (6.21) can be rewritten as: rd

kD D

H kD D

Q P

P

E E

E E

is not a feasible EOQ-JIT cost indifference point when ξ is less than zero and if the price discount rate πE is small Nevertheless, D indrd2 is still a feasible EOQ-JIT cost indifference point Furthermore, it can be proved that D indrd2 is greater than

(P P ) k

kH

E E

kH

E E

a price discount is not available, which was discussed in the earlier section

6.5 Summary

This chapter developed the JPTV models for the RMC industry The JPTV models suggest that the local market conditions determine whether the EOQ or JIT purchasing method is preferred

The JPTV models can have three implications First, when the additional costs of JIT purchasing cannot be ignored and the annual demand is low, JIT purchasing may be an expensive alternative Second, when the additional costs of JIT purchasing is substantially high, the EOQ purchasing approach may always be more cost effective than the JIT purchasing approach Third, when a material can be alternatively purchased in a JIT fashion with a higher price and an EOQ fashion with a lower price, the EOQ approach can be more cost effective than the JIT approach, if the sum of the additional costs and benefits resulting from JIT purchasing is insignificant, the order quantity under the EOQ system cannot be economically split, and the annual demand is high enough The additional costs of JIT purchasing include mainly the increased out-of-stock costs

The additional benefits of JIT purchasing include mainly reduced waste and increased quality and production flexibility

The JPTV models are tested with data from the RMC industry in Chapter 7

CHAPTER 7 TESTING THE JPTV MODELS

7.1 Introduction

The aim of this chapter is to test the JIT Purchasing Threshold Value (JPTV) models developed in the previous chapter with the data on inventory procurement approaches adopted by the Ready Mixed Concrete (RMC) firms in Chongqing (China) and Singapore

The JPTV models can have three implications These implications were summarized in Section 6.5 The JPTV models were thus tested through the verification of each of these implications in real-life scenarios Section 7.2 verifies the first implication of the JPTV models by a case study pertaining to a contractor in San Francisco Section 7.3 verifies the second implication of the JPTV models by a case study pertaining to a RMC supplier

in Chongqing (China) Section 7.4 verifies the third implication of the JPTV models by a case study pertaining to a RMC supplier in Singapore The JPTV models suggest that the local market conditions determine the purchasing approach of materials Hence, the three implications of the JPTV models may not be experienced in one market Therefore, the cases presented here were from three different locations The case relating to the contractor in San Francisco was based on the information provided in Tommelein and Li’s (1999) study The data on the two cases in Chongqing and Singapore were obtained

by face-to-face interviewing the production managers or directors of the respective RMC suppliers

7.2 Verification of the first implication of the JPTV models

This case study pertained to the procurement of concrete by a private contractor in San Francisco This section aims to verify the first implication of the JPTV models

The first implication of the JPTV model is that when the additional costs of JIT purchasing cannot be ignored and the annual demand is low, JIT purchasing may be an expensive alternative It was derived from Eq (6.12) and Eq (6.22)

This contractor bided on projects from the City and County of San Francisco, the Public Utilities Commission, together with the Water Department in the US This contractor had

a fairly steady need for concrete from one project to the next However, the amount of concrete needed for most of the projects were usually small compared to what was needed for residential or office building projects

Tommelein and Li (1999) observed that this contractor might purchase his concrete from

a RMC supplier in two approaches In the first approach, the contractor placed his order according to the construction activities Based on the schedule from the contractor, the RMC batching plant prepared the mix design and order quantity one truckload at a time and then promptly delivered the concrete to the appropriate construction site of the contractor for placement This approach was shown in Figure 2.5

In the second approach, the contractor acquired his own revolving-drum trucks and drivers When concrete was needed, the contractor had his trucks pulled into any batching

plant during operating hours The contractor-owned trucks simply joined the line of plant trucks waiting to be loaded The driver then went to the batching plant operators’ walk-up window and ordered the needed mix design and quantity The batching plant filled the contractor’s trucks in the same ways as it filled its own The contractor will then be billed

on a regular basis for the exact amount loaded This approach is shown in Figure 7.1 The unit price of concrete was the same in the two approaches

Figure 7.1 Integrated ready mixed concrete delivery and placement by contractor

Source: Adapted from Tommelein and Li (1999)

Legend

A value adding process or a task An order to produce product

An accumulation of materials or information An order to withdraw product

A store in a batching plant or a market A physical pull of materials

Information is pushed to the contractor The transportation of concrete to

construction sites

Mix Concrete Batching plant

Raw material Vendor

Reorder Truck

Order raw material Batching plant

DESIGNER

BATCHING PLANT

CONTRACTOR

Transport Contractor

Specify mix

Designer

In terms of RMC purchasing by the contractor, the first approach was a typical JIT purchasing approach Nevertheless, it should be noted that sand, aggregates and cement needed by the RMC batching plant in Figure 7.1 was also purchased in an EOQ (or non-JIT) approach The purchasing of sand, aggregates and cement by RMC batching plants

in Figure 7.1 is similar to that as depicted in Figure 2.5 The second approach for purchasing of RMC by the contractor was not geared to JIT, as the contractor needed to have his capital tied up in trucks and be responsible for hiring and training drivers This was despite that the contractor had to pay the same unit price of concrete as that in the first approach It was for this reason that the second approach was a non-JIT approach, even though the concrete was also purchased by demand from the construction activities

Tommelein and Li (1999) observed that this contractor acquired a fleet of small (5 to 7

3

yd ) revolving-drum trucks as well as dump trucks (used for filling “potholes” with

concrete) and adopted the second approach to purchase his concrete They argued that to avoid the costs resulting from the tardiness in concrete delivery was the main motivation for the contractor to adopt this approach There were two specific reasons for this motivation

First, this approach could overcome many scheduling hassles No advance order needed

to be placed to reserve plant capacities as only a few cubic yards of commodity mix were needed each time By taking control of the transportation process, the contractor’s crews could work at their own pace and not have to fret when concrete would arrive Second, this approach can avoid the tardiness in concrete delivery All projects of the contractor

were in the urban area The owners of these projects thus imposed limits on working hours This was to avoid congestion during peak traffic times, excessively long closure of road for vehicular- or of a sidewalk for pedestrian traffic, and complaints about noise from citizens or residents However, this contractor could not get any batching plant’s attention, because each of his orders was only about a few cubic yards each time Hence, the tardiness in concrete delivery could not be avoided, provided that the concrete was delivered by means of the first approach The contractor might be fined or even lose his contract, if the site could not be open frequently to traffic when needed

Based on the analysis above and Eqs (6.1) and (6.4) in Chapter 6, the total annual costs under the second approach (TC ) are given by: Er

=

Er

TC Inventory holding costs + PD (7.1)

where: inventory holding costs are the costs of the capital tied up by the revolving-drum

trucks as well as dump trucks,

P is the purchase price per cubic meter of concrete, and

D is the annual demand of concrete

The total annual costs under the first approach are given by:

=

Jr

TC PD+ ξ (7.2) where: ξ is the sum of the additional costs and benefits resulting from JIT purchasing It

is mainly the additional costs resulting from the tardiness in concrete delivery by the RMC supplier

Tommelein and Li (1999) also observed that those contractors who engaged in residential

or office building projects usually adopted the first approach for purchasing their concrete, as the amount of concrete needed in those projects were usually high Hence, there should be a break-even point between the total annual costs under the first approach and that under the second approach However, the value of the break-even point could not

be computed here, as the relevant cost information was not provided in the study published by Tommelein and Li (1999)

RMC purchasing by the private contractor in San Francisco showed that the JIT

purchasing approach might be an expensive alternative In the RMC industry, Wang et al

(2001b) also suggested that 10 per cent of the concrete needed by the construction industry in Singapore was site mixed, rather than delivered in a JIT fashion from off-site RMC batching plants The Chongqing Construction Committee stipulated that concrete was allowed to be site mixed for a construction project in the urban area, provided that the amount of concrete needed by the construction project is less than 500

3

m (Chongqing Construction Committee, 2000)

Outside the RMC industry, Temponi (1995) also observed that JIT usually could not be effectively implemented in small-sized manufacturing firms There were two possible reasons First, the material supplier might not have interest to act in a JIT fashion when the annual demand was low This is because the low annual demand of the buyer might mean insignificant profit reaped by the material supplier Second, the material supplier might have difficulties in delivering the material to the small buyer in a JIT fashion, as

his facilities have to be arranged to serve the larger buyer, leading to high out-of-stock costs faced by the small buyer

This case study suggested that it might not be economical to adopt the JIT purchasing approach to purchase materials, if the annual demand was low and the additional costs resulting from JIT purchasing could not be ignored This is despite that the JIT operations could capitalize on physical plant space reduction This conclusion supports Eq (6.12) and Eq (6.22) in the JPTV models It should be noted that Eqs (7.1), (7.2), (6.12) and (6.22) were all developed based on Eqs (6.1) and (6.4)

7.3 Verification of the second implication of the JPTV models

This case study pertained to the procurement of sand by RMC supplier L in Chongqing This section aims to verify the second implication of the JPTV models

The second implication of the JPTV models is that when the additional costs of JIT purchasing is substantially high, the EOQ purchasing approach may be more cost effective than the JIT purchasing approach

7.3.1 The background of RMC supplier L

This RMC supplier was located in the Yuzhong District in Chongqing It had one batching plant (60 m /3 h), three cement silos (100 ton / silo), five RMC revolving trucks,

38 staff (10 management staff and 28 technicians) and two concrete pumps This RMC supplier used an EOQ system to procure its sand The data for this case study were