CHAPTER INTRODUCTION 1.1 Background The percentage of the inventory investment with respect to the total assets in a firm, although varies from industry to industry, can make up as much as 49 per cent in some firms (ROI, 2004) Among others, the stockpile of inventory gives a firm the flexibility to take an unexpected order (Wu and Low, 2005a) But redundant inventories tie up capitals Hence, inventories are important assets in many firms and inventory control is crucial (Axsater, 2000) With inventory control, there are two conflicting goals: minimizing the amount of money tied up in inventory and never be out of inventory when an order is received (AAX, 2004) How much to order is, therefore, one of the problems that have to be addressed when purchasing raw materials (Silver, 1998) The quantity of material within an order can be worked out through the Economic Order Quantity (EOQ) approach EOQ is the quantity of material within an order that minimizes the total costs that are required to order and hold inventory (Harris, 1915; Peterson and Silver, 1979; Fazel, 1997) EOQ, also called the optimum economic order quantity or optimum order quantity, is regarded as the conventional method for purchasing materials This approach leads to the placing of large-sized and infrequent orders (Schonberger, 1982a) The EOQ approach was originally conceptualized by Harris (1915) Ray and Chaudhuri (1997) and Charabarty et al (1998) suggested that this approach had been a fundamental technique for inventory management decisions and continued to be the starting point for the development of many subsequent inventory purchasing models The quantity of material within an order can also be determined through the Just-In-Time (JIT) approach (Monden, 1983; Low and Chan, 1997), which advocates smaller-sized and more frequent orders This approach, originally explored by Kanzler as a method for reducing inventory levels at the Fordson Tractor Plant in the 1920s (Peterson, 2002), attracted much attention because of the excellent productivity and quality achieved in Toyota Motor Company (Monden, 1993) JIT purchasing is an important technique of the JIT philosophy, which is regarded as one of the most important productivity enhancement management innovations of the 20th century in the manufacturing industry (Schonberger, 1982a) The JIT approach provides the right materials, in the right quantities and quality, just in time for production (Vokurka and Davis, 1996) This approach, also widely referred to as the Toyota Production System (Monden 1998), has evolved into the Lean Manufacturing System (Womack, et al., 1990; Watanabe, 1999; Feld, 2001; Askin and Goldberg, 2002; Strategosinc, 2004) Although it was originally introduced in the manufacturing industry, the implementation of the JIT purchasing approach has been extended beyond that Its successful implementation in many industries prompted many companies that are still using the EOQ approach to ponder whether they should switch to the JIT purchasing approach for managing their inventories 1.2 Research problem Ready Mixed Concrete (RMC) is an important building material that is widely used today in the construction industry (Anson et al., 2002) RMC mixing is a prototypical example of JIT construction processes (Tommelein and Li, 1999) Inspired by the success achieved through the implementation of the JIT philosophy in the manufacturing industry, Wu and Low (2003) and Low and Wu (2005a, b) investigated the implementation status of JIT purchasing in the RMC industries in Chongqing and Singapore through surveys The results of the surveys are presented in Chapter The surveys found that both the EOQ approach and the JIT purchasing approach were adopted by companies to manage the procurement of raw materials in the RMC industry The JIT purchasing approach results in an advantage of maintaining relatively smaller inventories and thereby reducing the plant space Hence, the existing EOQ-JIT cost indifference point models concluded that the JIT purchasing approach was always preferred to the EOQ approach, provided that the JIT purchasing approach could experience and capitalize on this physical plant space reduction (Schniederjans and Olsen, 1999; Schniederjans and Cao, 2000, 2001) The EOQ-JIT cost indifference point is the level of demand at which the costs of the two inventory management systems are the same However, this conclusion was not consistent with the industry practice, leading to a need to re-examine the presently available EOQ-JIT cost indifference point models In a closer examination of the existing EOQ-JIT cost indifference point models, it could be found that these models had two limitations First, these models did not either theoretically or empirically ascertain the capability of an inventory facility to hold the EOQ-JIT cost indifference point’s amount of inventory Second, these models also ignored some important cost components of the inventory purchasing systems These costs included, but not limited to, the impact of inventory purchasing policy on product quality, production flexibility and out-of-stock costs These costs are the additional costs resulting from JIT purchasing Because of these two limitations, these models cannot clearly explain the inventory purchasing approaches adopted in the RMC industry The research problem is further explained in Section 3.2 1.3 Research aim and objectives Based on the above background, the aim of this study is to develop JIT Purchasing Threshold Value (JPTV) models for a RMC supplier The study is based mainly on the information obtained from two RMC markets, namely, Chongqing in China and Singapore The reasons for investigating these two cities are presented in the first paragraph in Section 2.1 The objectives of this study are: • To investigate the implementation status of JIT in the RMC industry in Chongqing and Singapore; • To introduce two new concepts, namely, the annual carrying capacity of an inventory facility, and the break-even point between the annual carrying capacity of an inventory facility and the EOQ-JIT cost indifference point This is to examine the capability of an inventory facility to hold the EOQ-JIT cost indifference point’s amount of inventory under the EOQ without price discount system; • To extend these two new concepts from the EOQ without price discount system to the EOQ with a price discount system This is to examine the capability of an inventory facility to hold the EOQ-JIT cost indifference point’s amount of inventory under the EOQ with a price discount system; and • To develop and test the JPTV models for the RMC industry This is to investigate the additional costs and benefits resulting from JIT purchasing in the RMC industry and examine how the additional costs and benefits resulting from JIT purchasing may impact on the EOQ-JIT cost indifference point Inventory facility is defined as a physical plant space where raw materials, goods or merchandise are stored In the RMC industry, an inventory facility can be a storehouse, a warehouse, an aggregates depot, a sand yard or a cement terminal The annual carrying capacity of an inventory facility is defined as the amount of inventory that can be held by the inventory facility in a year, assuming each unit of inventory takes up a fixed amount of area of the inventory facility and the inventory is ordered at its optimal economic order quantity 1.4 Significance of this study The JPTV models are revised EOQ-JIT cost indifference point models derived by the author in which the additional costs and benefits resulting from JIT purchasing, including reduced inventory physical storage cost, have been considered These JPTV models would be able to overcome the two limitations of the presently available EOQ-JIT cost indifference models The JPTV models can help the RMC supplier to decide whether the company should switch to the JIT purchasing approach if the RMC supplier is still adopting the EOQ approach to manage the procurement of his raw materials 1.5 Research hypothesis The research hypothesis for this study is that the EOQ approach is preferred to the JIT purchasing approach in managing material’s procurement when the additional costs resulting from the JIT purchasing approach is high and when the annual demand is extremely low or high This is evident even when the JIT operation can experience and capitalize on physical plant space reduction 1.6 Research strategy and assumptions in this study The research strategy of this study is to expand upon only one of the assumptions of the platform created by Fazel (1997), Fazel et al (1998) and Schniederjans and Cao (2000, 2001) to develop the JPTV models for the RMC industry This study is based mainly on the platform created by these researchers This is to demonstrate that the reasonable extension of only one assumption can lead to substantially different conclusions than those reached by the previous researchers Based on the research strategy, the study consists of three phases, as shown in Figure 1.1 Phase of this study identifies the research problem through literature review and field study The EOQ-JIT cost indifference point models of previous researchers cannot ascertain the capability of the inventory facility to hold the cost indifference point’s amount of inventory Hence, Phase theoretically and empirically examines this capability of the inventory facility The examination is approached by analyzing both the EOQ system and the EOQ with a price discount system This is because the previous researchers’ EOQ-JIT cost indifference points were developed for both the EOQ with or Literature review on JIT elements Literature review on EOQ-JIT cost indifference point Survey of JIT implementation status in RMC industry in Chongqing JIT purchasing is virtually always preferred to EOQ purchasing when JIT purchasing can capitalize on physical plant space reduction Survey of JIT implementation status in RMC industry in Singapore EOQ and JIT purchasing are concurrently adopted in the RMC industry Phase Identification of research problem Theoretically examine the capability of the inventory to hold the EOQ-JIT cost indifference point’s amount of inventory under the EOQ system Theoretically examine the capability of the inventory to hold the EOQ-JIT cost indifference point’s amount of inventory under the EOQ with a price discount system Empirically examine the capability of the inventory to hold the EOQ-JIT cost indifference point’s amount of inventory Phase Development of the JPTV models for the RMC industry Testing of the JPTV models in the RMC industry Phase Figure 1.1 The research strategy without a price discount systems The JPTV models for the RMC industry developed in Phase also cover these systems The detailed work of each phase is presented in Section 1.7 This study is based on nine assumptions shown in Table 1.1 The first eight assumptions made up the platform created by Schniederjans and Cao (2000, 2001), which was developed from the studies of Harris (1915), Fazel (1997) and Fazel et al (1998) Table 1.1 Assumptions made in the study Assumptions made by previous researchers Ordering cost under the EOQ system is fixed per order (Harris, 1915) Carrying cost under the EOQ system for the inventory item is constant on a per unit basis (Harris, 1915) The inventory physical storage costs, for example, rental, utilities and personnel salaries should be treated as variable costs (Schniederjans and Cao, 2000, 2001) Annual demand for the item is known and constant (Harris, 1915) The unit price per item under the EOQ or JIT purchasing system remain constant (Fazel, 1997; Fazel et al., 1998) Orders under the EOQ system are arranged in such a way that the succeeding delivery arrives at the time that the quantity from the previous delivery has just been depleted (Harris, 1915); or “safety stock costs required in an EOQ model are balanced out by other costs incurred in the use of a JIT model”(Schniederjans and Cao, 2001, p.112) Hence, safety stocks under the inventory systems are not considered The order under the EOQ system are raised at the optimal economic order quantity (Fazel, 1997; Fazel et al., 1998) The materials suppliers of the JIT companies produce and store their products in large batches and respond to the JIT challenge by delivering them in small quantities The carrying and ordering costs (e.g storage, inspection, transportation, preparation of purchasing orders for each delivery, etc ) of the JIT company were mainly transferred to the material suppliers and solely reflected in the unit price to the JIT company Therefore, the unit price under the JIT purchasing system, which includes the portion of carrying and ordering costs that are passed onto the the buyer, is higher than the unit price under the EOQ system (Fazel, 1997; Fazel et al., 1998) Assumption made by the author The inventory physical storage costs, for example, rental, utilities and personnel salaries under the EOQ system are linearly related to the average inventory level Assumption No states the author’s own position It assumes that the inventory physical storage costs under the EOQ system, for example, rental, utilities and personnel salaries are linearly related to the average inventory level Assumption No was expanded from assumption No This is to expand the “total carrying costs” in the classical EOQ model to include the inventory physical storage costs This assumption is possible when selecting an inventory purchasing approach either for a new entrant or for an existing company which is considering switching from the EOQ approach to the JIT purchasing approach The rationale for Assumption No is presented in Section 3.3.1 In this study, the scenario, in which the assumptions No to No are satisfied concurrently, is defined as boundary condition The scenario, in which the assumptions No to No and assumptions No to No are satisfied concurrently, is defined as boundary condition Boundary condition is a sub-set of boundary condition (see Figure 1.2) Boundary condition (Assumptions 1, 2, 3, 4, 5, 6, 7, 8) Boundary condition (Assumptions 1, 2, 4, 5, 6, 7, 8, 9) Figure 1.2 Boundary condition versus boundary condition It may be argued that the inventory physical storage costs under the EOQ system is not necessarily linearly related to the average inventory level However, it can be argued that assumption No has a bias against the EOQ system This study shows that it is still possible for the EOQ system to be more cost effective than the JIT purchasing system even when a) the JIT operation can experience physical plant space reduction; and b) an unfavorable assumption is made against the EOQ system It should also be noted that assumptions No to No are seldom met exactly in real life situations However, they can help develop models to select an appropriate inventory purchasing approach In addition, these assumptions are the components of the platform created by previous researchers For these reasons, they are also adopted in this study 1.7 Structure of the thesis Following the research strategy, the study is presented in eight chapters Figure 1.3 shows the relationship between the chapters and the three phases of the research strategy Figure 1.3 should be read together with Figure 1.1, as Figure 1.3 was developed from Figure 1.1 The content of the chapters are as follows: Chapter describes the JIT techniques and investigates the implementation status of JIT techniques in the RMC industry in Chongqing and Singapore The field study conducted in the two cities revealed that almost all the RMC suppliers were using the demand pull system to manage RMC production and delivery The field study also found that the raw 10 Again, it is essential to highlight that although the term “EOQ-JIT cost indifference ∗∗ point” is used to refer to Eq (4.41), DinddEo may not be a feasible cost indifference point between the EOQdAboveQmax system and JIT purchasing system, as the initial size of the ∗∗ inventory facility ( N Eo ) may not be capable of accommodating DinddEo amount of inventories 4.5.2 Annual carrying capacity of an inventory facility under the AboveQmax system EOQd The formula of the annual carrying capacity of an inventory facility under the AboveQmax system can also be derived from the concept of “the carrying capacity of an EOQd inventory facility” and the concept of “the optimal economic order quantity” under the AboveQmax system Based on the definition of the carrying capacity of an inventory EOQd facility under the EOQ system, the “the carrying capacity of an inventory facility” under the AboveQmax system is also defined as the amount of inventory that can be held by the EOQd inventory facility at a specific time, or: N ∗∗ Qhd = αE ∗∗ where: Qhd is the carrying capacity of an inventory facility under (4.42) AboveQmax system, EOQd α is the area occupied by an unit of inventory in the inventory facility To allow for flexibility, the size of the inventory facility also should be designed to be greater than the size needed to hold the exact amount of optimal economic order quantity amount of inventory Assuming the size of the inventory facility under the 123 AboveQmax system is b times the size which holds the optimal economic order quantity EOQd amount of inventory, would result in ∗∗ ∗ Qhd = bQd ∗ (4.43) Where: b is the stock flexibility parameter and has been explained earlier Supposing the size of the inventory facility under the AboveQmax system is designed EOQd based on its optimal economic order quantity and the carrying capacity of the inventory facility is as suggested by Eq (4.43), substitute Eq (4.43) into Eq (4.42), the floor area of an inventory facility under the AboveQmax system governed by its optimal order size EOQd can then be derived as: ∗ N E = αbQd ∗ (4.44) N ∗ ∗ Eq (4.4) can be rewritten as D = h Qd ∗2 Eq (4.44) can be rewritten as Qd ∗ = E αb 2k NE ∗ Substituting Qd ∗ = h ∗∗2 αb into D = 2k Qd , the annual inventory demand indicated by the floor area of the inventory facility under the D = AboveQmax system can be derived as: EOQd hN E 2kb2α (4.45) According to the definition of the annual carrying capacity of an inventory facility under the EOQ with a price discount system, the annual carrying capacity of an inventory facility under AboveQmax system is the carrying capacity of an inventory facility EOQd multiplied by the annual inventory ordering frequency, or: 124 ∗∗ ∗∗ Dhd = Qhd D∗ ∗ Qd (4.46) ∗∗ where: Dhd is the annual carrying capacity of an inventory facility under AboveQmax system, and EOQd D ∗ Qd ∗ is the annual inventory ordering frequency Substituting Eq (4.43) and Eq (4.45) into Eq (4.46), would result in the annual carrying capacity of an inventory facility under the ∗∗ Dhd = AboveQmax system as: EOQd hN E 2kbα (4.47) For the purpose of flexibility and safety, again, it is essential to revise the annual carrying capacity of an inventory facility under the ∗∗ AboveQmax system by dividing Dhd by the EOQd stock flexibility parameter ( b ), resulting in: safe Dhd ∗∗ = hN E 2kb2α (4.48) safe where: Dhd ∗∗ is the revised annual carrying capacity of an inventory facility for the AboveQmax system EOQd safe Dhd ∗∗ has considered the flexibility and safety factor Hence, the term “the annual carrying capacity of an inventory facility under the AboveQmax system” in the EOQd safe ∗∗ remaining analysis refers to Dhd ∗∗ in Eq (4.48), rather than Dhd in Eq (4.47) 125 Substituting the initial size of the inventory facility ( N Eo ) for N E in Eq (4.48), yields the annual carrying capacity of an inventory facility system at its initial size under the AboveQmax as: EOQd ∗∗ DhdEo = hN Eo 2α 2kb (4.49) ∗∗ where: DhdEo is the annual carrying capacity of an inventory facility system at its initial size under the AboveQmax EOQd Based on the function of the annual carrying capacity of an inventory facility under the AboveQmax system (Eq (4.48)), the condition for Eq (4.40) may be mathematically EOQd rewritten as: ( ) FN E PJ − PEmin +kh+ k h + 2kh(PJ − PEmin )FN E (P J ≤ ) E −P hN E 2α 2kb (4.50) Taking the first order derivative of the inventory facility size ( N E ) with respect to the optimal economic order quantity under the ∗ AboveQmax system ( Qd ∗ ) in Eq (4.44), EOQd would result in dN E ∗ = αb dQd ∗ (4.51) Note that α and b are always positive Hence the slope of the inventory facility size with respect to the optimal economic order quantity under the AboveQmax system ( EOQd dN E ) is ∗ dQd ∗ always positive The size of the inventory facility ( N E ) will thus increase with the 126 ∗ optimal economic order quantity ( Qd ∗ ) Since the optimal economic order quantity under the ∗ AboveQmax system ( Qd ∗ ) is above Qmax , the size of the inventory facility ( N E ) EOQd should be above αbQmax αbQmax is the lowest limit in terms of the inventory facility size for the inventory to be purchased at PEmin , supposing all the inventory is ordered at its optimal economic order quantity The implication of Eq (4.51) is in agreement with that of Eq (4.30) 4.5.3 A summary of the annual carrying capacity By scrutinizing Eq (4.48) in Chapter and Eq (3.17) in Chapter 3, it can be found that the annual carrying capacity of an inventory facility under the AboveQmax system is the EOQd same as that under an EOQ without price discount system, provided that the size of the inventory facility under the EOQ without price discount system is greater than αbQmax The annual carrying capacity of an inventory facility under the EOQ without price discount system and that under the BelowQmax system and the EOQd AboveQmax system are EOQd shown in Figure 4.4 Figure 4.4 showed that the annual carrying capacity of the inventory facility under the EOQ without price discount system overlaps with the annual carrying capacity of the inventory facility under the AboveQmax system, when the area of the inventory facility EOQd under the EOQ without price discount system is greater than αbQmax Figure 4.4 also shows that when the size of the inventory facility is less than αbQmax , the annual carrying capacity of the inventory facility under the BelowQmax system is less than that under the EOQd 127 EOQ without price discount system, after assuming that the other conditions are the same among the two inventory ordering systems Annual carrying capacity of the Inventory Facility (unit) h Q2 2k max Qmax h 2π EQmax +2k O ∗ ∗ αbQmax Size of the inventory facility m2 Figure 4.4 Annual carrying capacity of an inventory facility Legend Represents the annual carrying capacity of an inventory facility under the EOQ without price discount system Dhsafe (see Eq (3.17)) Represents the annual carrying capacity of an inventory facility under the EOQdBelowQmax system (see Eq (4.27)) 128 4.5.4 Break-even point under the AboveQmax system EOQd The break-even point between the annual carrying capacity of an inventory facility under AboveQmax system and the EOQ-JIT cost indifference point under the the EOQd ∗∗ ∗∗ ∗∗ AboveQmax system can be represented by ( N eqd , Deqd ), where N eqd is the inventory EOQd facility break-even point under the break-even point under the ∗∗ AboveQmax system and Deqd is the annual demand EOQd ∗∗ AboveQmax system N eqd is the floor area of an inventory EOQd facility at which the function of the annual carrying capacity of an inventory facility under the AboveQmax system equals the function of the EOQ-JIT cost indifference point EOQd under the same system The difference between the annual carrying capacity of an inventory facility (see Eq (4.48)) and the EOQ-JIT cost indifference point (see Eq (4.40)) under the ∗∗ d Y [ AboveQmax system can be presented as: EOQd ] (PJ − PEmin )FN E + kh + 2(PJ − PEmin )FN E kh + k h hN E = − 2kb2α PJ − PEmin ( (4.52) ) where: Yd∗∗ is The difference between the annual carrying capacity of an inventory facility and the EOQ-JIT cost indifference point under the AboveQmax system EOQd Yd∗∗ is continuous and differentiable, as the floor area of the inventory facility ( N E ) is above αbQmax Taking the first order derivative of Yd∗∗ with respect to N E , would result in: dYd∗∗ Fkh F = h N − − dN E kα 2b2 E PJ − PE ( PJ − PE ) 2( PJ − PEmin ) FN E kh + k h (4.53) Taking the second order derivative of Yd∗∗ in Eq (4.52) with respect to N E , would result in: 129 [ d 2Yd∗∗ = h + F k h 2(PJ − PEmin )FN E kh + k h dN E kα 2b2 Note that ] −3 / (4.54) [ h is always positive F k h 2(PJ − PEmin )FN E kh + k h kα 2b2 ] −3 / always positive Hence, the second order derivative of Yd∗∗ with respect to N E ( is also d 2Yd∗∗ ) is dN E always positive According to the theorem of the second derivative test for maxima and minima of functions, the curve of Yd∗∗ with respect to N E is concave upwards As this section focuses on the case where the EOQ with a price discount system is less cost effective than the JIT purchasing system when its optimal economic order quantity is less ∗ ∗ than or equal to Qmax , the value of Yd∗αbQmax is thus always negative Yd∗αbQmax is the value of Yd∗∗ at αbQmax , that is, the difference between the function of the annual carrying capacity of an inventory facility and the function of the EOQ-JIT cost indifference point when the floor area of an inventory facility equals αbQmax and the optimal economic ∗ order quantity is given in Eq (4.4) Since Yd∗αbQmax is always a negative value and, since the curve of Yd∗∗ with respect to N E is concave upwards, there must be a break-even point at which Yd∗∗ equals zero Setting Yd∗∗ in Eq (4.52) to be zero, the root of Yd∗∗ ( N ) = is the break-even point represented by the floor area of an inventory facility under the AboveQmax system, and EOQd can be given by: ∗∗ N eqd = 2αbk (αbF + h ) PJ − PEmin h ( ) (4.55) 130 ∗∗ where: N eqd is the inventory facility break-even point under the AboveQmax system EOQd ∗∗ Substituting the break-even point ( N eqd ) for N E in Eq (4.48), yields the break-even point represented by the annual demand under the ∗∗ Deqd = AboveQmax system as: EOQd 2k (αbF + h ) ( h PJ − PEmin (4.56) ) ∗∗ where: Deqd is annual demand break-even point under the AboveQmax system EOQd It is essential to note that Eq (4.55) and Eq (4.56) were developed based on Eq (4.37), Eq (4.40) and Eq (4.43) Hence, to apply Eq (4.55) and Eq (4.56) to compute the break-even point, the conditions of Eq (4.40) and Eq (4.43) should be satisfied 4.5.5 Ultimate EOQ-JIT cost indifference point under the The ultimate EOQ-JIT cost indifferent point under the AboveQmax system EOQd ∗∗ AboveQmax system ( Duid ) is EOQd defined as the annual demand at which the inventory can be accommodated by the existing inventory facility and at which the total annual cost under the JIT purchasing system equals the total annual cost under the AboveQmax system Having developed the EOQd concept of the annual carrying capacity of an inventory facility under the AboveQmax system and the concept of the break-even point between the annual carrying EOQd capacity of an inventory facility and the EOQ-JIT cost indifference point under the same system, the ultimate EOQ-JIT cost indifference point under the AboveQmax system can EOQd be presented as: 131 ∗∗ N E ≥ N eqd = ∗∗ uid D [(P = 2αb(αbF + h ) PJ − PEmin h ( ) ) ] ( (4.57) ) − PEmin FN E + kh + PJ − PEmin FN E kh + k h J (P J − PEmin ) ∗∗ where: Duid is the ultimate EOQ-JIT cost indifference point under the ∗∗ AboveQmax system, Duid is the dependent variable, EOQd N E is the independent variable, k , h , PJ , PEmin , F , α and b are constants The values of k , h , PEmin , F , α and b are the respective values when inventory is ordered at its optimal economic order quantity under the EOQdAboveQmax system The first equation in Eq (4.57) indicates that for an AboveQmax system to be more cost EOQd effective than a JIT purchasing system, the floor area of the inventory facility should be ∗∗ greater than the inventory facility break-even point ( N eqd ) The second equation in Eq (4.57) states how the ultimate EOQ-JIT cost indifference point under ∗∗ the EOQdAboveQmax system ( Duid ) can be worked out It is essential to highlight that Eq (4.57) is only applicable to situations, where the inventory is ordered at its optimal economic order quantity and the optimal economic order quantity is above Qmax 4.5.6 Discussion ∗∗ The ultimate EOQ-JIT cost indifference point under the EOQdAboveQmax system ( Duid ) is further illustrated in Figure 4.5 To compare the present study with the models of Schniederjans and Cao (2000) and Fazel et al (1998), the EOQ-JIT cost indifference 132 point at the initial size of an inventory facility under the ∗∗ AboveQmax system ( DinddEo ), EOQd the annual carrying capacity of an inventory facility at its initial size under the ∗∗ AboveQmax system ( DhdEo ) and the break-even point under the EOQdAboveQmax system EOQd ∗∗ ∗∗ ( N eqd , Deqd ) are also indicated in Figure 4.5 Figure 4.5 assumes that the JIT purchasing system is more cost effective than the EOQ with a price discount system when the optimal economic order quantity of the inventory is less than Qmax The implications of Figure 4.5 are two-fold Firstly, an inventory facility under the AboveQmax system is not capable of carrying the EOQd EOQ-JIT cost indifference point’s amount of inventory when the floor area of an inventory facility is below the break-even point under the ∗∗ AboveQmax system ( N eqd ) EOQd This is demonstrated by the annual carrying capacity of an inventory facility at its initial ∗∗ ∗∗ size ( DhdEo ) and the EOQ-JIT cost indifference point at its initial size ( DinddEo ), where ∗∗ ∗∗ ∗∗ ∗∗ DhdEo is less than DinddEo DhdEo is less than DinddEo as far as the size of the inventory ∗∗ facility is within the interval of ( αbQmax , N eqd ) A JIT system can be more cost effective ∗∗ than the EOQ system within the interval ( αbQmax , N eqd ) It would appear that some of the cases observed by Schniederjans and Cao (2000) probably fell within the interval of ∗∗ ( αbQmax , N eqd ) 133 EOQ-JIT cost indifference point (Unit) Annual carrying capacity of inventory facility (unit) I I I ∗ ∗ ∗∗ Deqd ∗ ∗∗ DinddEo ∗∗ DhdEo ∗ O ∗ ∗ αbQmax Size of the inventory N Eo facility m2 ∗∗ N eqd ∗∗ Figure 4.5 Break-even point Deqd Legend Represents annual carrying capacity of an inventory facility under the AboveQmax system EOQd safe Dhd ∗∗ (see Eq (4.48)) Represents the EOQ-JIT cost indifference point ∗∗ Dindd (see Eq (4.40)) Represents the ultimate EOQ-JIT cost indifference point under the AboveQmax system (see EOQd Eq (4.57)) 134 Secondly, an inventory facility under the AboveQmax system is capable of EOQd accommodating the EOQ-JIT cost indifference point’s amount of inventory when the floor area of an inventory facility is greater than or equal to the break-even point under ∗∗ AboveQmax system ( N eqd ) It seems plausible that Schniederjans and Cao (2000) the EOQd 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 the break-even point of the inventory facility under the AboveQmax system EOQd ∗∗ ( N eqd ) Hence, another expression of the second implication is that the AboveQmax system can be more cost effective than the JIT purchasing system when the EOQd size of the inventory facility is greater than the break-even point under the ∗∗ AboveQmax system ( N eqd ), or the magnitude of the annual demand is greater than the EOQd annual demand break-even point under the ∗∗ AboveQmax system ( Deqd ), if the conditions EOQd of Eq (4.57) can be satisfied This implication again invalidated Schniederjans and Cao’s (2000, p.294) conclusion that a JIT ordering system was preferable at any level of annual demand and with almost any cost structure when JIT operations could capitalize on inventory physical plant space reduction Hence, this section theoretically proves that the research hypothesis of this thesis is valid under the AboveQmax system EOQd The EOQ-JIT cost indifference point that can be derived from the models proposed by Fazel et al (1998) for the AboveQmax system is given by: EOQd 135 ∗∗ DinddF = 2kh PJ − PEmin ( (4.58) ) ∗∗ where: DinddF is the EOQ-JIT cost indifference point that can be derived from the models proposed by Fazel et al (1998) for the AboveQmax system EOQd Eq (4.56) and Eq (4.57) suggest that the ultimate EOQ-JIT cost indifference points ∗∗ ∗∗ ( Duid ) and the annual demand break-even point ( Deqd ) are substantially greater than ∗∗ DinddF in Eq (4.58) As mentioned earlier, this could be for two reasons First, the savings of the inventory physical plant space under the JIT system were not accounted for in the EOQ-JIT cost indifference point of Fazel et al.(1998), (Schniederjans and Cao, 2000) Second, some other “fixed costs” such as utilities and personnel salaries were also omitted from the EOQ-JIT cost difference function proposed by these researchers This finding again suggests that the JIT purchasing system can still remain cost effective even at a higher level of annual demand than that suggested by the models of Fazel et al (1998) The break-even points and the ultimate EOQ-JIT cost indifference points under the EOQ with a price discount system and the impact of the annual demand on the adoption of appropriate purchasing systems are further illustrated by a case study in the RMC industry in Singapore in Chapter 136 4.6 Summary By extending the two new concepts developed in Chapter from the EOQ without price discount system to the EOQ with a price discount system, four additional new concepts were developed in Chapter These are: • The annual carrying capacity of an inventory facility under the • The break-even point between the annual carrying capacity of an inventory facility and the EOQ-JIT cost indifference point under the • BelowQmax system, EOQd BelowQmax system, EOQd The annual carrying capacity of an inventory facility under the AboveQmax system, EOQd and • The break-even point between the annual carrying capacity of an inventory facility and the EOQ-JIT cost indifference point under the AboveQmax system EOQd This chapter theoretically demonstrated that by including the “physical plant space” factor, as well as all other “fixed costs” which were omitted by Fazel et al (1998), it is still possible for an EOQ with a price discount system to be more cost effective than a JIT purchasing system, even if the JIT operations can take advantage of physical plant space reduction Chapter and Chapter theoretically demonstrated that JIT and EOQ may be preferred under different conditions A case study from the ready mixed concrete industry in Singapore is presented in Chapter to examine the models developed in these two chapters 137 ... 720 /17 0=4.2 11 0 90x4+60x5 =660 660 /11 0=6 12 5 90x5+60 = 510 510 /12 5=4 .1 10 10 0 90x6+60x4 =780 780 /10 0=7.8 14 4 12 0+90x5 =570 570 /14 4=3.96 11 0 90x9= 810 810 /11 0=7.4 (m / h) BATCHING CAPACITY/ NUMBERS OF TRUCKS... McGuire, 19 84; Schonberger, 19 82a, 19 82b, 19 84, 19 86 Finch, 19 86; Heard, 19 85, 19 86; Schonberger, 19 82a, 19 82b, 19 84, 19 86; Williams and Tice, 19 84; Youngkin, 19 84 Ramarapu et al., 19 94 Hall, 19 83;... 60x3 16 60x3 =18 0 18 0 /16 =11 .25 H Shapingba District Sha Ping Ba 60 60x1=60 60/8=7.5 I Jiulongpuo District Jiu Long Puo 60x2 12 60x2 =12 0 12 0 /12 =10 J Jiangbei District Miao Kou 60, 90 15 60+90 =15 0 15 0 /15 =10