CHAPTER TESTING THE ULTIMATE EOQ-JIT COST INDIFFERENCE POINT MODEL 5.1 Introduction Chapter and Chapter theoretically suggested that it was possible for an EOQ system to be more cost effective than a JIT purchasing system when the inventory annual demand was greater than its break-even point, even when the JIT operations could experience or take advantage of inventory physical plant space reduction A case study relating to the procurement of cement in the ready mixed concrete (RMC) industry in Singapore is presented in this chapter to empirically examine this proposition The case study was conducted in the cement division of RMC supplier I S in November 2003 Section 5.2 describes the background of RMC supplier I S Section 5.3 states the assumptions (boundary conditions) for this test Section 5.4 and 5.5 derive the ultimate EOQ-JIT cost indifference points for the procurement of cement Section 5.6 discuss on the ultimate EOQ-JIT cost indifference points and the cost indifference points derived by previous researchers Section 5.7 performs sensitivity analyses to inform readers concerning the application and limitations of models developed 5.2 The background of RMC supplier I S The group of companies in which RMC supplier I S was a subsidiary, was incorporated in April 1973 and listed in the Singapore Stock Exchange in 1979 The business scope of the group included the sale of RMC, dry mix mortar products and cement The group also 138 had four cement manufacturing plants in China when the case study was carried out in November 2003 The cement division of RMC supplier I S in Singapore built two huge silos on the Pulau Damar Laut Island and adopted an EOQ system to procure its cement from Japan The designed carrying capacity of each of the silos was approximately 25,000 tonnes The average area occupied by one silo was about 2,800 m The sum of the carrying capacities of the two silos was approximately 40,000 tonnes, where safety and flexibility factors had been considered Stock flexibility parameter was b = 1.25 Cement imported by the cement division of supplier I S was mainly shipped using 40,000-tonne cement carriers Supplier I S placed an order approximately once a month for about 40,000 tonnes of cement The annual demand ( D ) was 520,000 tonnes in 2003 The annual cost of carrying one tonne of cement was h = S$ 321 The carrying cost can be split into cement check-in cost ( hcheckin ), cement storage costs ( hstorage1 and hstorage ) and cement check-out cost ( hcheckout ) The cement check-in cost was the depreciation and operating costs of the facilities to unload cement from a cement carrier to a silo and hcheckin = S $ 199 /year per tonne The cement storage costs were hstorage1 = S$ / year per tonne and hstorage = S$ 14 / year per tonne The cement storage costs hstorage1 included insurance, cement spoilage cost and opportunity cost of the working capital tied up with the cement purchased The cement storage costs hstorage2 included the depreciation cost of the silo facilities, utilities, personnel salaries and property tax 139 Mankiw (1997, p.6) defined the opportunity cost of an item as “what you give up to get that item.” Potts (2002) suggested that based on the principle of opportunity cost, the economic value of a resource was determined by its next best alternative use Potts’ (2002) suggestion indicates that to compute the opportunity cost of the working capital tied up with the cement purchased accurately, the alternative investment plans for the amount of capital have to be worked out This is however a difficult task Nevertheless, Heyne (1996) showed that the opportunity cost of the working capital tied up with an inventory could be practically computed through such low-risk investments as government bonds Hence, the average interest rate of government bonds in Singapore in the year 2003 was used to compute the opportunity cost of the working capital tied up with the cement purchased The cement check-out cost was the depreciation cost and operating cost of the facilities, mainly cement trucks, to deliver cement from the silo to a RMC batching plant and hcheckout =S$ 100 / year per tonne Typical cement unloading facilities, storage facilities, and delivery facilities are shown in Figures 5.1, 5.2 and 5.3 respectively The cost of placing an order was k = S$ 432,000 / order for transportation alone A 40,000-tonne cement carrier is shown in Figure 5.4 Each tonne of cement took up α = 0.112 m of the inventory facility space The annual cost to rent a square meter of inventory facility was F = S$ 84 If cement was purchased under a JIT system in Singapore, the cost was PJ = S$ 69 / tonne 140 (a) Cement unloading facilities (b) Cement transportation belt Figure 5.1 Facilities at a cement bulk terminal (a) Packing facility (b) Control panel Figure 5.2 Cement storage facilities Figure 5.3 Cement check out facility: a cement truck 141 Figure 5.4 A 40,000-tonne cement carrier The order was often raised one or two months before the departure of a cement carrier from Japan The Japanese cement manufacturers offered a few alternative pricing strategies Two of the pricing strategies are discussed below Pricing strategy is suitable for the EOQ without price discount system Pricing strategy is suitable for the EOQ with a price discount system Purchasing cement according to the pricing strategy cost PE =S$ 42 / tonne Under pricing strategy 2, the delivery price started at PEO = S$ 45 / tonne For every additional tonne ordered, the price would decrease by π E = S $ 7.5 x10 −5 for the entire order lot The discount could be valid for order quantity up to Qmax = 50,000 tonnes, when the price per unit became PEmin = S$ 41.25 / tonne Beyond this level, the price remained the same It is essential to note that the information for this case study was collected through interviews with the overseas investment manager, the financial manager, the production manager and the customer service supervisor of the cement division of supplier I S in November 2003 At this point, it should be noted that the examples given by Fazel (1997, 142 p.502), Fazel et al (1998, p.107) and Schniederjans and Cao (2000, p.291; 2001, p.115) were hypothetical It is also important to note that although the cement division of RMC supplier I S ordered its cement in an EOQ fashion, the accounting system adopted by them did not exactly follow the EOQ approach However, it was suggested that the cost information could be structured as above to fit the EOQ model The value of each parameter was the average value 5.3 Boundary conditions To compare the present study with the study of previous researchers and to make the problem simple, demand variability and safety stock were not considered in this case study In addition, it was found that each tonne of cement took up approximately 0.115 m of the 100-tonne silo and approximately 0.109 m of the 25,000-tonne silo The annual cost of holding one tonne of cement in a 100-tonne silo was slightly higher than S$ 321 and the annual cost of holding one tonne of cement in a 25,000-tonne silo was slightly lower than S$ 321 /year per tonne This shows that the annual cost of holding one tonne of cement in silos can roughly be assumed to be a constant Each order of cement was delivered by the 40,000 tonne cement carrier Hence, the ordering cost under the EOQ system can be assumed to be fixed per order Under the EOQ without price discount system, the optimal economic order quantity was close to the routine order quantity The annual inventory ordering cost item ( kD ) (i.e., Q 432,000 x 520,000 / 40,000), was S$ 5,616,000 / year The annual inventory carrying cost 143 ( Qh ) was S$ 6,420,000 / year This shows that the annual inventory ordering cost item Qh ( kD ) was close to the annual inventory carrying cost item ( ) Based on Eq (3.2), the Q economic order quantity was Q ∗ = 37,411 tonnes / order Hence, the economic order quantity ( Q ∗ ) was close to the routine order quantity 40,000 tonnes / order Under the EOQ with a price discount system, the optimal economic order quantity was also close to the routine order quantity The routine cement order quantity for cement, 40,000 tonnes / order, was less than Qmax , the maximum order quantity that can be ordered and still receives a price discount at rate π E under the EOQ with a price discount model Hence, the EOQ with a price discount system in the case study was actually a BelowQmax system Based on Eq (4.3), the optimal economic order quantity was EOQd ∗ Qd = 42,998 tonnes / order Hence, the optimal economic order quantity was close to the routine order quantity Based on the above background, the assumptions of boundary condition 2, namely, assumptions No.1 to No.2 and No to No in Table 1.1 can, thus, be roughly satisfied Therefore, the EOQ-JIT cost indifference points for cement purchasing in the cement division of RMC supplier I S can be computed by the models developed in Chapters and It should be noted that the additional costs and benefits resulting from JIT purchasing are not considered in this case study 144 5.4 Ultimate EOQ-JIT cost indifference point under the EOQ without price discount system Eq (3.24) and Eq (3.25) can be used to derive the break-even points under the EOQ without price discount system Eq (3.26) can be used to derive the ultimate EOQ-JIT cost indifference point under the EOQ without price discount system According to Eq (3.24), the inventory facility break-even point was 4,644 m According to Eq (3.25), the annual demand break-even point was 408,830 tonnes Based on Eq (3.26), the ultimate EOQ-JIT cost indifference point represented by the annual demand in the cement division of RMC supplier I S was 414,557 tonnes Since a) the floor area of the two silos, 5600 m , was greater than the break-even point, 4,644 m , and b) the ultimate EOQ-JIT cost indifference point, 414,557 tonnes, was greater than the break-even point, 408,830 tonnes; therefore, the value of the ultimate EOQ-JIT cost indifference point under the EOQ without price discount system was confirmed to be 414,557 tonnes According to Eq (3.17), the annual carrying capacity of the two silos was 594,444 tonnes, which was capable of accommodating 520,000 tonnes of cement The annual carrying capacity of these two silos under the EOQ without price discount system can be as high as 928,818 tonnes, which is substantially greater than the annual demand in 2003, if the flexibility parameter b is set to be If the annual cost of holding one unit of cement, h , in Eq (3.7) was replaced by the cement storage cost, hstorage1 , this equation was then converted to be the formula for computing the EOQ-JIT cost indifference point proposed by Fazel (1997, p.499) 145 According to Fazel’s (1997, p.499) model, the EOQ-JIT cost indifference point for cement purchasing should have been 9,481 tonnes / year Each tonne of cement occupied at least 0.1 m of the silo Hence, JIT purchasing of cement could have taken advantage of inventory physical plant space reduction Based on the models proposed by Schniederjans and Cao (2001, p.116), when “saving space and using it to house additional increasing amounts of inventory to meet larger annual demand are juxtaposed issues … a JIT system would virtually always be preferable to an EOQ system” Hence, the EOQ-JIT cost indifference point would be + ∞ The EOQ-JIT cost indifference points, worked out with the models proposed by Fazel (1997), Schniederjans and Cao (2001) and the author, are shown in Table 5.1 Table 5.1 A comparison of the EOQ-JIT cost indifference points under the EOQ without price discount system Cement purchasing EOQ-JIT cost indifference point Fazel’s (1997) model 9,481 (tonnes / year) Schniederjans and Cao’s (2001) model +∞ (tonnes / year) Author’ model 414,557 (tonnes / year) 5.5 Ultimate EOQ-JIT cost indifference point under the EOQ with a price discount system Eq (4.31) and Eq (4.19) can be used to derive the break-even points under the EOQdBelowQmax system Eq (4.36) can be used to derive the ultimate EOQ-JIT cost indifference point under the EOQdBelowQmax system Setting Yd∗ in Eq (4.31) to zero and solving it with Matlab, the inventory facility break-even point under ∗ the EOQdBelowQmax system ( N eqd ) was worked out to be 5,270 m Substituting N E with 146 this amount in Eq (4.19), the annual demand break-even point under ∗ the EOQdBelowQmax system ( Deqd ) was worked out to be 422,518 tonnes The Matlab code and the figure of the difference between the function of the annual carrying capacity of the inventory facility and the function of the EOQ-JIT cost indifference point, Yd∗ , with respect to N E are attached in Appendix Based on Eq (4.36), the ultimate EOQ-JIT cost indifference point under the EOQdBelowQmax system was 424,322 tonnes The upper limit of the silo size that can still reap the benefit of π E was αbQmax = 7,000 m The upper limit of the annual demand that could still reap the benefit of π E was Qmax h = 647,700 tonnes Hence, the value of the ultimate EOQ-JIT cost 2π EQmax +2k indifference point under the EOQdBelowQmax system was confirmed to be 424,322 tonnes This was because a) the floor area of the two silos, 5600 m , was less than the upper limit 7,000 m and greater than the break-even point, 5,270 m ; and b) the computed ultimate EOQ-JIT cost indifference point, 424,322 tonnes, was above the break-even point, 481,271 tonnes, and less than the upper limit, 647,700 tonnes; According to Eq (4.27), the annual carrying capacity of the two silos was 465,217 tonnes, which was capable of accommodating 424,322 tonnes of cement The annual carrying capacity of these two silos could be as high as 647,700 tonnes, which was substantially greater than the annual demand in 2003, if the flexibility parameter b was set to If the annual cost of holding one unit of cement, h , in Eq (4.18) was replaced by the cement storage costs, hstorage1 , this equation was then converted to be the formula for 147 computing the EOQ-JIT cost indifference point proposed by Fazel (1998, p.106) According to the model of Fazel et al (1998, p.106), the EOQ-JIT cost indifference point for cement purchasing was 9,796 tonnes / year Schniederjans and Cao (2000, p.294) argued that a JIT ordering system was preferable to an EOQ system at any level of annual demand and with almost any cost structure, the EOQ-JIT cost indifference point proposed by them thus should be + ∞ The EOQ-JIT cost indifference points, worked out with the models proposed by Fazel, et al (1998), Schniederjans and Cao (2000) and the author, are shown in Table 5.2 Table 5.2 A comparison of the EOQ-JIT cost indifference points under the EOQ with a price discount system Cement purchasing EOQ-JIT cost indifference point Model of Fazel et al (1998) 9,796 (tonnes / year) Author’s model 424,322 (tonnes / year) Schniederjans and Cao’s (2000) model +∞ (tonnes / year) 5.6 Discussion The batching capacity of the widely used batching plant was 90 m / hr in Singapore The average demand for cement of the 90 m / hr batching plant was approximately 40,500 tonnes / year in 2003 as estimated by the production manager of the RMC batching plant division of RMC supplier I S Based on the surveys presented in Chapter 2, the numbers of batching plants owned by RMC suppliers in Singapore were arranged from one to seventeen Hence, the annual cement demand of each RMC supplier surveyed was at least 40,500 tonnes / year This figure was significantly greater than the EOQ-JIT cost indifference point worked out from the models proposed by Fazel (1997) or by Fazel et al (1998) Hence, the EOQ-JIT cost indifference point derived from the models of these 148 researchers suggested that all the RMC suppliers should operate in an EOQ fashion However, RMC supplier AS , BS , C S , H S , J S , K S , LS , M S , N S and OS were purchasing their cement in a JIT fashion These RMC suppliers used a number of 100tonne silos to store their buffer stock, as shown in Figure 5.5 The 100-tonne silos were filled on a daily basis Hence, the EOQ-JIT cost indifference point derived from Fazel’s (1997) model and the model of Fazel et al (1998) were not supported by the information on cement purchasing in the RMC industry in Singapore At the same time, the EOQ-JIT cost indifference point models proposed by Schniederjans and Cao (2000, 2001) suggested that all the RMC suppliers should operate in a JIT fashion, as cement purchasing can take advantage of physical plant space reduction However, the cement division of RMC supplier DS , E S , FS , G S , together with I S were purchasing their cement in an EOQ fashion This is shown in Table 2.6 To reap economies of scale, the cement division of these RMC suppliers built a number of huge multi-cells silos on the Pulau Damar Laut island, as shown in Figure 5.6 The cement received at the Pulau Damar Laut Island was then delivered to their RMC batching plant divisions and batching plants of other RMC suppliers Hence, cement purchasing in the RMC industry in Singapore did not support the EOQ-JIT cost indifference point proposed by Schniederjans and Cao (2000); rather it supported the one developed in this study It is important to highlight the economies of scale in cement storage As stated earlier, a representative tonne of cement takes up approximately 0.115 m of floor area in a 100tonne silo and approximately 0.109 m in a 25,000-tonne silo In addition, in terms of the overall throughput, the annual cost of holding one tonne of cement in a 100-tonne silo is 149 approximately S$ 330 /year per tonne, which is slightly above S$ 321 /year per tonne; while the annual cost of holding one tonne of cement in a 25,000-tonne silo is approximately S$ 312 /year per tonne, which is slightly below S$ 321 /year per tonne The difference in the construction costs of many small silos as opposed to one large silo should also be addressed However, the construction cost of a silo has already been considered as a component of the depreciation cost of the silo facilities The annual cost of holding one tonne of cement in a cement silo is calculated based on the property tax, insurance, cement spoilage cost, opportunity cost of the working capital tied up in the purchased cement, the depreciation cost of the silo facilities, utilities, personnel salaries, and the depreciation cost and operating cost of the facilities to unload cement from a cement carrier to a silo The annual cost of holding one tonne of cement in a 100-tonne silo is close to that of a 25,000-tonne silo, as bulk cement must be stored in silos that are waterproof, clean and protected from contamination, dry (internal condensation minimized) and with stocks rotated in chronological order of the dispatch dates marked on delivery documents (Zacharia, 1985; Singapore Productivity and Standards Board, 1986; Mao, 1997) The fact that the annual cost of holding one tonne of cement in a 25,000-tonne silo lies slightly below S$ 321 /year per tonne can shift the actual EOQ-JIT cost indifference point to be lower than 414,557 tonne / year (for the EOQ without a price discount system) or 424,322 tonne / year (for the EOQ with a price discount system) Furthermore, the actual EOQ-JIT cost indifference point could be modified to an even lower value, if the out-of-stock cost was considered On the other hand, the EOQ-JIT cost indifference may shift to be a greater value if the impact of inventory policy on quality 150 and flexibility were considered This will be further discussed in Chapter and Chapter It is also important to note that the case study also suggested that the annual carrying capacity of an inventory facility dropped from 594,444 tonnes to 465,217 tonnes when a price discount rate 7.5 x10 −5 was offered, where the flexibility parameter was 1.25 The reason for this reduction in annual carrying capacity has already been explained in Section 4.4.5.1 The EOQ models assume that the demand of an inventory is known and fixed Hence, the optimal economic order quantity is fixed However, the annual demand of an inventory in practice is seldom a constant The company may have difficulties to rent additional inventory facility when the annual demand of the inventory increases In such a case, the inventory order frequency can be increased to match the increased annual inventory demand, and the inventory order size may remain the same as the routine order size This suggests that the carrying capacity of an inventory facility in practice can be greater than “the annual carrying capacity of an inventory facility”, thus again making it possible for an inventory facility to hold the EOQ-JIT cost indifference point’s amount of inventory One important reference quoted by Schniederjans and Cao (2001) to support their argument that JIT was virtually always the preferable alternative for inventory purchasing decisions was the study conducted by Pan and Liao (1989) In Pan and Liao’s (1989) study, the EOQ model was converted into a series of JIT purchasing models that could be used to determine inventory deliveries and cost savings, and demonstrated that there was 151 Figure 5.5 100-tonne cement silos Figure 5.6 25,000-tonne cement silos 152 no limitation on the cost advantage of using JIT, based on the model parameter of annual demand This raises the question whether it was economical to use 2,500-tonne cement carriers, rather than 40,000-tonne cement carriers, to conduct frequent deliveries This question was raised to the production manager of the cement division of supplier I S The production manager explained that the transportation of bulk Portland cement must use specialized transportation vehicles, such as cement trucks or cement carriers, as shown in Figure 5.3 and Figure 5.4 The transportation cost of bulk Portland cement from Japan to Singapore by a 40,000-tonne cement carrier was about S$ 10.8 / tonne The transportation cost of bulk Portland cement from Japan to Singapore by a 2,500-tonne cement carrier was about S$ 20.0 / tonne The transportation cost of bulk Portland cement in Singapore by a cement truck was as high as S$ 0.3 / tonne per kilometer In addition, as indicated by π E the purchase price could be increased if cement was ordered in small lot sizes The difference between the selling price, PJ and the purchase price, PEO , was only S$ 24 The average delivery cost of cement was around S$ 4.0 / tonne in Singapore, where it was assumed that the average transportation distance was between 10 and 20 kilometers, because Singapore is a relatively small island In addition, the expensive operating and depreciation costs of the cement silos and cement check-in facilities must be paid To sum up, it was not economically justifiable for the cement division of supplier I S to split its order size from 40,000 to 2,500 tonne to match the available cement carriers and to deliver in a JIT pattern 153 5.7 Sensitivity analyses Sensitivity analyses were carried out to determine how the ultimate EOQ-JIT cost indifference point models were affected by variations in the parameters in the models The analyses were used to identify parameters on which more attention should be concentrated when selecting cement purchasing approaches Following Kometa et al (1996), Ling (1998) and Schniederjans and Cao (2001), sensitivity analyses were restricted to the major parameters only, so as to limit the complexity of the results These parameters were 1) the price difference between the JIT purchasing system and the EOQ system ( PJ − PE ) or ( PJ − PE0 ), 2) the annual cost of carrying one unit of inventory in stock ( h ), 3) the cost of placing an order ( k ), 4) the annual cost to own and maintain a square meter of physical plant space ( F ), and 5) the price discount ( π E ) The steps for undertaking the sensitivity analysis, following Schniederjans and Cao (2001), are given below: • Step 1: The ultimate EOQ-JIT cost indifference point was computed in a normal way using data given in Section 5.2 for the ultimate EOQ-JIT cost indifference point model (see Eq (3.26) and Eq (4.36)) This step was performed in Sections 5.4 and 5.5 • Step 2: The value of the first parameter was varied from -10% to +10% and the percentage change in the ultimate EOQ-JIT cost indifference points was computed • Step 3: Step was repeated for the remaining parameters to compute the percentage change in the ultimate EOQ-JIT cost indifference point 154 The sensitivity analyses for cement purchasing by the cement division of RMC supplier I S were conducted under the EOQ without price discount system and EOQ with a price discount system Table 5.3 shows the change in the ultimate EOQ-JIT cost indifference points when the changes were made to the parameters individually under the EOQ without price discount system The ultimate cost indifference points were computed by using Eq (3.26) Table 5.3 Percentage change in the ultimate EOQ-JIT cost indifference point under the EOQ without price discount system Percentage change in parameter Percentage change in the cost indifference point h k ( PJ − PE ), holding F PJ as a constant -10% -5% 5% 10% 22.5% 10.4% -8.9% -16.7% -9.2% -4.6% 4.6% 9.2% -9.2% -4.6% 4.6% 9.2% -0.8% -0.4% 0.4% 0.8% Table 5.4 shows the change in the ultimate cost indifference points when the changes were made to the parameters individually under the EOQ with a price discount system The ultimate cost indifference points were computed by using Eq (4.36) Table 5.4 Percentage change in the ultimate EOQ-JIT cost indifference point under the EOQ with a price discount system Percentage change in parameter -10% -5% 5% 10% Percentage change in the cost indifference point ( PJ − PE0 ), holding h k F πE -9.3% -4.6% 4.6% 9.3% -7.6% -3.8% 3.7% 7.3% -0.7% -0.4% 0.4% 0.7% 1.9% 0.9% -0.9% -1.8% PJ as a constant 17.5% 8.3% -7.4% -14% 155 The implications of Tables 5.3 and 5.4 are three-fold First, the changes in the cost indifference points were not linearly related to the changes with the parameters This is explicit in Eqs (3.26) and (4.36) Second, the price factor was the most sensitive parameter for cement purchasing in the cement section of RMC supplier I S Tables 5.3 and 5.4 show that the ultimate EOQ-JIT cost indifference point changes the most when the value of the purchase prices were varied Third, among the parameters listed in Tables 5.3 and 5.4, the rental was the least sensitive parameter This is not unexpected, because rental was only a component of the physical storage costs for cement storage The major components of the physical storage costs, for example, cement check in-facilities, cement check-out facilities, personnel salaries, etc were considered in h in the models developed in this study 5.8 Summary Chapter is dedicated to a case study in the RMC industry in Singapore which showed that it is possible for the EOQ system to be more cost effective than the JIT system, when the annual demand is greater than the ultimate EOQ-JIT cost indifference point, even when the JIT operation can take advantage of inventory physical plant space reduction The case study also suggests that this conclusion can be valid only if the order quantity under the EOQ system cannot be economically split As suggested in Chapter 1, the intention of Chapters and was to theoretically examine the capability of an inventory facility to hold the EOQ-JIT cost indifference point’s amount of inventories based on the mathematical models developed by previous 156 researchers Hence, the additional costs and benefits of EOQ or JIT purchasing were not considered in the models developed The additional costs and benefits of the EOQ and JIT purchasing of cement in the RMC industry in Singapore may be balanced by each other Hence, the EOQ-JIT cost indifference point models developed in the previous chapters were still well supported by the data on cement purchasing in the RMC industry in Singapore even though the additional cost components were not considered in models developed in these chapters However, these additional cost components may not always be balanced by each other Based on the studies conducted by other researchers, for example, the studies of Rao and Sheraga (1988), Johnson and Stice (1993), Cheng and Podolsky (1996), Low and Chan (1997), Low and Choong (2001d), Singh (2003), Low and Wu (2005a, b), Wu and Low (2005a, b, c, d) and others, the impact of inventory purchasing policy on quality and production flexibility and out-of-stock costs should be considered in the EOQ-JIT cost difference models In addition, the models developed in Chapter and Chapter were general models, rather than particularly designed for the RMC industry Hence, Chapter will consider these additional cost components and examine how these additional cost components may affect the selection of inventory purchasing policy in the RMC industry 157 ... supported by the information on cement purchasing in the RMC industry in Singapore At the same time, the EOQ-JIT cost indifference point models proposed by Schniederjans and Cao (20 00, 20 01) suggested... cement purchasing in the RMC industry in Singapore did not support the EOQ-JIT cost indifference point proposed by Schniederjans and Cao (20 00); rather it supported the one developed in this... 424 , 322 tonnes, was above the break-even point, 481 ,27 1 tonnes, and less than the upper limit, 647,700 tonnes; According to Eq (4 .27 ), the annual carrying capacity of the two silos was 465 ,21 7