CHAPTER 5 TESTING THE ULTIMATE EOQ-JIT COST INDIFFERENCE POINT MODEL

Transcription

1 CHAPTR 5 TTING TH ULTIMAT OQ-JIT COT INDIFFRNC POINT MODL 5.1 Introduction Chapter 3 and Chapter 4 theoretically suggested that it was possible for an OQ 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 ingapore is presented in this chapter to empirically examine this proposition. The case study was conducted in the cement division of RMC supplier I in November 003. ection 5. describes the background of RMC supplier I. ection 5.3 states the assumptions (boundary conditions) for this test. ection 5.4 and 5.5 derive the ultimate OQ-JIT cost indifference points for the procurement of cement. ection 5.6 discuss on the ultimate OQ-JIT cost indifference points and the cost indifference points derived by previous researchers. ection 5.7 performs sensitivity analyses to inform readers concerning the application and limitations of models developed. 5. The background of RMC supplier I The group of companies in which RMC supplier I was a subsidiary, was incorporated in April 1973 and listed in the ingapore tock xchange in The business scope of the group included the sale of RMC, dry mix mortar products and cement. The group also 138

2 had four cement manufacturing plants in China when the case study was carried out in November 003. The cement division of RMC supplier I in ingapore built two huge silos on the Pulau Damar Laut Island and adopted an OQ system to procure its cement from Japan. The designed carrying capacity of each of the silos was approximately 5,000 tonnes. The average area occupied by one silo was about,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. tock flexibility parameter was b = 1.5. Cement imported by the cement division of supplier I was mainly shipped using 40,000-tonne cement carriers. upplier I placed an order approximately once a month for about 40,000 tonnes of cement. The annual demand ( D ) was 50,000 tonnes in 003. The annual cost of carrying one tonne of cement was h = $ 31. The carrying cost can be split into cement check-in cost ( h checkin ), cement storage costs ( h storage1 and h storage ) and cement check-out cost ( h checkout ). 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 h checkin = $ 199 /year per tonne. The cement storage costs were h storage1 = $ 8 / year per tonne and h storage = $ 14 / year per tonne. The cement storage costs h storage1 included insurance, cement spoilage cost and opportunity cost of the working capital tied up with the cement purchased. The cement storage costs h storage included the depreciation cost of the silo facilities, utilities, personnel salaries and property tax. 139

3 Mankiw (1997, p.6) defined the opportunity cost of an item as what you give up to get that item. Potts (00) suggested that based on the principle of opportunity cost, the economic value of a resource was determined by its next best alternative use. Potts (00) 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 ingapore in the year 003 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 h checkout =$ 100 / year per tonne. Typical cement unloading facilities, storage facilities, and delivery facilities are shown in Figures 5.1, 5. and 5.3 respectively. The cost of placing an order was k = $ 43,000 / order for transportation alone. A 40,000-tonne cement carrier is shown in Figure 5.4. ach tonne of cement took up α = 0.11 m of the inventory facility space. The annual cost to rent a square meter of inventory facility was F = $ 84. If cement was purchased under a JIT system in ingapore, the cost was P = $ 69 / tonne. J 140

4 (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. Cement storage facilities Figure 5.3 Cement check out facility: a cement truck 141

5 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 1 is suitable for the OQ without price discount system. Pricing strategy is suitable for the OQ with a price discount system. Purchasing cement according to the pricing strategy 1 cost O P =$ 4 / tonne. Under pricing strategy, the delivery price started at P = $ 45 / tonne. For every additional tonne ordered, the price would decrease by = $ π 5 7.5x 10 for the entire order lot. The discount could be valid for order quantity up to min Q = 50,000 tonnes, when the price per unit became P = $ 41.5 / tonne. Beyond max 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 in November 003. At this point, it should be noted that the examples given by Fazel (1997, 14

6 p.50), Fazel et al. (1998, p.107) and chniederjans and Cao (000, p.91; 001, p.115) were hypothetical. It is also important to note that although the cement division of RMC supplier I ordered its cement in an OQ fashion, the accounting system adopted by them did not exactly follow the OQ approach. However, it was suggested that the cost information could be structured as above to fit the OQ 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 m of the 100-tonne silo and approximately m of the 5,000-tonne silo. The annual cost of holding one tonne of cement in a 100-tonne silo was slightly higher than $ 31 and the annual cost of holding one tonne of cement in a 5,000-tonne silo was slightly lower than $ 31 /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. ach order of cement was delivered by the 40,000 tonne cement carrier. Hence, the ordering cost under the OQ system can be assumed to be fixed per order. Under the OQ without price discount system, the optimal economic order quantity was close to the routine order quantity. The annual inventory ordering cost item ( Q kd ) (i.e., 43,000 x 50,000 / 40,000), was $ 5,616,000 / year. The annual inventory carrying cost 143

7 Qh ( ) was $ 6,40,000 / year. This shows that the annual inventory ordering cost item ( kd Qh ) was close to the annual inventory carrying cost item ( ). Based on q. (3.), 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 OQ 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 Q max, the maximum order quantity that can be ordered and still receives a price discount at rate π under the OQ with a price discount model. Hence, the OQ with a price discount system in the case study was actually a OQdBelowQ max system. Based on q. (4.3), the optimal economic order quantity was Qd = 4,998 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, namely, assumptions No.1 to No. and No. 4 to No. 9 in Table 1.1 can, thus, be roughly satisfied. Therefore, the OQ-JIT cost indifference points for cement purchasing in the cement division of RMC supplier I can be computed by the models developed in Chapters 3 and 4. It should be noted that the additional costs and benefits resulting from JIT purchasing are not considered in this case study. 144

8 5.4 Ultimate OQ-JIT cost indifference point under the OQ without price discount system q. (3.4) and q. (3.5) can be used to derive the break-even points under the OQ without price discount system. q. (3.6) can be used to derive the ultimate OQ-JIT cost indifference point under the OQ without price discount system. According to q. (3.4), the inventory facility break-even point was 4,644 m. According to q. (3.5), the annual demand break-even point was 408,830 tonnes. Based on q. (3.6), the ultimate OQ-JIT cost indifference point represented by the annual demand in the cement division of RMC supplier I was 414,557 tonnes. ince a) the floor area of the two silos, 5600 m, was greater than the break-even point, 4,644 m, and b) the ultimate OQ-JIT cost indifference point, 414,557 tonnes, was greater than the break-even point, 408,830 tonnes; therefore, the value of the ultimate OQ-JIT cost indifference point under the OQ without price discount system was confirmed to be 414,557 tonnes. According to q. (3.17), the annual carrying capacity of the two silos was 594,444 tonnes, which was capable of accommodating 50,000 tonnes of cement. The annual carrying capacity of these two silos under the OQ without price discount system can be as high as 98,818 tonnes, which is substantially greater than the annual demand in 003, if the flexibility parameter b is set to be 1. If the annual cost of holding one unit of cement, h, in q. (3.7) was replaced by the cement storage cost, h storage1, this equation was then converted to be the formula for computing the OQ-JIT cost indifference point proposed by Fazel (1997, p.499). 145

9 According to Fazel s (1997, p.499) model, the OQ-JIT cost indifference point for cement purchasing should have been 9,481 tonnes / year. ach 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 chniederjans and Cao (001, 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 OQ system. Hence, the OQ-JIT cost indifference point would be +. The OQ-JIT cost indifference points, worked out with the models proposed by Fazel (1997), chniederjans and Cao (001) and the author, are shown in Table 5.1. Table 5.1 A comparison of the OQ-JIT cost indifference points under the OQ without price discount system Cement purchasing OQ-JIT cost indifference point Fazel s (1997) model 9,481 (tonnes / year) chniederjans and Cao s (001) model + (tonnes / year) Author model 414,557 (tonnes / year) 5.5 Ultimate OQ-JIT cost indifference point under the OQ with a price discount system q. (4.31) and q. (4.19) can be used to derive the break-even points under the OQdBelowQmax indifference point under the system. q. (4.36) can be used to derive the ultimate OQ-JIT cost OQdBelowQmax system. etting Y d in q. (4.31) to zero and solving it with Matlab, the inventory facility break-even point under the OQd system ( BelowQmax N eqd ) was worked out to be 5,70 m. ubstituting N with 146

10 this amount in q. (4.19), the annual demand break-even point under the OQd system ( D BelowQmax eqd ) was worked out to be 4,518 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 OQ-JIT cost indifference point, respect to Y d, with N are attached in Appendix 4. Based on q. (4.36), the ultimate OQ-JIT cost indifference point under the OQdBelowQmax limit of the silo size that can still reap the benefit of π was system was 44,3 tonnes. The upper α bqmax = 7,000 m. The upper limit of the annual demand that could still reap the benefit of π was Q π Q h max max+ k = 647,700 tonnes. Hence, the value of the ultimate OQ-JIT cost indifference point under the OQdBelowQmax This was because a) the floor area of the two silos, 5600 limit 7,000 m and greater than the break-even point, 5,70 system was confirmed to be 44,3 tonnes. m, was less than the upper m ; and b) the computed ultimate OQ-JIT cost indifference point, 44,3 tonnes, was above the break-even point, 481,71 tonnes, and less than the upper limit, 647,700 tonnes; According to q. (4.7), the annual carrying capacity of the two silos was 465,17 tonnes, which was capable of accommodating 44,3 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 003, if the flexibility parameter b was set to 1. If the annual cost of holding one unit of cement, h, in q. (4.18) was replaced by the cement storage costs, h storage1, this equation was then converted to be the formula for 147

11 computing the OQ-JIT cost indifference point proposed by Fazel (1998, p.106). According to the model of Fazel et al. (1998, p.106), the OQ-JIT cost indifference point for cement purchasing was 9,796 tonnes / year. chniederjans and Cao (000, p.94) argued that a JIT ordering system was preferable to an OQ system at any level of annual demand and with almost any cost structure, the OQ-JIT cost indifference point proposed by them thus should be +. The OQ-JIT cost indifference points, worked out with the models proposed by Fazel, et al. (1998), chniederjans and Cao (000) and the author, are shown in Table 5.. Table 5. A comparison of the OQ-JIT cost indifference points under the OQ with a price discount system Model of Fazel et al. (1998) Author s model chniederjans and Cao s (000) model Cement purchasing OQ-JIT cost indifference point 9,796 (tonnes / year) 44,3 (tonnes / year) + (tonnes / year) 5.6 Discussion The batching capacity of the widely used batching plant was 90 m 3 / hr in ingapore. The average demand for cement of the 90 m 3 / hr batching plant was approximately 40,500 tonnes / year in 003 as estimated by the production manager of the RMC batching plant division of RMC supplier I. Based on the surveys presented in Chapter, the numbers of batching plants owned by RMC suppliers in ingapore 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 OQ-JIT cost indifference point worked out from the models proposed by Fazel (1997) or by Fazel et al. (1998). Hence, the OQ-JIT cost indifference point derived from the models of these 148

12 researchers suggested that all the RMC suppliers should operate in an OQ fashion. However, RMC supplier A, B, C, H, J, K, L, M, N and O were purchasing their cement in a JIT fashion. These RMC suppliers used a number of 100- tonne silos to store their buffer stock, as shown in Figure 5.5. The 100-tonne silos were filled on a daily basis. Hence, the OQ-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 ingapore. At the same time, the OQ-JIT cost indifference point models proposed by chniederjans and Cao (000, 001) 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 D,, F, G, together with I were purchasing their cement in an OQ fashion. This is shown in Table.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 ingapore did not support the OQ-JIT cost indifference point proposed by chniederjans and Cao (000); 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 tonne silo and approximately m of floor area in a 100- m in a 5,000-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

13 approximately $ 330 /year per tonne, which is slightly above $ 31 /year per tonne; while the annual cost of holding one tonne of cement in a 5,000-tonne silo is approximately $ 31 /year per tonne, which is slightly below $ 31 /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 5,000-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; ingapore Productivity and tandards Board, 1986; Mao, 1997). The fact that the annual cost of holding one tonne of cement in a 5,000-tonne silo lies slightly below $ 31 /year per tonne can shift the actual OQ-JIT cost indifference point to be lower than 414,557 tonne / year (for the OQ without a price discount system) or 44,3 tonne / year (for the OQ with a price discount system). Furthermore, the actual OQ-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 OQ-JIT cost indifference may shift to be a greater value if the impact of inventory policy on quality 150

14 and flexibility were considered. This will be further discussed in Chapter 6 and Chapter 7. 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 465,17 tonnes when a price discount rate x 10 was offered, where the flexibility parameter was 1.5. The reason for this reduction in annual carrying capacity has already been explained in ection The OQ 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 OQ-JIT cost indifference point s amount of inventory. One important reference quoted by chniederjans and Cao (001) 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 OQ 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

15 Figure tonne cement silos Figure 5.6 5,000-tonne cement silos 15

16 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,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. 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 ingapore by a 40,000-tonne cement carrier was about $ 10.8 / tonne. The transportation cost of bulk Portland cement from Japan to ingapore by a,500-tonne cement carrier was about $ 0.0 / tonne. The transportation cost of bulk Portland cement in ingapore by a cement truck was as high as $ 0.3 / tonne per kilometer. In addition, as indicated by π the purchase price could be increased if cement was ordered in small lot sizes. The difference between the selling price, P J and the purchase price, O P, was only $ 4. The average delivery cost of cement was around $ 4.0 / tonne in ingapore, where it was assumed that the average transportation distance was between 10 and 0 kilometers, because ingapore 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 to split its order size from 40,000 to,500 tonne to match the available cement carriers and to deliver in a JIT pattern. 153

17 5.7 ensitivity analyses ensitivity analyses were carried out to determine how the ultimate OQ-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 chniederjans and Cao (001), 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 OQ system ( P P ) or ( P J 0 J P ), ) 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 ). The steps for undertaking the sensitivity analysis, following chniederjans and Cao (001), are given below: tep 1: The ultimate OQ-JIT cost indifference point was computed in a normal way using data given in ection 5. for the ultimate OQ-JIT cost indifference point model (see q. (3.6) and q. (4.36)). This step was performed in ections 5.4 and 5.5. tep : The value of the first parameter was varied from -10% to +10% and the percentage change in the ultimate OQ-JIT cost indifference points was computed. tep 3: tep was repeated for the remaining parameters to compute the percentage change in the ultimate OQ-JIT cost indifference point. 154

18 The sensitivity analyses for cement purchasing by the cement division of RMC supplier I were conducted under the OQ without price discount system and OQ with a price discount system. Table 5.3 shows the change in the ultimate OQ-JIT cost indifference points when the changes were made to the parameters individually under the OQ without price discount system. The ultimate cost indifference points were computed by using q. (3.6). Table 5.3 Percentage change in the ultimate OQ-JIT cost indifference point under the OQ without price discount system Percentage change in parameter Percentage change in the cost indifference point P P ), holding h k F ( J P as a constant J -10%.5% -9.% -9.% -0.8% -5% 10.4% -4.6% -4.6% -0.4% % -8.9% 4.6% 4.6% 0.4% 10% -16.7% 9.% 9.% 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 OQ with a price discount system. The ultimate cost indifference points were computed by using q. (4.36). Table 5.4 Percentage change in the ultimate OQ-JIT cost indifference point under the OQ with a price discount system Percentage change in parameter Percentage change in the cost indifference point ( P ), holding h k F 0 J P P as a constant J -10% 17.5% -9.3% -7.6% -0.7% 1.9% -5% 8.3% -4.6% -3.8% -0.4% 0.9% % -7.4% 4.6% 3.7% 0.4% -0.9% 10% -14% 9.3% 7.3% 0.7% -1.8% π 155

19 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 qs. (3.6) and (4.36). econd, the price factor was the most sensitive parameter for cement purchasing in the cement section of RMC supplier I Tables 5.3 and 5.4 show that the ultimate OQ-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 ummary Chapter 5 is dedicated to a case study in the RMC industry in ingapore which showed that it is possible for the OQ system to be more cost effective than the JIT system, when the annual demand is greater than the ultimate OQ-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 OQ system cannot be economically split. As suggested in Chapter 1, the intention of Chapters 3 and 4 was to theoretically examine the capability of an inventory facility to hold the OQ-JIT cost indifference point s amount of inventories based on the mathematical models developed by previous 156

20 researchers. Hence, the additional costs and benefits of OQ or JIT purchasing were not considered in the models developed. The additional costs and benefits of the OQ and JIT purchasing of cement in the RMC industry in ingapore may be balanced by each other. Hence, the OQ-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 ingapore 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 heraga (1988), Johnson and tice (1993), Cheng and Podolsky (1996), Low and Chan (1997), Low and Choong (001d), ingh (003), Low and Wu (005a, b), Wu and Low (005a, 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 OQ-JIT cost difference models. In addition, the models developed in Chapter 3 and Chapter 4 were general models, rather than particularly designed for the RMC industry. Hence, Chapter 6 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