Showing papers by "Pusan National University published in 1998"

Adaptive Hopfield neural networks for economic load dispatch

Abstract: A large number of iterations and oscillations are those of the major concern in solving the economic load dispatch problem using the Hopfield neural network. This paper develops two different methods, the slope adjustment and bias adjustment methods, in order to speed up the convergence of the Hopfield neural network system. Algorithms of economic load dispatch for piecewise quadratic cost functions using the Hopfield neural network have been developed for the two approaches. The results are compared with those of a numerical approach and the traditional Hopfield neural network approach. To guarantee and for faster convergence, adaptive learning rates are also developed by using energy functions and applied to the slope and bias adjustment methods. The results of the traditional, fixed learning rate and adaptive learning rate methods are compared in economic load dispatch problems.

Insulin-like Growth Factor II Induced by Hypoxia May Contribute to Angiogenesis of Human Hepatocellular Carcinoma

Abstract: Insulin-like growth factor II (IGF-II) is highly expressed during hepatocarcinogenesis (P. Schirmacher et al. , Cancer Res., 52: 2549–2556, 1992; B. C. Park et al. , J. Hepatol., 22: 286–294, 1995). However, the mechanism of its enhanced expression is largely unknown. In this study, we show that IGF-II mRNA levels are increased within six h of exposing human hepatoma cell cultures to hypoxia, suggesting that hypoxia may be a strong stimulus for the induction of IGF-II expression in the process of hepatocarcinogenesis. This finding and the fact that hepatocellular carcinoma (HCC) is a typical hypervascular tumor (M. Mise et al. , Hepatology, 23: 455–464, 1996) imply that IGF-II may play an important role in the development of neovascularization of HCC. Here we demonstrate that IGF-II substantially increases vascular endothelial growth factor (VEGF) mRNA and protein levels in a time-dependent manner in human hepatoma cells. The induction of VEGF by IGF-II was additively increased by hypoxia. Moreover, the direct angiogenic activity of IGF-II was observed in the quantitative chick chorioallantoic membrane assay (M. Nguyen et al. , Microvasc. Res., 47: 31–40, 1994). These data suggest that IGF-II may be a hypoxia-inducible angiogenic factor in HCC.

Re-marshaling export containers in port container terminals

Abstract: In order to speed up the loading operation of export containers onto a ship, the re-marshaling operation is an usual practice in port container terminals. It is assumed that the current yard map for containers is available and a desirable bay layout is provided. A methodology is proposed to convert the current bay layout into the desirable layout by moving the fewest possible number of containers and in the shortest possible travel distance. The problem is decomposed into three sub-problems such as the bay matching, the move planning, and the task sequencing. The bay matching is to match a specific current bay with a bay configuration in the target layout. In the move planning stage, the number of containers to be moved from a specific bay to another is determined. The completion time of the re-marshaling operation is minimized by sequencing the moving tasks in the final stage. A mathematical model is suggested for each sub-problem. A numerical example is provided to illustrate the solution procedure.

In vitro activation of pro-phenol-oxidase by two kinds of pro-phenol-oxidase-activating factors isolated from hemolymph of coleopteran, Holotrichia diomphalia larvae

Abstract: Previously, we purified and characterized a pro-phenol-oxidase (pro-PO) of 79 kDa from coleopteran insect, Holotrichia diomphalia larvae [Kwon et al. (1997) Mol. Cells 7, 90−97]. Here, we describe the identification of two pro-PO-activating factors (PPAF), named PPAF-I and PPAF-II, directly involved in the activation of the isolated pro-PO. When pro-PO was incubated with either PPAF-I or PPAF-II, no phenol oxidase activity was observed. However, incubation of pro-PO with both PPAF-I and PPAF-II specifically exhibited phenol oxidase activity. The purified PPAF-I with a molecular mass of 33 kDa on SDS/PAGE had characteristics of a serine protease. It exhibited amidase activity against fluorogenic peptide substrates, tert-butoxycarbonyl-phenylalanyl-seryl-arginyl-4-methylcoumaryl-7-amide being the best among the substrates examined. The activity was completely inhibited by 0.02 mM p-nitrophenyl-p′-guanidinobenzoate HCl and diisopropylflurophosphate. The NH2-terminal sequence of PPAF-I had significant sequence similarity to those of serine proteases. On the other hand, the purified PPAF-II had a molecular mass of 40 kDa on SDS/PAGE and 400 kDa determined by gel filtration, indicating an oligomeric protein. The NH2-terminal sequence of PPAF-II showed no similarity to known proteins. PPAF-II exhibited no amidase activity against the fluorogenic substrates. Reconstitution experiments and immunoblotting analysis using affinity-purified antibody against pro-PO demonstrated that PPAF-I first cleaves the intact pro-PO to an intermediate of 76 kDa with no phenol oxidase activity, and then, PPAF-I converts the intermediate to the active phenol oxidase of 60 kDa in the presence of PPAF-II. These results indicate that the activation of pro-PO system in hemolymph of H. diomphalia larvae is accomplished by at least two activating factors, a serine protease and a protein cofactor.

In vitro and in vivo studies on the radical-scavenging activity of tea

Abstract: The effects of tea (Camellia sinensis L.) of three types on excessive free radicals were examined utilizing spin trapping, 1,1-diphenyl-2-picrylhydrazyl radical, lipid peroxidation, and lactate dehydrogenase leakage from cultured cells. Green tea extract presented significant antiradical effects in these four assay systems, whereas oolong tea and black tea extracts showed a rather weak protective effect against free radicals. A more potent scavenger effect using cultured cells was found with a green tea tannin mixture. Similarly to the effects of the green tea tannin mixture, (−)-epigallocatechin 3-O-gallate, its main ingredient, had an inhibitory effect on oxidative stress-induced apoptosis. The activities of the antioxidation enzymes in rats after subtotal nephrectomy were increased, suggesting a protective action against oxidative stress. The increased levels of uremic toxins in the blood were also reduced in rats given (−)-epigallocatechin 3-O-gallate. These findings indicate that (−)-epigallocatechin...

Molecular cloning of cDNA for pro-phenol-oxidase-activating factor I, a serine protease is induced by lipopolysaccharide or 1,3-β-glucan in coleopteran insect, Holotrichia diomphalia larvae

Abstract: Previously, we identified two pro-phenol oxidase-activating factors, named PPAF-I and PPAF-II, directly involved in the activation of the purified pro-phenol oxidase (pro-PO) from the hemolymph of the coleopteran, Holotrichia diomphalia larvae [Lee, S. Y., Kwon, T. H., Hyun, J. H., Choi, J. S., Kawabata, S. I., Iwanga, S, & Lee, B. L. (1998) Eur. J. Biochem. 254, 90-97]. Here, we report molecular cloning of cDNA for PPAF-I. Based on the sequence of the cloned cDNA, the PPAF-I gene appears to encode a member of serine protease zymogen consisting of 365 amino acid residues with a molecular mass of 40193 Da. The 109 amino acid residues preceding the amino-terminus Ile residue of the mature protein seem to constitute a prepro-sequence. The mature protein is a serine protease composed of 256 amino acids with a calculated molecular mass of 28009 Da. The overall structure is highly similar to that of Drosophila easter serine protease (42.9% identity), an essential serine protease zymogen for pattern formation in normal embryonic development. The locations of disulfide linkages in the pro-segment of PPAF-I were similar to those of Tachypleus proclotting enzyme and the mammalian neutrophil-derived defensin. Furthermore, [3H]diisopropylphosphate (iPr2P)-labeled PPAF-I was specifically produced from the crude preparation of PPAF-I zymogen by incubation with lipopolysaccharide or 1,3-beta-glucan, whereas [3H]iPr2P-labeled PPAF-I was not produced under the same conditions in the absence of these microbial polysaccharides. These results indicate that the pro-PO-activation system in H. diomphalia larvae may proceed with the activation of PPAF-I zymogen by microbial polysaccharides.

Ursolic acid-induced down-regulation of MMP-9 gene is mediated through the nuclear translocation of glucocorticoid receptor in HT1080 human fibrosarcoma cells.

Abstract: We have previously reported that ursolic acid, a pentacyclic triterpene acid, inhibited the invasion of HT1080 human fibrosarcoma cells by reducing the expression of matrix metalloproteinase-9. Since the chemical structure of ursolic acid is very similar to that of dexamethasone, a synthetic glucocorticoid, we investigated whether ursolic acid acts through the glucocorticoid receptor. The expression of matrix metalloproteinase-9 is thought to be regulated similarly with matrix metalloproteinase-1 and matrix metalloproteinase-3 as containing common 2-O-tetradecanoylphorbol-acetate responsible region, where AP-1 proteins can bind. Dexamethasone has been studied to repress the 2-O-tetradecanoylphorbol-acetate-induced expression of matrix metalloproteinase-1 and matrix metalloproteinase-3 through a glucocorticoid receptor-mediated manner. In Northern blot analysis, we found that ursolic acid reduced the expression of matrix metalloproteinase-1 and matrix metalloproteinase-3 induced by 2-O-tetradecanoylphorbol-acetate. Similarly, ursolic acid down-regulated 2-O-tetradecanoylphorbol-acetate-induction of matrix metalloproteinase-9 gene in the same manner of dexamethasone. RU486, a potent glucocorticoid receptor antagonist, was used for identifying that ursolic acid-induced down-regulation of matrix metalloproteinase-9 expression is mediated by its binding to glucocorticoid receptor. The effect of ursolic acid on the matrix metalloproteinase-9 expression was blocked by RU486, suggesting that ursolic acid acts via a glucocorticoid receptor in the regulation of matrix metalloproteinase-9. Western blot analysis and immunocytochemistry showed that ursolic acid increased glucocorticoid receptor fraction in the nucleus, although it decreased the synthesis of glucocorticoid receptor mRNA. In addition, ursolic acid did not decrease the expression of c-jun and DNA-binding activity of AP-1 to its cognate sequences. Taken together, we suggest that ursolic acid may induce the repression of matrix metalloproteinase-9 by stimulating the nuclear translocation of glucocorticoid receptor, and the translocated glucocorticoid receptor probably down-modulating the trans-activating function of AP-1 to 2-O-tetradecanoylphorbol-acetate responsible element of matrix metalloproteinase-9 promoter region.

Identification and Characterization of Novel Antimicrobial Decapeptides Generated by Combinatorial Chemistry

Abstract: Novel combinatorial libraries consisting of simplified amino acid sequences were designed to screen for peptides active against the Candida albicans membrane. A novel decapeptide, KKVVFKVKFK, that had a unique primary amino acid sequence was identified in this work. This peptide irreversibly inhibited the growth of C. albicans and showed a broad range of antibacterial activity but no hemolytic activity. Circular dichroism spectra revealed that the predominant secondary structure of this peptide strongly depended on the membrane-mimetic environments; the peptide preferred to form an amphipathic alpha-helical structure in the presence of 50% trifluoroethanol, while it preferred to adopt a distorted alpha-helical structure in the presence of sodium dodecyl sulfate micelles. Experiments in which dye was released from vesicles indicated that this novel antimicrobial peptide killed microorganisms through the action on the membrane as its primary target. Replacement of amino acids in this active decapeptide on the basis of information from the libraries could provide unique information about factors affecting its antimicrobial activity such as its secondary structure, net positive charge, and hydrophobicity.

The optimal determination of the space requirement and the number of transfer cranes for import containers

Abstract: It is discussed how to determine the optimal amount of storage space and the optimal number of transfer cranes for import containers. A cost model is developed for the decision making. It includes the space cost, the fixed cost of transfer cranes which corresponds to the investment cost, the variable cost of transfer cranes and outside trucks which is related to the time spent for the transfer of containers. A simple solution procedure for the optimal solution is provided. The solution procedure is illustrated using a numerical example.

One-Sided Stress Wave Velocity Measurement in Concrete

Abstract: Measurement of the velocity of stress waves in concrete provides valuable information on the state of the material. Recently, a number of papers have been published on wave velocity measurements in concrete when access to only one surface of the structure is possible, such as for the case of concrete pavements. In this paper, the existing one-sided methods for stress wave measurement in concrete are reviewed. Then, a modified method for one-sided stress wave velocity determination in concrete is introduced; the novel aspect of the modified technique is the data collection and processing system, which more accurately determines the arrival of the generated longitudinal and surface waves. The modified method, which is demonstrated on a variety of materials including steel, PMMA, and concretes of varying composition, is shown to be superior to existing one-sided techniques. Using the developed technique, the significant effect of the moisture content gradient within concrete on one-sided velocity measurements is demonstrated. Finally, one-sided velocity measurements are shown to be useful for monitoring the strength gain of early age concrete.

Development of a polymerase chain reaction (PCR) procedure for the detection of baculovirus associated with white spot syndrome (WSBV) in penaeid shrimp

Abstract: The causative viral agent was purified from diseased shrimp Penaeus japonicus with white spot syndrome (WSBV). Several hundred clones were obtained from libraries of the purified viral genomic DNA. According to the results of nucleotide sequence analysis, none of the WSBV clones showed considerable sequence homology with those of other known viruses, indicating that WSBV is a new virus causing a serious disease in shrimp. Based on the sequence data of WSBV genomic DNA, a pair of polymerase chain reaction (PCR) primers was designed. After 30 cycles of PCR amplification of viral genomic DNA extracted from WSBV, a single product of the expected size was detected. Southern blot hybridization confirmed that the amplified product was specific to the DNA of WSBV. The PCR system was able to detect 1 pg of WSBV DNA after 30 cycles, and efficiently amplify the target region of WSBV gene in the total nucleic acids extracted either from the diseased shrimp or hatchery shrimp with no signs of viral infection.

Identification and characterization of the antimicrobial peptide corresponding to c-terminal beta -sheet domain of tenecin 1, an antibacterial protein of larvae of tenebrio molitor

Abstract: An active fragment was identified from tenecin 1, an antibacterial protein belonging to the insect defensin family, by synthesizing the peptides corresponding to the three regions of tenecin 1. Only the fragment corresponding to the C-terminal beta-sheet domain showed activity against fungi as well as Gram-positive and Gram-negative bacteria, whereas tenecin 1, the native protein, showed activity only against Gram-positive bacteria. CD spectra indicated that each fragment in a membrane-mimetic environment might adopt a secondary structure corresponding to its region in the protein. The leakage of dye from liposomes induced by this fragment suggested that this fragment acts on the membrane of pathogens as a primary mode of action. A comparison between the structure and the activity of each fragment indicated that a net positive charge was a prerequisite factor for activity. To the best of our knowledge this is the first report in which the fragment corresponding to the beta-sheet region in antibacterial proteins, which consists of alpha-helical and beta-sheet regions, has been identified as a primary active fragment.

Caspase 3 specifically cleaves p21WAF1/CIP1 in the earlier stage of apoptosis in SK‐HEP‐1 human hepatoma cells

Abstract: We report here that p21WAF1/CIP1, an inhibitor of cyclin kinases, underwent proteolytic processing into a smaller fragment, p14, in the early stage of apoptosis in SK-HEP-1 cells. Apoptosis was induced by either staurosporine or ginsenoside Rh2, a ginseng saponin with a dammarane skeleton. Proteolytic processing was the result of caspase-3 activity, which accompanied the early changes in cell morphology and DNA fragmentation. p21WAF1/CIP1 translated in vitro was cleaved into a p14 fragment when incubated with cell extracts obtained from either ginsenoside Rh2-treated or staurosporine-treated cells. Cleavage was equally inhibited in both cases by adding Ac-DEVD-CHO, a specific caspase-3 inhibitor, but not by Ac-YVAD-CHO, a specific caspase-1 inhibitor. Similarly, p21WAF1/CIP1 was efficiently cleaved by recombinant caspase-3, overexpressed in Escherichia coli. Moreover, the endogenous p21WAF1/CIP1 of untreated cell extracts was also cleaved by recombinant caspase 3, as measured by immunoblotting. Mutation analysis allowed identification of two caspase-3 cleavage sites, DHVD112/L and SMTD149/F, which are located within or near the interaction domains for cyclins, Cdks, and proliferating cell nuclear antigen (PCNA). Taken together, these results show that ginsenoside Rh2 and staurosporine increase caspase-3 activity, which in turn directly cleaves p21WAF1/CIP1 during the early stages of apoptosis. We propose that proteolytic cleavage of p21WAF1/CIP1 is a functionally relevant event that allows release of the cyclin/Cdk complex from the p21WAF1/CIP1 inhibitor, resulting in the elevated levels of cyclin/Cdk kinase activity seen in the earlier stage of apoptosis.

Hepatoprotective activity of scopoletin, a constituent of Solanum lyratum.

Abstract: Scopoletin (7-hydroxy-6-methoxycoumarin), a coumarin, was isolated from the aerial part ofSolanum lyratum Thunb. by the activity-guided fractionation employing carbon tetrachloride-intoxicated primary cultured rat hepatocytes as a screening system. Its hepatoprotective activity was first evaluated by measuring the release of glutamic pyruvic transaminase and sorbitol dehydrogenase from carbon tetrachloride-intoxicated rat hepatocytes into the culture medium. Scopoletin significantly reduced the releases of glutamic pyruvic transaminase and sorbitol dehydrogenase from the carbon tetrachloride-intoxicated primary cultured rat hepatocytes by 53% and 58%, respectively, from the toxicity in a dose-dependent manner over concentration ranges of 1 μM to 50 μM. Further studies revealed that at the concentration of 10 μM, scopoletin significantly preserved glutathione content by 50% and the activity of superoxide dismutase by 36% and also inhibited the production of malondialdehyde to the degree as seen in the control.

Effect of urbanization on runoff characteristics of the On-Cheon Stream watershed in Pusan, Korea

Abstract: This study investigated the effect of urbanization on runoff from the On-Cheon Stream watershed in Pusan, Korea. This watershed has been experiencing considerable urbanization since the 1960s. There are two gauging stations in the watershed. For one of the stations there are recent flow data and for the other flow data were observed in the past. A linear reservoir model was chosen and runoff was analysed for several flood events. The linear reservoir model has been found to generate flood hydrographs accurately for both gauging stations, and its applicability to the study area has also been established. Using two methods of computing effective rainfall or rainfall excess (ϕ-index and constant percentage method), the results of runoff analyses were investigated. The ϕ-index method yielded better results than the constant percentage method. A comparison of hydrographs observed in the past with the simulation results at the Ie-Sup bridge site revealed that the peak discharge increased and the mean lag time of the study area decreased owing to urbanization over the past two decades. It is also possible to evaluate the effect of urbanization quantitatively. © 1998 John Wiley & Sons, Ltd.

The phytoplankton succession in the lower part of hypertrophic Nakdong River (Mulgum), South Korea

Abstract: Investigations were carried out to determine the mechanism of phytoplankton succession in the lower part of Nakdong River. Intensive monitoring was conducted from April 1993 to April 1995 at weekly or biweekly intervals. This river is the main source of drinking water for more than 8 million residents living in Pusan and the Southeastern region of Korea, and it is also important for industrial purposes. Due to the rapid urbanization and industrialization, this river has become hypertrophic and it is heavily regulated (mean chl. a, 79 ± 232 µg 1−1 n = 76; mean TN, 4.3 ± 2.0 mg 1−1 n = 30; mean TP, 165 + 108 µg 1−1 n = 45). Bacillariophyceae were dominant year-round in 1993, with spring and late fall peaks. Dominant communities in 1994 were Bacillariophyceae in March and April, Chlorophyceae and Cryptophyceae in May, Cyanobacteria in July and August, Chlorophyceae and Cryptophyceae in October, and Bacillariophyceae in December. As drought persisted through the summer of 1994, elevated water temperature (over 30 °C) possibly triggered Cyanobacteria bloom (mainly Microcystis aeruginosa, maximum cell density, 1.6 × 107 cells m1−1). The most common diatom, Stephanodiscus hantzschii, repeatedly dominated from late fall to next spring (mean and maximum cell density, 7.5 × 104, 1.2 × 105 cells m1−1, respectively). This small centric diatom was favored by the low discharge and the cold water (water temperature, 3–10 °C). After the diatom bloom, this community shifted to peaks of colonial Chlorophyceae and motile Cryptophyceae, owing to the high rate of zooplankton grazing activity and increased water temperature. Overall, the phytoplankton periodicity was primarily governed by the hydrologic regime (discharge). Changes in silica concentration, water temperature and high zooplankton density might have played an important role in phytoplankton dynamics during the non-flooding periods. Compared to other large rivers, strong Microcystis bloom events in summer and Stephanodiscus bloom events in winter were noticeable in the dry year. The patterns of phytoplankton succession observed in this study may have a significance since most of the large rivers in Far Eastern Asian countries are subjected to eutrophication and regulation of discharge.

Effect of Low Temperature Plasma Treatment on Color of Wool and Nylon 6 Fabrics Dyed with Natural Dyes

Abstract: In a previous article, we reported that oxygen low temperature plasma treatment of wool fibers increases both the dyeing rate and saturation dye exhaustion of acid dyes, despite increased electronegativity of the fiber surface with the treatment. In this article, wool and nylon 6 fabrics treated with oxygen, carbon tetrafluoride, and ammonia low temperature plasmas are dyed with several natural dyes, such as cochineal, Chinese cork tree, madder, and gromwell. The dyeing rate of the plasma-treated wool increases con siderably with cochineal, Chinese cork tree, and madder, but not with gromwell. How ever, the dyeing rate of nylon 6 with cochineal and Chinese cork tree is not changed by the plasma pretreatment. Furthermore, plasma-treated wool fabrics dyed with cochineal and Chinese cork tree have increased brightness compared with untreated wool.

Suppression of multidrug resistance via inhibition of heat shock factor by quercetin in MDR cells.

Abstract: MDR1 promoter has been shown to contain heat shock elements (HSE), and it has been reported that FM3A/M and P388/M MDR cells show a constitutively activated heat shock factor (HSF), suggesting that HSF might be an important target for reversing the multidrug resistance. Therefore, it was examined whether quercetin, which has been shown to interfere with the formation of the complex between HSE and HSF, and to downregulate the level of HSF1, can sensitize MDR cells against anticancer drugs by inhibition of HSF DNA-binding activity. In this study, quercetin appeared to inhibit the constitutive HSF DNA-binding activity and the sodium arsenite-induced HSF DNA-binding activity in the MDR cells. The basal and sodium arsenite-induced MDRCAT activities were remarkably suppressed by the treatment of quercetin. These results were well consistent with the finding that the treatment of quercetin decreased the expression level of P-gp, MDR1 gene product, in dose-dependent manner, and markedly increased the sensitivity of MDR cells to vincristine or vinblastine. These results suggest that quercetin can decrease the expression of P-gp via inhibition of HSF DNA-binding activity, and might be useful as a chemosensitizer in MDR cells.

Process of Pb2 accumulation in Saccharomyces cerevisiae

Abstract: Most of the Pb2+ taken up by Saccharomyces cerevisae was deposited in the inner part of the cells after 2 h. In the Pb2 accumulation experiments, the time to reach an equilibrium state was significantly shortened from 96 h to 24 h as the cell dry weight increased from 0.56 g/l to 5.18 g/l. The penetration time of Pb2+ to reach on the interacellular region (2 h) was quite different from that on the extracellular region (3 min). In the case of S. cerevisiae, the first step which a Pb2+ binds to cell wall within 3[f]5 min is metabolism-independent and the second step within 24 h is metabolism-dependent followed by the third step which is metabolism-dependent or -independent after 24 h.

Preparation and properties of UV-curable polyurethane acrylate ionomers

Abstract: Ultraviolet (UV)-curable polyurethane acrylate ionomer (PUAI) prepolymers were synthesized from isophorone diisocyanate (IPDI), poly(methylene ether) glycol (PTMG), 2,2-bis(hydroxymethyl) propionic acid (DMPA), triethylamine (TEA), 2-hydroxy ethyl acrylate (HEA), and dibutyl tin dilaurate (DBT) as a catalyst. UV-curable polyurethane acrylate ionomer aqueous dispersion was formulated from the prepolymers, water (30 wt %), and 1-hydroxycyclohexylhenyl ketone (Irgacure 184) as a photoinitiator. The films of UV-cured polyurethane acrylate ionomer were formed by curing the dispersion using a medium-pressure mercury lamp (80 W/cm; λ max = 365 nm). Gel content decreased with increasing water content in the aqueous dispersion. Effects of DMPA content and molecular weight of PTMG and the degree of neutralization on the physical properties were investigated. It was found that the storage modulus increased with increasing DMPA content. Tensile modulus and strength decreased with increasing the molecular weight of PTMG from 650 to 2000. The glass transition temperature shifted to a higher temperature as the content of DMPA increased. As the degree of neutralization increased, the tensile strength and modulus decreased. However, the elongation at break increased. © 1998 John Wiley & Sons, Inc. J Appl Polym Sci 67:2153–2162, 1998

Rationing policies for some inventory systems

Abstract: This paper considers inventory systems which maintain stocks to meet various demand classes with different priorities. We use the concept of a support level control policy. That is rationing is accomplished by maintaining a support level, say K, such that when on hand stock reaches K, all low priority demands are backordered. We develop four analytical and simulation models to improve the existing models. Firstly, multiple support levels are used instead of using a single support level. Secondly, a simulation model with a more realistic assumption on the demand process has been provided. Thirdly, a single period deterministic cost minimisation model has been developed analytically. Finally, we address a continuous review (Q, r) model with a compound Poisson process.