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Asia-Pacific Journal of Operational Research c World Scientific Publishing Company & Operational Research Society of Singapore Instructions for Typesetting Manuscripts Using L A TEX First Author University Department, University Name, Address City, State ZIP/Zone,Country author id@domain name http://<webaddress> Second Author Group, Laboratory, Address City, State ZIP/Zone, Country author id@domain name Received (Day Month Year) Revised (Day Month Year) The abstract should summarize the context, content and conclusions of the paper in less than 200 words. It should not contain any reference citations or displayed equations. Typeset the abstract in 8 pt roman with baselineskip of 10 pt, making an indentation of 1.5 pica on the left and right margins. Keywords: Keyword1; keyword2; keyword3. 1. General Appearance Contributions to the Asia-Pacific Journal of Operational Research will mostly be processed by using the authors source files. These should be submitted with the manuscripts, and resubmitted in the final form if a paper requires revision before being accepted for publication. 2. The Main Text Authors are encouraged to have their contribution checked for grammar. American spelling should be used. Abbreviations are allowed but should be spelt out in full For the title, try not to use more than 3 lines. Typeset the title in 10 pt bold and title case. Typeset names in 8 pt roman, title case. Use the footnote to indicate the present or permanent address of the author. State completely without abbreviations, the affiliation and mailing address, including country. Typeset in 8 pt italic. Typeset author e-mail address in single line. 1

2 Authors Names when first used. Integers ten and below are to be spelt out. Italicize foreign language phrases (e.g. Latin, French). The text should be in 10 pt roman, single spaced with baselineskip of 13 pt. Text area (excluding copyright block and folio) is 6.75 inches high and 5 inches wide for the first page. Text area (excluding running title) is 7.7 inches high and 5 inches wide for subsequent pages. Final pagination and insertion of running titles will be done by the publisher. 3. Major Headings Major headings should be typeset in boldface with the first letter of important words capitalized. 3.1. Sub-headings Sub-headings should be typeset in boldface italic and capitalize the first letter of the first word only. Section number to be in boldface roman. 3.1.1. Sub-subheadings Typeset sub-subheadings in medium face italic and capitalize the first letter of the first word only. Section numbers to be in roman. 3.2. Numbering and spacing Sections, sub-sections and sub-subsections are numbered in Arabic. Use double spacing before all section headings, and single spacing after section headings. Flush left all paragraphs that follow after section headings. 3.3. Lists of items List may be presented with each item marked by bullets and numbers. Bulleted items item one, item two, item three. Numbered items 1. item one, 2. item two, 3. item three. The order of subdivisions of items in bullet and numbered lists may be presented as follows:

Instructions for Typing Manuscripts (Paper s Title) 3 Bulleted items First item in the first level Second item in the first level First item in the second level Second item in the second level First item in the third level Second item in the third level Third item in the second level Fourth item in the second level Third item in the first level Fourth item in the first level Numbered items 1. First item in the first level 2. Second item in the first level (a) First item in the second level (b) Second item in the second level i. First item in the third level ii. Second item in the third level iii. Third item in the third level (c) Third item in the second level (d) Fourth item in the second level 3. Third item in the first level 4. Fourth item in the first level 4. Equations Displayed equations should be numbered consecutively in the paper, with the number set flush right and enclosed in parentheses. For numbered display formulae, use the displaymath environment: \begin{equation}... \end{equation}. For unnumbered display formulae, use \[... \]. For numbered displayed, oneline formulae always use the equation environment. Do not use $$... $$. For example, the input for 1(d i < t, N(d i ) = n) i=1 µ(n, t) = (1) t 1(N(σ) = n)dσ is: σ=0

4 Authors Names \begin{equation} \mu(n, t) = \frac{\sum\limits^\infty_{i=1}1 (d_i < t, N(d_i) = n)} {\int\limits^t_{\sigma=0}1 (N(\sigma)=n)d\sigma} \label{eq1} \end{equation} For displayed multi-line formulae, use the eqnarray environment. For example, \begin{eqnarray} \zeta\mapsto\hat{\zeta}&=&a\zeta+b\eta\,,\\ \eta\mapsto\hat{\eta}&=&c\zeta+d\eta\,. \label{eq2n3} \end{eqnarray} produces: ζ ˆζ = aζ + bη, (2) η ˆη = cζ + dη. (3) L A TEX does not break long equations to make them fit within the margins as it does with normal text. It is therefore up to you to format the equation appropriately (if they overrun the margin). This typically requires some creative use of an eqnarray to get elements shifted to a new line and to align nicely, e.g., (1 + x) n n (n 1) = 1 + nx + x 2 2! n (n 1) (n 2) + x 3 3! n (n 1) (n 2) (n 3) + x 4 4! +... nth. (4) Superscripts and subscripts that are words or abbreviations, as in π low, should be typed as roman letters; this is done as \( \pi_{\mathrm{low}} \) instead of π low done with \( \pi_{low} \) For geometric functions, e.g., exp, sin, cos, tan, etc., please use the macros \sin, \cos, \tan. These macros give proper spacing in mathematical formulae. It is also possible to use the AMS-L A TEX package, which can be obtained from the AMS and various TEX archives. Equations should be referred to in abbreviated form, e.g., Eq. (1) or (2). In multiple-line equations, the number should be given on the last line. Displayed equations are to be centered on the page width. Standard English letters like x are to appear as x (italicized) in the text if they are used as mathematical

Instructions for Typing Manuscripts (Paper s Title) 5 symbols. Punctuation marks are used at the end of equations as if they appeared directly in the text. 5. Theorem environments Theorem 5.1. Theorems, lemmas, definitions, etc. are set on a separate paragraph, with extra 1 line space above and below. They are to be numbered consecutively within each section. i=1 µ(n, t) = 1(d i < t, N(d i ) = n) t σ=0 1(N(σ) = n)dσ. (5) Numbering by sections refers only to the large main sections, i.e. to those with Level 1 headings. Thus the numbering style in Section 5 would be labeled (5), etc. Lemma 5.1 (Optional Title). Theorems, lemmas, definitions, etc. are set on a separate paragraph, with extra 1 line space above and below. They are to be numbered consecutively within each section. Numbering by sections refers only to the large main sections, i.e. to those with Level 1 headings. Thus the numbering style in Section 5 would be labeled (5), etc. Proof. Proofs should end with a square box. 6. Illustrations and Photographs Figures are to be inserted in the text nearest their first reference. Figure placements can be either top or bottom. Original india ink drawings of glossy prints are preferred. Please send one set of originals with copies. If the author requires the publisher to reduce the figures, ensure that the figures (including letterings and S SL 4m2 π Fig. 1. A schematic illustration of dissociative recombination. The direct mechanism, 4m 2 π is initiated when the molecular ion S L captures an electron with kinetic energy.

6 Authors Names numbers) are large enough to be clearly seen after reduction. If photographs are to be used, only black and white ones are acceptable. Figures are to be sequentially numbered in Arabic numerals. The caption must be placed below the figure. Typeset in 8 pt roman with baselineskip of 10 pt. Long captions are to be justified by the page-width. Use double spacing between a caption and the text that follows immediately. Previously published material must be accompanied by written permission from the author and publisher. 7. Tables Tables should be inserted in the text as close to the point of reference as possible. Some space should be left above and below the table. Tables should be numbered sequentially in the text in Arabic numerals. Captions are to be centralized above the tables. Typeset tables and captions in 8 pt roman with baselineskip of 10 pt. Long captions are to be justified by the table-width. Table 1. Comparison of acoustic for frequencies for piston-cylinder problem. Piston mass Analytical frequency TRIA6-S 1 model % Error (Rad/s) (Rad/s) 1.0 281.0 280.81 0.07 0.1 876.0 875.74 0.03 0.01 2441.0 2441.0 0.0 0.001 4130.0 4129.3 0.16 Note: Table notes. a Table footnote A. b Table footnote B. If tables need to extend over to a second page, the continuation of the table should be preceded by a caption, e.g. Table 2. (Continued). Notes to tables are placed below the final row of the table and should be flushleft. Footnotes in tables should be indicated by superscript lowercase letters and placed beneath the table. 8. Running Heads Please provide a shortened runninghead (not more than eight words) for the title of your paper. This will appear on the top right-hand side of your paper. 9. Footnotes Footnotes should be numbered sequentially in superscript Arabic numeral. a a Footnotes should be typeset in 8 pt roman at the bottom of the page.

Instructions for Typing Manuscripts (Paper s Title) 7 Appendix A. Appendices Appendices should be used only when absolutely necessary. They should come before the Acknowledgments. If there is more than one appendix, number them alphabetically. Number displayed equations occurring in the Appendix in this way, e.g. (A.1), (A.2), etc. i=1 µ(n, t) = 1(d i < t, N(d i ) = n) t σ=0 1(N(σ) = n)dσ, (A.1) and g E µν e 4(φ 0 φ) n 2 g µν. (A.2) Acknowledgments This section should come before the References. Funding information may also be included here. References References are to be listed in alphabetical order using the last name of the firstnamed contributor. They can be cited in text as, e.g. According to Tapley and Lewallen (1967) or... (Tapley and Lewallen, 1967). Please list using the style shown in the following examples. Full journal titles should be used. Typeset references in 9 pt roman. References Hadley, G (1970). Nonlinear and Dynamic Programming. Reading, Massachusetts: Addision-Wesley Publishing Co. Powell, MJD (1970). A new algorithm for unconstrained optimization. In Nonlinear Programming, J Rosen, O Mangasarian and K Ritter (eds.), 291 312. New York: Academic Press. Tapley, BP and JM Lewallen (1967). Comparison of several numerical optimization methods. Journal of Optimization Theory and Applications, 1, 1 32.