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<p class="MsoNormal"><span style="font-family:"Times New Roman",serif">Dear SCIP-Team,<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-family:"Times New Roman",serif"><o:p> </o:p></span></p>
<p class="MsoNormal"><span lang="EN-GB" style="font-family:"Times New Roman",serif">Thank you very much for sharing this amazing solver!<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-GB" style="font-family:"Times New Roman",serif"><o:p> </o:p></span></p>
<p class="MsoNormal"><span lang="EN-GB" style="font-family:"Times New Roman",serif">I have the following question:<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-GB" style="font-family:"Times New Roman",serif"><o:p> </o:p></span></p>
<p class="MsoNormal"><span lang="EN-GB" style="font-family:"Times New Roman",serif">f(x, y, z) = (x – a) * b * y * (1 – exp(-c / (b * y))) + z<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-GB" style="font-family:"Times New Roman",serif">f(x, y, z) = 0<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-GB" style="font-family:"Times New Roman",serif"><o:p> </o:p></span></p>
<p class="MsoNormal"><span lang="EN-GB" style="font-family:"Times New Roman",serif">With y running to zero the division is not defined and SCIP does not find a solution (infeasible, solution for z is 1e-20).
<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-GB" style="font-family:"Times New Roman",serif">Adding a tiny number to y makes SKIP finding a solution.<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-GB" style="font-family:"Times New Roman",serif"><o:p> </o:p></span></p>
<p class="MsoNormal"><span lang="EN-GB" style="font-family:"Times New Roman",serif">f(x, y, z) = (x – a) * b * y * (1 – exp(-c / (b * (y + 1e-20)))) + z<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-GB" style="font-family:"Times New Roman",serif">f(x, y, z) = 0<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-GB" style="font-family:"Times New Roman",serif"><o:p> </o:p></span></p>
<p class="MsoNormal"><span lang="EN-GB" style="font-family:"Times New Roman",serif">The question is how to determine the thiny number beforehand. The tiny number seems to depend on the size of the problem (for many x, y, z it happens that no solution can be
found).<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-GB" style="font-family:"Times New Roman",serif">However, is there a better technique to solve the undefined problem for –c / (b * y) for y == 0, or to even linearize the function?<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-GB" style="font-family:"Times New Roman",serif"><o:p> </o:p></span></p>
<p class="MsoNormal"><span lang="EN-GB" style="font-family:"Times New Roman",serif">I am looking forward to your response.<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-GB" style="font-family:"Times New Roman",serif"><o:p> </o:p></span></p>
<p class="MsoNormal"><span lang="EN-GB" style="font-family:"Times New Roman",serif">Kind regards,<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-GB" style="font-family:"Times New Roman",serif">Johannes Pelda<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-GB" style="font-family:"Times New Roman",serif"><o:p> </o:p></span></p>
<p class="MsoNormal"><span lang="EN-GB" style="font-family:"Times New Roman",serif"><o:p> </o:p></span></p>
<p class="MsoNormal"><span lang="EN-GB" style="font-family:"Times New Roman",serif"><o:p> </o:p></span></p>
<p class="MsoNormal"><span lang="EN-GB" style="mso-fareast-language:DE">Johannes Pelda<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-GB" style="color:black;mso-fareast-language:DE">Nachhaltige Energie- und Umwelttechnik (NEUTec)<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-GB" style="mso-fareast-language:DE"><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="mso-fareast-language:DE">HAWK <o:p></o:p></span></p>
<p class="MsoNormal"><span style="mso-fareast-language:DE">Hochschule für angewandte Wissenschaft und Kunst Hildesheim/Holzminden/Göttingen
<o:p></o:p></span></p>
<p class="MsoNormal"><span style="mso-fareast-language:DE">Fakultät Ressourcenmanagement | Rudolf-Diesel-Straße 12 | 37075 Göttingen<o:p></o:p></span></p>
<p class="MsoNormal"><span style="mso-fareast-language:DE">E-Mail: <a href="mailto:johannes.pelda@hawk.de">
<span style="color:blue">johannes.pelda@hawk.de</span></a> | Telefon: +49 551 5032 185<o:p></o:p></span></p>
<p class="MsoNormal"><span style="mso-fareast-language:DE"><a href="http://www.hawk.de/"><span style="color:blue">www.hawk.de</span></a><o:p></o:p></span></p>
<p class="MsoNormal"><span style="mso-fareast-language:DE"><o:p> </o:p></span></p>
<p class="MsoNormalCxSpMiddle" style="margin-bottom:12.0pt;mso-add-space:auto"><span style="mso-fareast-language:DE">Präsident: Dr. Marc Hudy | Hauptberuflicher Vizepräsident: Martin Böhnke<o:p></o:p></span></p>
<p class="MsoNormalCxSpMiddle" style="margin-bottom:12.0pt;mso-add-space:auto"><span style="mso-fareast-language:DE">USt.-ID-Nr.: 154 261 014 | Steuernummer: 30/210/09001<o:p></o:p></span></p>
<p class="MsoNormal"><o:p> </o:p></p>
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