<div dir="ltr"><img width="0" height="0" class="mailtrack-img" alt="" style="display:flex" src="https://mailtrack.io/trace/mail/c5e369fce80cb747161f44ddd6327337d65b5d41.png?u=108612"><div></div>
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<div style="color:rgb(34,34,34);font-family:arial,sans-serif;font-size:12.8px;font-style:normal;font-variant-ligatures:normal;font-variant-caps:normal;font-weight:400;letter-spacing:normal;text-align:start;text-indent:0px;text-transform:none;white-space:normal;word-spacing:0px;background-color:rgb(255,255,255);text-decoration-style:initial;text-decoration-color:initial">
<div style="color:rgb(34,34,34);font-family:arial,sans-serif;font-size:12.8px;font-style:normal;font-variant-ligatures:normal;font-variant-caps:normal;font-weight:400;letter-spacing:normal;text-align:start;text-indent:0px;text-transform:none;white-space:normal;word-spacing:0px;background-color:rgb(255,255,255);text-decoration-style:initial;text-decoration-color:initial">Hello,<br></div><div style="color:rgb(34,34,34);font-family:arial,sans-serif;font-size:12.8px;font-style:normal;font-variant-ligatures:normal;font-variant-caps:normal;font-weight:400;letter-spacing:normal;text-align:start;text-indent:0px;text-transform:none;white-space:normal;word-spacing:0px;background-color:rgb(255,255,255);text-decoration-style:initial;text-decoration-color:initial">Please, can someone help me the complexity of my MILP formualtion that can determine the assignment of resources to tasks.</div><div style="color:rgb(34,34,34);font-family:arial,sans-serif;font-size:12.8px;font-style:normal;font-variant-ligatures:normal;font-variant-caps:normal;font-weight:400;letter-spacing:normal;text-align:start;text-indent:0px;text-transform:none;white-space:normal;word-spacing:0px;background-color:rgb(255,255,255);text-decoration-style:initial;text-decoration-color:initial"><br></div><div style="color:rgb(34,34,34);font-family:arial,sans-serif;font-size:12.8px;font-style:normal;font-variant-ligatures:normal;font-variant-caps:normal;font-weight:400;letter-spacing:normal;text-align:start;text-indent:0px;text-transform:none;white-space:normal;word-spacing:0px;background-color:rgb(255,255,255);text-decoration-style:initial;text-decoration-color:initial"><br></div><div style="color:rgb(34,34,34);font-family:arial,sans-serif;font-size:12.8px;font-style:normal;font-variant-ligatures:normal;font-variant-caps:normal;font-weight:400;letter-spacing:normal;text-align:start;text-indent:0px;text-transform:none;white-space:normal;word-spacing:0px;background-color:rgb(255,255,255);text-decoration-style:initial;text-decoration-color:initial"><br></div><div style="color:rgb(34,34,34);font-family:arial,sans-serif;font-size:12.8px;font-style:normal;font-variant-ligatures:normal;font-variant-caps:normal;font-weight:400;letter-spacing:normal;text-align:start;text-indent:0px;text-transform:none;white-space:normal;word-spacing:0px;background-color:rgb(255,255,255);text-decoration-style:initial;text-decoration-color:initial"><br></div><div style="color:rgb(34,34,34);font-family:arial,sans-serif;font-size:12.8px;font-style:normal;font-variant-ligatures:normal;font-variant-caps:normal;font-weight:400;letter-spacing:normal;text-align:start;text-indent:0px;text-transform:none;white-space:normal;word-spacing:0px;background-color:rgb(255,255,255);text-decoration-style:initial;text-decoration-color:initial"><img src="https://mail.google.com/mail/u/1/?ui=2&ik=89f903daac&view=fimg&th=161b89dd218d6e62&attid=0.1&disp=emb&realattid=ii_161b8958bfbce909&attbid=ANGjdJ8Zo7UUkakdhKzbAYHQTr9izzgYqQ8b6i5VT8zAE1egFst6-w27tn8PnOERhi2sbAMv1P6tO2YE_tMRqwd2lM6mUFL6WUXpVaMQtfhRFNoQVD1eG_6LC-zDqV8&sz=w860-h630&ats=1519220814025&rm=161b89dd218d6e62&zw&atsh=1" alt="Images intégrées 1" width="430" height="315" class="gmail-CToWUd gmail-a6T" tabindex="0" style="cursor: pointer; outline: 0px;"></div><div style="color:rgb(34,34,34);font-family:arial,sans-serif;font-size:12.8px;font-style:normal;font-variant-ligatures:normal;font-variant-caps:normal;font-weight:400;letter-spacing:normal;text-align:start;text-indent:0px;text-transform:none;white-space:normal;word-spacing:0px;background-color:rgb(255,255,255);text-decoration-style:initial;text-decoration-color:initial"><div>Here are the details</div><div><br></div><div>My assignment problem is modeled as a mixed integer linear program (MILP) and solved by CPLEX in order to determine the VM type of each task. </div><div>X(i,t) i = 1 means that the task Ti is assigned to VM of type t, otherwise X(i,t) = 0.</div><div>fi denotes the finish time of task Ti. Our MILP problem can be formally described as follows (an objective function (1)</div><div>and some constraints (2 to 7)):</div><div>The goal of the objective function (1) is to minimize the total execution cost of the workflow.</div><div> Each task is assigned to one and only one VM type according to constraint (2).</div><div>Constraints (3) and (4) guarantee the precedence constraints.</div><div>Constraint (5) denotes a binary decision variable. According</div><div>to constraint (6), the execution times of tasks are integers (in minutes).</div><div>Finally, the deadline is met according to the constraint (7).</div></div>
<br></div><div style="color:rgb(34,34,34);font-family:arial,sans-serif;font-size:12.8px;font-style:normal;font-variant-ligatures:normal;font-variant-caps:normal;font-weight:400;letter-spacing:normal;text-align:start;text-indent:0px;text-transform:none;white-space:normal;word-spacing:0px;background-color:rgb(255,255,255);text-decoration-style:initial;text-decoration-color:initial">Thanks</div><div style="color:rgb(34,34,34);font-family:arial,sans-serif;font-size:12.8px;font-style:normal;font-variant-ligatures:normal;font-variant-caps:normal;font-weight:400;letter-spacing:normal;text-align:start;text-indent:0px;text-transform:none;white-space:normal;word-spacing:0px;background-color:rgb(255,255,255);text-decoration-style:initial;text-decoration-color:initial"><br></div><div style="color:rgb(34,34,34);font-family:arial,sans-serif;font-size:12.8px;font-style:normal;font-variant-ligatures:normal;font-variant-caps:normal;font-weight:400;letter-spacing:normal;text-align:start;text-indent:0px;text-transform:none;white-space:normal;word-spacing:0px;background-color:rgb(255,255,255);text-decoration-style:initial;text-decoration-color:initial">Best Regards, </div><div style="color:rgb(34,34,34);font-family:arial,sans-serif;font-size:12.8px;font-style:normal;font-variant-ligatures:normal;font-variant-caps:normal;font-weight:400;letter-spacing:normal;text-align:start;text-indent:0px;text-transform:none;white-space:normal;word-spacing:0px;background-color:rgb(255,255,255);text-decoration-style:initial;text-decoration-color:initial">Faten</div></div></div><img src="https://my-email-signature.link/signature.gif?u=47536&e=18280654&v=80e9f3efd7ce37072b0bba2cc750b7e4b15d342955807957c7c98b99c35c051f" style="width:0;max-height:0;overflow:hidden"><div id="DAB4FAD8-2DD7-40BB-A1B8-4E2AA1F9FDF2"><br> <table style="border-top:1px solid #d3d4de">
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