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<!doctype html>
<html lang="en">
<head>
<title>Assignment 1 Combinatorial Optimization</title>
<meta charset="utf-8">
<meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no">
<!-- Bootstrap CSS -->
<script src="https://ajax.googleapis.com/ajax/libs/jquery/3.4.1/jquery.min.js"></script>
<script src="https://maxcdn.bootstrapcdn.com/bootstrap/4.0.0/js/bootstrap.min.js"
integrity="sha384-JZR6Spejh4U02d8jOt6vLEHfe/JQGiRRSQQxSfFWpi1MquVdAyjUar5+76PVCmYl"
crossorigin="anonymous"></script>
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href="https://stackpath.bootstrapcdn.com/bootstrap/4.3.1/css/bootstrap.min.css"
integrity="sha384-ggOyR0iXCbMQv3Xipma34MD+dH/1fQ784/j6cY/iJTQUOhcWr7x9JvoRxT2MZw1T"
crossorigin="anonymous">
<script src="scripts.js"></script>
</head>
<body>
<!-- -->
<!--UTILITY FUNCTIONS-->
<!-- -->
<div id="util_functions_div_id" class="container">
<div class="container">
<nav class="navbar navbar-expand-lg bg-light navbar-light justify-content-center">
<!-- <div class="collapse navbar-collapse">-->
<!-- <ul class="nav navbar-nav">-->
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<ul class="navbar-nav">
<li class="nav-item">
<a class="nav-link" href="instructionsAssignment1.html">Instructions</a>
</li>
<li class="nav-item">
<a class="nav-link" href="question1.html">Exercise 1</a>
</li>
<li class="nav-item active">
<a class="nav-link" href="#">Exercise 2</a>
</li>
<li class="nav-item">
<a class="nav-link" href="question3.html">Exercise 3</a>
</li>
<li class="nav-item">
<a class="nav-link" href="question4.html">Exercise 4</a>
</li>
</ul>
</nav>
<div class="jumbotron text-center">
<h1>Combinatorial Optimization 2020-2021</h1>
<h2>Exercise 2</h2>
</div>
</div>
<form id="my_form">
<div class="container">
<hr>
<h4>MIP with 6 depots/clients</h4>
<hr>
<h6>Question 1</h6>
<p>
For the instance with 6 depots/clients, state the optimal MIP objective value.
</p>
<div class="input-group">
<input type="number" class="form-control"
id="_num_auto_decimals_2_question_1_ip_val_6_id_"
name="_num_auto_decimals_2_question_1_ip_val_6"
value="0" min="-Infinity"
max="Infinity" step="0.01"
required=>
</div>
<br>
<h6>Question 2</h6>
<p>
For the instance with 6 depots/clients, state the x-matrix of the optimal MIP
solution. Your answer should be a numeric 6 x 6 matrix.
</p>
<div class="form-group">
<textarea class="form-control" rows="5"
id="_numarea_manual_decimals_2_question_2_ip_sol_x_6_id__shadow"
required
oninput="updateTextAreaAndLabel('_numarea_manual_decimals_2_question_2_ip_sol_x_6_id__shadow','_numarea_manual_decimals_2_question_2_ip_sol_x_6_id_','_numarea_manual_decimals_2_question_2_ip_sol_x_6_id__label',6,6,2)"></textarea>
<p>The parsed result is:</p>
<textarea class="form-control" rows="5"
id="_numarea_manual_decimals_2_question_2_ip_sol_x_6_id_"
name="_numarea_manual_decimals_2_question_2_ip_sol_x_6"
readonly></textarea>
<label for="_numarea_manual_decimals_2_question_2_ip_sol_x_6_id_"
id="_numarea_manual_decimals_2_question_2_ip_sol_x_6_id__label"></label>
</div>
<h6>Question 3</h6>
<p>
For the instance with 6 depots/clients, state the y-matrix of the optimal MIP
solution. Your answer should be a numeric 6 x 6 matrix.
</p>
<div class="form-group">
<textarea class="form-control" rows="5"
id="_numarea_manual_decimals_2_question_3_ip_sol_y_6_id__shadow"
required
oninput="updateTextAreaAndLabel('_numarea_manual_decimals_2_question_3_ip_sol_y_6_id__shadow','_numarea_manual_decimals_2_question_3_ip_sol_y_6_id_','_numarea_manual_decimals_2_question_3_ip_sol_y_6_id__label',6,6,2)"></textarea>
<p>The parsed result is:</p>
<textarea class="form-control" rows="5"
id="_numarea_manual_decimals_2_question_3_ip_sol_y_6_id_"
name="_numarea_manual_decimals_2_question_3_ip_sol_y_6"
readonly></textarea>
<label for="_numarea_manual_decimals_2_question_3_ip_sol_y_6_id_"
id="_numarea_manual_decimals_2_question_3_ip_sol_y_6_id__label"></label>
</div>
<h6>Question 4</h6>
<p>
For the instance with 6 depots/clients, state the running time needed to solve the
MIP to optimality.
Round your answer to 2 decimal places.
</p>
<div class="input-group">
<input type="number" class="form-control"
id="_num_auto_decimals_2_question_4_ip_time_6_id_"
name="_num_auto_decimals_2_question_4_ip_time_6"
value="0" min="-Infinity"
max="Infinity" step="0.01"
required=>
</div>
<br>
<h6>Question 5</h6>
<p>
For the instance with 6 depots/clients, state the number of nodes needed to solve
the MIP to optimality.
</p>
<div class="input-group">
<input type="number" class="form-control"
id="_num_auto_decimals_2_question_5_ip_nodes_6_id_"
name="_num_auto_decimals_2_question_5_ip_nodes_6"
value="0" min="-Infinity"
max="Infinity" step="1"
required=>
</div>
<br>
<hr>
<h4>LP with 6 depots/clients</h4>
<hr>
<h6>Question 6</h6>
<p>For the instance with 6 depots/clients, state the optimal LP relaxation objective
value.
If needed, round your answer to 2 decimal places.
</p>
<div class="input-group">
<input type="number" class="form-control"
id="_num_auto_decimals_2_question_6_lp_val_6_id_"
name="_num_auto_decimals_2_question_6_lp_val_6"
value="0" min="-Infinity"
max="Infinity" step="0.01"
required>
</div>
<br>
<h6>Question 7</h6>
<p>
For the instance with 6 depots/clients, state the running time needed to solve the
LP relaxation to optimality.
Round your answer to 2 decimal places.
</p>
<div class="input-group">
<input type="number" class="form-control"
id="_num_auto_decimals_2_question_7_lp_time_6_id_"
name="_num_auto_decimals_2_question_7_lp_time_6"
value="0" min="-Infinity"
max="Infinity" step="0.01"
required>
</div>
<br>
</div>
<div class="container">
<hr>
<h4>MIP with 7 depots/clients</h4>
<hr>
<h6>Question 8</h6>
<p>
For the instance with 7 depots/clients, state the optimal MIP objective value.
</p>
<div class="input-group">
<input type="number" class="form-control"
id="_num_auto_decimals_2_question_8_ip_val_7_id_"
name="_num_auto_decimals_2_question_8_ip_val_7"
value="0" min="-Infinity"
max="Infinity" step="0.01"
required>
</div>
<br>
<h6>Question 9</h6>
<p>
For the instance with 7 depots/clients, state the x-matrix of the optimal MIP
solution. Your answer should be a numeric 7 x 7 matrix.
</p>
<div class="form-group">
<textarea class="form-control" rows="5"
id="_numarea_manual_decimals_2_question_9_ip_sol_x_7_id__shadow"
required
oninput="updateTextAreaAndLabel('_numarea_manual_decimals_2_question_9_ip_sol_x_7_id__shadow','_numarea_manual_decimals_2_question_9_ip_sol_x_7_id_','_numarea_manual_decimals_2_question_9_ip_sol_x_7_id__label',7,7,2)"></textarea>
<p>The parsed result is:</p>
<textarea class="form-control" rows="5"
id="_numarea_manual_decimals_2_question_9_ip_sol_x_7_id_"
name="_numarea_manual_decimals_2_question_9_ip_sol_x_7"
readonly="true"></textarea>
<label for="_numarea_manual_decimals_2_question_9_ip_sol_x_7_id_"
id="_numarea_manual_decimals_2_question_9_ip_sol_x_7_id__label"></label>
</div>
<h6>Question 10</h6>
<p>
For the instance with 7 depots/clients, state the y-matrix of the optimal MIP
solution. Your answer should be a numeric 7 x 7 matrix.
</p>
<div class="form-group">
<textarea class="form-control" rows="5"
id="_numarea_manual_decimals_2_question_10_ip_sol_y_7_id__shadow"
required
oninput="updateTextAreaAndLabel('_numarea_manual_decimals_2_question_10_ip_sol_y_7_id__shadow','_numarea_manual_decimals_2_question_10_ip_sol_y_7_id_','_numarea_manual_decimals_2_question_10_ip_sol_y_7_id__label',7,7,2)"></textarea>
<p>The parsed result is:</p>
<textarea class="form-control" rows="5"
id="_numarea_manual_decimals_2_question_10_ip_sol_y_7_id_"
name="_numarea_manual_decimals_2_question_10_ip_sol_y_7"
readonly="true"></textarea>
<label for="_numarea_manual_decimals_2_question_10_ip_sol_y_7_id_"
id="_numarea_manual_decimals_2_question_10_ip_sol_y_7_id__label"></label>
</div>
</div>
<div class="container">
<hr>
<h4>LP with 7 depots/clients</h4>
<hr>
<h6>Question 11</h6>
<p>
For the instance with 7 depots/clients, state the optimal LP relaxation objective
value.
If needed, round your answer to 2 decimal places.
</p>
<div class="input-group">
<input type="number" class="form-control"
id="lp_time_7"
name="_num_auto_decimals_2_question_11_lp_val_7"
value="0" min="-Infinity"
max="Infinity" step="0.01"
required>
</div>
<br>
</div>
<div class="container">
<hr>
<h4>MIP with 8 depots/clients</h4>
<hr>
<h6>Question 12</h6>
<p>
For the instance with 8 depots/clients, state the best found lower bound for the
optimal MIP objective value.
If needed, round your answer to 2 decimal places.
</p>
<div class="input-group">
<input type="number" class="form-control"
id="_num_auto_decimals_2_question_12_ip_lower_bound_8_id"
name="_num_manual_decimals_2_question_12_lb_8"
value="0"
min="-Infinity" max="Infinity" step="0.01" required>
</div>
<br>
<h6>Question 13</h6>
<p>
For the instance with 8 depots/clients, state the best found upper bound for the
optimal MIP objective value.
If needed, round your answer to 2 decimal places.
</p>
<div class="input-group">
<input type="number" class="form-control"
id="_num_auto_decimals_2_question_12_ip_upper_bound_8_id"
name="_num_manual_decimals_2_question_13_ub_8"
value="0"
min="-Infinity" max="Infinity" step="0.01" required>
</div>
</div>
<div class="container">
<hr>
<h4>LP with 8 depots/clients</h4>
<hr>
<h6>Question 14</h6>
<p>
For the instance with 8 depots/clients, state the optimal LP relaxation objective
value.
If needed, round your answer to 2 decimal places.
</p>
<div class="input-group">
<input type="number" class="form-control"
id="_num_auto_decimals_2_question_14_lp_val_8_id"
name="_num_auto_decimals_2_question_14_lp_val_8"
value="0"
min="-Infinity" max="Infinity" step="0.01" required>
</div>
</div>
<div class="container">
<hr>
<h4>Theory</h4>
<hr>
<h6>Question 15</h6>
<p>
Based on the three instances and the relevant theory, as the number of
depots/clients increases by one the number of nodes needed to solve the MIP problem
seems to be:
</p>
<div class="radio">
<input type="radio"
id="_mc_auto_question_11_time_id___ans_1"
name="_mc_auto_question_15_nodes"
value="Decreasing faster than a linear function.">
<label for="_mc_auto_question_11_time_id___ans_1">Decreasing faster than a linear
function.</label>
</div>
<div class="radio">
<input type="radio"
id="_mc_auto_question_11_time_id___ans_2"
name="_mc_auto_question_15_nodes"
value="Linearly decreasing.">
<label for="_mc_auto_question_11_time_id___ans_2">Linearly decreasing</label>
</div>
<div class="radio">
<input type="radio"
id="_mc_auto_question_11_time_id___ans_3"
name="_mc_auto_question_15_nodes"
value="Decreasing slower than a linear function.">
<label for="_mc_auto_question_11_time_id___ans_3">Decreasing slower than a linear
function.</label>
</div>
<div class="radio">
<input
type="radio"
id="_mc_auto_question_11_time_id___ans_4"
name="_mc_auto_question_15_nodes"
value="Practically constant."
checked>
<label for="_mc_auto_question_11_time_id___ans_4">Practically constant.</label>
</div>
<div class="radio">
<input type="radio" id="_mc_auto_question_11_time_id___ans_5"
name="_mc_auto_question_15_nodes"
value="Increasing slower than a linear function.">
<label for="_mc_auto_question_11_time_id___ans_5">Increasing slower than a linear
function.</label>
</div>
<div class="radio">
<input type="radio" value="Linearly increasing." ,
id="_mc_auto_question_11_time_id___ans_6"
name="_mc_auto_question_15_nodes">
<label for="_mc_auto_question_11_time_id___ans_6">Linearly increasing.</label>
</div>
<div class="radio">
<input type="radio" value="Increasing faster than a linear function."
id="_mc_auto_question_11_time_id___ans_7"
name="_mc_auto_question_15_nodes">
<label for="_mc_auto_question_11_time_id___ans_7">Increasing faster than a linear
function.</label>
</div>
<div class="radio">
<input type="radio" value="None of the above."
id="_mc_auto_question_11_time_id___ans_8"
name="_mc_auto_question_15_nodes">
<label for="_mc_auto_question_11_time_id___ans_8">None of the above</label>
</div>
<br>
<h6>Question 16</h6>
<p>
Based on the three instances and the relevant theory, as the number of
depots/clients increases by one the running time needed to solve LP relaxation seems
to be:
</p>
<div class="radio">
<input type="radio"
id="_mc_auto_question_15_time_id___ans_1"
name="_mc_auto_question_16_time"
value="Decreasing faster than a linear function.">
<label for="_mc_auto_question_15_time_id___ans_1">Decreasing faster than a linear
function.</label>
</div>
<div class="radio">
<input type="radio"
id="_mc_auto_question_15_time_id___ans_2"
name="_mc_auto_question_16_time"
value="Linearly decreasing.">
<label for="_mc_auto_question_15_time_id___ans_2">Linearly decreasing</label>
</div>
<div class="radio">
<input type="radio"
id="_mc_auto_question_15_time_id___ans_3"
name="_mc_auto_question_16_time"
value="Decreasing slower than a linear function.">
<label for="_mc_auto_question_15_time_id___ans_3">Decreasing slower than a linear
function.</label>
</div>
<div class="radio">
<input
type="radio"
id="_mc_auto_question_15_time_id___ans_4"
name="_mc_auto_question_16_time"
value="Practically constant."
checked>
<label for="_mc_auto_question_15_time_id___ans_4">Practically constant</label>
</div>
<div class="radio">
<input type="radio" id="_mc_auto_question_15_time_id___ans_5"
name="_mc_auto_question_16_time"
value="Increasing slower than a linear function.">
<label for="_mc_auto_question_15_time_id___ans_5">Increasing slower than a linear
function</label>
</div>
<div class="radio">
<input type="radio" value="Linearly increasing."
id="_mc_auto_question_15_time_id___ans_6"
name="_mc_auto_question_16_time">
<label for="_mc_auto_question_15_time_id___ans_6">Linearly increasing</label>
</div>
<div class="radio">
<input type="radio" value="Increasing faster than a linear function."
id="_mc_auto_question_15_time_id___ans_7"
name="_mc_auto_question_16_time">
<label for="_mc_auto_question_15_time_id___ans_7">Increasing faster than a linear
function</label>
</div>
<div class="radio">
<input type="radio" value="None of the above."
id="_mc_auto_question_15_time_id___ans_8"
name="_mc_auto_question_16_time">
<label for="_mc_auto_question_15_time_id___ans_8">None of the above</label>
</div>
<br>
</div>
</form>
<div class="container">
<button type="submit" class="btn btn-primary btn-lg btn-block handin-btn"
onclick="download_file('Exercise2')">
Download Form
</button>
</div>
<br>
</div>
</body>
</html>