Find a matching or closest value in an array

Pass in the number you're searching for as the first parameter and the array of numbers to the second:

function getClosest($search, $arr) {
   $closest = null;
   foreach ($arr as $item) {
      if ($closest === null || abs($search - $closest) > abs($item - $search)) {
         $closest = $item;
      }
   }
   return $closest;
}

You could use JavaScript for doing the sorting on click, and use PHP only for passing the JSON to it.

After you provided the HTML structure you want to display the list in, I updated this answer to use div elements for the records and p elements for the fields.

We could replace the select list, for selecting the sort order, by two buttons.

Here is the PHP code:

<?php

$homepage = array();  

$homepage[]= '{  
   "info":{  
      "collection":[  
         {  
            "Name":"Charlie",
            "ID":"13"
         },
         {  
            "Name":"Emma",
            "ID":"9"
         }
      ]
   }
}';  

$homepage[] = '{  
   "info":{  
      "collection":[  
         {  
            "Name":"Bob",
            "ID":"10"
         }
      ]
   }
}';

$data = array();
foreach ($homepage as $homepage2) {
    $tmp=json_decode($homepage2, false);
    $data = array_merge($data,$tmp->info->collection);
}

?>

<div id="container"></div>

<button id="sort1">Alphabetical</button>
<button id="sort2">High to Low</button>

<script>
    var collection = <?=json_encode($data)?>;

    function populate(compareFunc) {
        collection.sort(compareFunc);
        var container = document.getElementById('container');
        container.innerHTML = '';
        collection.forEach(function (key) {
            var div = document.createElement("div");
            div.className = "inventory";
            var span = document.createElement("span");
            span.textContent = key.ID;
            div.appendChild(span);
            span = document.createElement("span");
            span.textContent = key.Name;
            div.appendChild(span);
            container.appendChild(div);
        });
    }

    var populateById = populate.bind(null, function (a, b) {
        return a.ID - b.ID;
    });

    var populateByName = populate.bind(null, function (a, b) {
        return a.Name.localeCompare(b.Name);
    });

    document.getElementById("sort1").addEventListener('click', populateByName);
    document.getElementById("sort2").addEventListener('click', populateById);
    document.addEventListener('DOMContentLoaded', populateById);

</script>

For the sample data this will result in the following JavaScript/HTML, which you can test here:

var collection = [{"Name":"Charlie","ID":"13"},{"Name":"Emma","ID":"9"},{"Name":"Bob","ID":"10"}];

function populate(compareFunc) {
    collection.sort(compareFunc);
    var container = document.getElementById('container');
    container.innerHTML = '';
    collection.forEach(function (key) {
        var div = document.createElement("div");
        div.className = "inventory";
        var span = document.createElement("span");
        span.textContent = key.ID;
        div.appendChild(span);
        span = document.createElement("span");
        span.textContent = key.Name;
        div.appendChild(span);
        container.appendChild(div);
    });
}

var populateById = populate.bind(null, function (a, b) {
    return a.ID - b.ID;
});

var populateByName = populate.bind(null, function (a, b) {
    return a.Name.localeCompare(b.Name);
});

document.getElementById("sort1").addEventListener('click', populateByName);
document.getElementById("sort2").addEventListener('click', populateById);
document.addEventListener('DOMContentLoaded', populateById);

span { margin-left: 5px }
div.inventory { border-bottom: 1px solid gray }

<div id="container"></div>

<button id="sort1">Alphabetical</button>
<button id="sort2">High to Low</button>

Note that I gave the three items different ID values than in your question, since otherwise the sort order would be the same for both ID and Name.

Using tables: alternative

There are nice JavaScript libraries which give much more features to represent data sets. Here is an example using jQuery with DataTables:

var collection = [{"Name":"Charlie","ID":"13"},{"Name":"Emma","ID":"9"},{"Name":"Bob","ID":"5"}];

function populate() {
  var tbody = $('#collection>tbody');
  collection.forEach(function (key) {
    var row = $('<tr>');
    row.append($('<td>').text(key.ID));
    row.append($('<td>').text(key.Name));
    tbody.append(row);
  });
}

$(document).ready(function(){
  populate();
  $('#collection').DataTable();
});

<script src="http://code.jquery.com/jquery-1.12.3.js"></script>
<link rel="stylesheet" type="text/css" href="https://cdn.datatables.net/1.10.12/css/jquery.dataTables.min.css">
<script src="https://cdn.datatables.net/1.10.12/js/jquery.dataTables.min.js"></script>

<table id="collection">
    <thead>
        <tr><th>ID</th><th>Name</th></tr>
    </thead>
    <tbody/>
</table>

The actual code is even smaller (not counting the included library) than a pure JavaScript solution would be with a basic table. But this has sorting up and down, filtering, pagination, nice styles, ...

You can use the jQuery.each method to loop the array, other than that it's just plain Javascript. Something like:

var theArray = [ 1, 3, 8, 10, 13 ];
var goal = 4;
var closest = null;

$.each(theArray, function(){
  if (closest == null || Math.abs(this - goal) < Math.abs(closest - goal)) {
    closest = this;
  }
});