Success handling in custom javascript function

Question

If I make an ajax call, I can add success handling. I want to add similar logic to my custom functions.

I have 6-10 custom functions that MUST be run sequentially or independently. They don't typically run independently so I have them daisy-chained now by calling the next function at the end of the previous but that is messy to read and does not allow for separate execution.

I would love to have something like this:

function runall(){
    runfirst().success(
        runsecond().success(
            runthird()
    ))
} 

I have had other situations were I would like to add .success() handling to a custom function, but this situation made it more important.

If there is another way to force 6-10 functions to run synchronously, that could solve this problem, but I would also like to know how to add success handling to my custom functions.

I tried the following based on @lanzz's suggestion:

I added .then() to my function(s):

$bomImport.updateGridRow(rowId).then(function () {
        $bomImport.toggleSubGrid(rowId, false);
});


var $bomImport = {
  updateGridRow: function (rowId) {
    $('#' + rowId + ' td[aria-describedby="bomImport_rev"]').html($("#mxRevTxt").val());
    $('#' + rowId + ' td[aria-describedby="bomImport_itemno"]').html($("#itemNoTxt").val());
    $('#' + rowId + ' td[aria-describedby="bomImport_used"]').html($("#usedTxt").val());
    $('#' + rowId + ' td[aria-describedby="bomImport_partSource"]').html($("#partSourceTxt").val());
    $('#' + rowId + ' td[aria-describedby="bomImport_partClass"]').html($("#partClassTxt").val());
    $('#' + rowId + ' td[aria-describedby="bomImport_partType"]').html($("#partTypeTxt").val());
    $('#' + rowId + ' td[aria-describedby="bomImport_partno"]').html($("#mxPnTxt").val());
    $('#' + rowId + ' td[aria-describedby="bomImport_descript"]').html($("#descTxt").val());
    $('#' + rowId + ' td[aria-describedby="bomImport_qty"]').html($("#qtyTxt").val());
    $('#' + rowId + ' td[aria-describedby="bomImport_custPartNo"]').html($("#custPartNoTxt").val());
    $('#' + rowId + ' td[aria-describedby="bomImport_crev"]').html($("#custRevTxt").val());
    $('#' + rowId + ' td[aria-describedby="bomImport_u_of_m"]').html($("#uomTxt").val());
    $('#' + rowId + ' td[aria-describedby="bomImport_warehouse"]').html($("#warehouseTxt").val());
    $('#' + rowId + ' td[aria-describedby="bomImport_standardCost"]').html($("#stdCostTxt").val());
    $('#' + rowId + ' td[aria-describedby="bomImport_workCenter"]').html($("#wcTxt").val());
    var defferred = new $.Deferred();
    return defferred.promise();
}};

The code correctly goes to the end of updateGridRow, gives no errors, but never gets back to call the second function.

I also tried the following as was suggested @Anand:

workSheetSaveExit(rowId, isNew).save().updateRow().toggle();
function workSheetSaveExit(){
    this.queue = new Queue;
    var self = this;
    self.queue.flush(this);
}
workSheetSaveExit.prototype = {
  save: function () {
    this.queue.add(function (self) {
        $bomImport.workSheetSave(rowId, isNew);
    });
    return this;
  },
  updateRow: function () {
    this.queue.add(function (self) {
        $bomImport.updateGridRow(rowId);
    });
    return this;
  },
  toggle: function () {
    this.queue.add(function (self) {
        $bomImport.toggleSubGrid(rowId, false);
    });
    return this;
  }
};

Which didn't work.

Final Solution
For a great explanation of how to use deferred and make this work see here: Using Deferred in jQuery

Solution

How to use Deferreds:

function somethingAsynchronous() {
    var deferred = new $.Deferred();
    // now, delay the resolution of the deferred:
    setTimeout(function() {
        deferred.resolve('foobar');
    }, 2000);
    return deferred.promise();
}

somethingAsynchronous().then(function(result) {
    // result is "foobar", as provided by deferred.resolve() in somethingAsynchronous()
    alert('after somethingAsynchronous(): ' + result);
});

// or, you can also use $.when() to wait on multiple deferreds:
$.when(somethingAsynchronous(), $.ajax({ something })).then(function() {
    alert('after BOTH somethingAsynchronous() and $.ajax()');
});

If your functions simply make an AJAX request, you can just return the actual promise returned by $.ajax():

function doAjax() {
    return $.ajax({ /* ajax options */ });
}

doAjax().then(function() {
    alert('after doAjax()');
});