I change my code because my SOQL limit was always going over and this map/list seemed to be the only way to make it work. Now I'm still getting a error : Compile Error: unexpected token: 'List' at line 50 column 12 (the problem marked red).

global class ServiceAvailabililtyUpdaterForCase implements Schedulable,
                                                           Database.Stateful/*,
                                                           Database.Batchable<sObject>*/ {

    // Implement Schedulable interface function for entry function to schedule this batch
    global void execute(SchedulableContext sc){
        
        ServiceAvailabililtyUpdaterForCase updater = new ServiceAvailabililtyUpdaterForCase();
        Date currentDate = Date.newinstance(DateTime.Now().Year(), DateTime.Now().Month(), DateTime.Now().Day());          
        updater.HandleServiceAvailabilityChange(currentDate);     
    }    
    
    /*
    * Execute method of Batchable interface
    */
    global void execute( Database.BatchableContext BC, List<sObject> records ) {
        System.debug('ServiceAvailabililtyUpdaterForCase.execute batch');               
    }       
            
    public void HandleServiceAvailabilityChange(Date currentDate) {
        
        /*
        1) Fetch not closed Support Cases
        2) Fetch valid Service Availability objects per Case
        3) Sort SAs by a) Case b) Name
        4) Update last SA with duration until end of the month
        5) Create new SA from the beginning of the new month (with same Fault Classification)       
        */
        RecordType recordType = [select Id, Name from RecordType where SObjectType = 'Case' and Name = 'Support' LIMIT 1];
        
        System.Debug('SCHEDULED: SUPPORT CASE REC TYPE ID: ' + recordType.Id);              
                               
        
        List<Case> suppportCases =[select Id, Fault_Classification__c, Setup_Name__c, CaseNumber, Related_Setup__c,Status_Explanation__c
                            from Case                                                       
                            where RecordTypeId =: recordType.Id
                            and IsClosed =: false                           
                            order by CreatedDate desc];
        //Create new list which contains supportcases records                   
        List<Id> idList = new List<Id>();
            for (Case c : suppportCases) {
               idList.add(c.Id);
             System.Debug('SCHEDULED: CASE ' + c.CaseNumber + ' HANDLING STARTED');
               }
               //Creating list which contains service availability + setup records
                List <Service_Availability__c> c = [SELECT setup__r.id,setup__r.name, setup__r.service_availability__c,setup__r.contract__c,setup__r.cost_center__c,ID, Name, Status__c, Duration__c, Start_DateTime__c,case__c FROM Service_Availability__c WHERE Case__c IN : idList];

        //Create map which has list of sa-records
        Map<Id, List<service_availability__c>> service_availability = new Map<Id, List<service_availability__c>>
            List value = m.get(Id);
                for(service_availability__c d: c) {
                    if service_availability.containsKey(d.case__c){
                        service_availability.get(d.case__c).add(d);
                    } else {
                        List<service_availability__c> s = new List<service_availability__c>();
                        s.add(d);
                        service_availability.put(d.case__c, s);
                    }
                }
        RecordType recordTypeIncident = [select Id, Name from RecordType where SObjectType = 'Service_Availability__c' and Name = 'Incident' LIMIT 1];
            for (Id currentcase:service_availability.keySet()) {
                for (service_availability__c sa:service_availability.get(currentcase)) {
                    Id hoursToUse = saHelper.GetHoursToUse(c, relatedSetup);
                    if(hoursToUse != null && relatedSetup != null) {                                            
                
                System.debug('SCHEDULED: DATE IN LAST SA: ' + oldSAsPerCase[0].Start_DateTime__c);
                System.debug('SCHEDULED: CURRENT DATE: ' + DateTime.Now());
                                                            
                // Check if month has changed, year not                     
                if (oldSAsPerCase[0].Start_DateTime__c.Month() < DateTime.Now().Month() && oldSAsPerCase[0].Start_DateTime__c.Year() == DateTime.Now().Year()) {
                    System.debug('SCHEDULED: MONTH HAS CHANGED from: ' + oldSAsPerCase[0].Start_DateTime__c.Month() + ' to: ' + DateTime.Now().Month());
                    
                    // Update last SA with duration until end of the month             
                    oldSAsPerCase[0].Duration__c = saHelper.CalculateDurationUntilEndOfMonth(hoursToUse, oldSAsPerCase[0].Start_DateTime__c, currentDate);
                    
                    // Start of current month
                    // TODO: THIS CAUSES TEST CASE TO FAIL, SINCE LOCAL TIME IS USED THERE                
                    DateTime startOfCurrentMonth = DateTime.newinstance(currentDate.Year(), currentDate.Month(), 1, 0, 0, 0);
                    System.debug('SCHEDULED: START OF CURRENT MONTH: ' + startOfCurrentMonth);
                                                    
                    saHelper.InsertServiceAvailabilityObjectToCase(c, startOfCurrentMonth, recordTypeIncident, true);
                    update oldSAsPerCase[0];
                    
                    // Update corresponding Setup SA objects
                    if (!alreadyHandled.Contains(relatedSetup)) {
                        saHelper.UpdateSetupServiceAvailability(c, relatedSetup, true);                   
                        alreadyHandled.Add(relatedSetup);
                    }                   
                    
                // Year changed, so did month
                } else if (DateTime.Now().Year() > oldSAsPerCase[0].Start_DateTime__c.Year()) {
                    System.debug('SCHEDULED: YEAR HAS CHANGED from: ' + oldSAsPerCase[0].Start_DateTime__c.Year() + ' to: ' + DateTime.Now().Year());
                    System.debug('SCHEDULED: MONTH HAS CHANGED from: ' + oldSAsPerCase[0].Start_DateTime__c.Month() + ' to: ' + DateTime.Now().Month());
                     
                    oldSAsPerCase[0].Duration__c = saHelper.CalculateDurationUntilEndOfYear(hoursToUse, oldSAsPerCase[0].Start_DateTime__c, currentDate);
                     
                    // Start of current month                
                    DateTime startOfCurrentMonth = DateTime.newinstance(currentDate.Year(), currentDate.Month(), 1, 0, 0, 0);
                    System.debug('SCHEDULED: START OF CURRENT MONTH: ' + startOfCurrentMonth);
                                                    
                    saHelper.InsertServiceAvailabilityObjectToCase(c, startOfCurrentMonth, recordTypeIncident, true);
                    update oldSAsPerCase[0];
                    
                    // Update corresponding Setup SA objects
                    if (!alreadyHandled.Contains(relatedSetup)) {
                        saHelper.UpdateSetupServiceAvailability(c, relatedSetup, true);
                        alreadyHandled.Add(relatedSetup);
                    }
                                                            
                } else {
                    System.debug('SCHEDULED: MONTH not CHANGED');
                    System.debug(' BUSINESS HOURS NO FOUND');
                }
               }
            }                                                              
        }                       
    }