Hi, I started making this kind of change in my code

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];

        System.Debug('SCHEDULED: SUPPORT CASE COUNT: ' + suppportCases.Size());     
        ServiceAvailability saHelper = new ServiceAvailability();
        
        // Setups that are already handled. We need to process each Setup only once.
       Set<Setup__c> alreadyHandled = new Set<Setup__c>();         

          List<Service_Availability__c> sList = new List<Service_Availability__c>();
            List<Id> idList = new List<Id>();
            for (Case c : suppportCases) {
               idList.add(c.Id);
             System.Debug('SCHEDULED: CASE ' + c.CaseNumber + ' HANDLING STARTED');
               }
                 sList = [SELECT ID, Name, Status__c, Duration__c, Start_DateTime__c, case__r.Id FROM service_availability__c WHERE case__r.Id IN : idList order by Name desc];
                 ID hoursToUse = [select related_setup__r.contract__r.contract_agreement__r.business_hours__c from case where Id IN : idList];
                                                        
            if (sList.Size() > 0) {             
              //  Setup__c relatedSetup = [select Id, Name, Service_Availability__c, Contract__c, Cost_Center__c from Setup__c where Id =: c.Related_Setup__c];      
              RecordType recordTypeIncident = [select Id, Name from RecordType where SObjectType = 'Service_Availability__c' and Name = 'Incident' LIMIT 1];
                        
              for (Service_Availability__c c : sList) {  
               // Id hoursToUse = saHelper.GetHoursToUse(c, relatedSetup);
                if(hoursToUse != null && relatedSetup != null) {                                            
                
                System.debug('SCHEDULED: DATE IN LAST SA: ' + sList[0].Start_DateTime__c);
                System.debug('SCHEDULED: CURRENT DATE: ' + DateTime.Now());

Does this look right way to create map ? I'm not sure is those Where Id sentences right because only lookup connecting Service_availability + Case is case__ c lookup field? 

Service_Availability__c c = [SELECT Id, name, recordtype, case__r.Id, duration__c, fault_classification__c, object_added_automatically__c, setup__c, start_datetime__c,status__c from service_availability__c  where id = case.case__c ];

Case Id = [Select Id, Name, RecordType, service_availability__c from case where Id = c.case__c];

Map<Id, List> service_availability = new Map<Id, List>
Map<cId, Set<List>> M = new Map <Id, Set<List>>();
List value = m.get(Id);