I have tried to tackle this question as follow.

The program Calculates the next Working day, taking into account:  
   - weekends (Saturdays and Sundays)  
   - holidays happening in the middle of the week 

param name="OrderDate" the date on which the order is placed
param name="workingDays" the number of workingdays to process the order      
returns the date on which the Order is Requested to Ship

    public static DateTime getNextWorkingDay(DateTime OrderDate, int workingDays)
    {
        DateTime Holiday = new DateTime();
        List<DateTime> SelectedHolidays = new List<DateTime>();
        List<HolidayList> HolidayList = new List<HolidayList>();

        int calculatedWorkingDays=0;
        if (workingDays <= 5)
            calculatedWorkingDays = workingDays;
        else if (workingDays % 6 == 0)
        {
            calculatedWorkingDays = workingDays + workingDays / 6 * 2;
        }
        else
        {
            calculatedWorkingDays = workingDays + workingDays / 7 * 2;
        }


                 
        HolidayList =  "Read the list from Json file";

        foreach (var holiday in HolidayList)
        {
            string year = DateTime.Today.Year.ToString();
            Holiday = DateTime.Parse(holiday.MonthAndDayValue + "-" + year);

            if (Holiday.Day == 1 && Holiday.Month == 1)
            {
                year = (DateTime.Today.Year + 1).ToString();
                Holiday = DateTime.Parse(holiday.MonthAndDayValue + "-" + year);
            }


            SelectedHolidays.Add(Holiday.Date);

            if (Holiday.DayOfWeek == DayOfWeek.Sunday || Holiday.DayOfWeek == DayOfWeek.Saturday)
            {
                //do nothing
            }
            else
            {
                if (Holiday.Date == OrderDate.Date)
                    OrderDate.AddDays(1);
                if (Holiday.Date > OrderDate.Date)
                {
                    int K = (int)(Holiday.Date - OrderDate.Date).TotalDays;
                    if (K <= calculatedWorkingDays)
                    {
                        calculatedWorkingDays++;
                    }
                }
            }
        }
        if (OrderDate.DayOfWeek == DayOfWeek.Sunday)
        {
            calculatedWorkingDays++;
        }
        else if (OrderDate.DayOfWeek == DayOfWeek.Saturday || OrderDate.DayOfWeek == DayOfWeek.Friday)
        {
            calculatedWorkingDays += 2;
        }

        // this is required date 
        DateTime date_OrderRequestedToShip = OrderDate.AddDays(calculatedWorkingDays);

        //check if the last date fall on a non working day(holiday  or weekend)
        calculatedWorkingDays = 0;
        foreach (DateTime d in SelectedHolidays)
            if (d.Date == date_OrderRequestedToShip.Date)
                calculatedWorkingDays++;
        date_OrderRequestedToShip = date_OrderRequestedToShip.AddDays(calculatedWorkingDays);
        if (date_OrderRequestedToShip.DayOfWeek == DayOfWeek.Sunday)
        {
            calculatedWorkingDays = 1;
        }
        else if (date_OrderRequestedToShip.DayOfWeek == DayOfWeek.Saturday)
        {
            calculatedWorkingDays = 2;
        }

        return date_OrderRequestedToShip.AddDays(calculatedWorkingDays);
    }

The holiday list contains the month and day (MM/dd) part only with out the year part:

{
    "holidayName": "Memorial Day",
    "MonthAndDayValue": "05-30"
}

Can anyone help to tune up or suggest changes to make the code more efficient?