A company is planning to hire employee on different day-shifts to meet its workload demand. The employees in each day-shift can work for at most five consecutive days and require two days weekly off. For example, if the day-shift for an employee starts on Monday, he/she will have weekly off on Saturday and Sunday, whereas, a day-shift starting on Wednesday will have weekly off on Monday and Tuesday. A day-shift can start on any day of the week (day 1 = Monday, ……, day 7 = Sunday). If cost of each shift is c_1,⋯,c_7 and workload demand for number of people on any given day i in the month is D_i,0≤i≤N (where N is the number of days in the week). Write a Mixed Integer Programming formulation to minimize the total wage cost by the company while ensuring that workload demand is fulfilled.
