I am trying to solve this staff planning optimization problem but not able to create the objective function, decision variables and constraints. Need help please.
The company operates in three states: A, B and C. The state-wise demand for insurance for the year is shown in the table provided below: State A - Jan - (demand1); Feb - (demand2); March - (demand3)..... State B - Jan - (demand1); Feb - (demand2); March - (demand3).... State C - Jan - (demand1); Feb - (demand2); March - (demand3)....
The company can either handle an application with the staff that they hire or outsource it to a vendor. Assume that there is no capacity limitation to outsourcing. If they hire staff, he/she can handle 40 insurance applications per month when he/she works 100% of the workdays. However, there are days that he/she will be unavailable to process applications due to training, off days, etc. A staff member’s availability (in percentage) to work on processing the insurance applications for each month is shown in the table given below. As mentioned before, with 100% availability, each member can handle 40 applications. State A - Jan - (x%); Feb - (y%); March - (z%)..... State B - Jan - (x%); Feb - (y%); March - (z%)..... State C - Jan - (x%); Feb - (y%); March - (z%).....
States A and B have a regulatory restriction that the outsourced insurance applications cannot be more than 30% and 40% of the total number of applications for each month, respectively. The table given below shows the cost of the staff vs external resources: State A - Annual Salary of Staff - $60000; Outsourcing Cost Per Application - $180 State B - Annual Salary of Staff - $55000; Outsourcing Cost Per Application - $150 State C - Annual Salary of Staff - $53000; Outsourcing Cost Per Application - $160
The objective is to optimise the total cost for the application approval process by distributing the right number of applications between the FTEs and the vendors while meeting the monthly demand for each state at the same time.
I have defined the sets and parameters using the below code:
model.i = Set(initialize=State.tolist(),doc='States')
model.j = Set(initialize=Month.tolist(),doc='Months')
model.demand = Param(model.i,model.j,initialize = Demand,doc='Demand')
model.sa = Param(model.i,model.j,initialize = StaffAvPer,doc = 'StaffAvPercent')
Also, my decision variables as follows:
model.x = Var(model.i,model.j,doc='No of FTE',domain = NonNegativeReals) model.y = Var(model.i,model.j,doc='No of Outsource App',domain = NonNegativeIntegers)
And, this is the code for my constraints :
model.demand_constraint2 = ConstraintList()
for i in model.i:
for j in model.j:
model.demand_constraint2.add(expr = model.x[i,j]*40*model.sa[i,j] + model.y[i,j] == model.demand[i,j])
I am not able to formulate the objective function though
