Mathematical Programming: Formulation of ILP Model

Mathematical Programming 2
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Mathematical Programming 2
Question 1(a)
Formulation of ILP Model:
Decision variables: Allow Xij to address the number of tasks for a client i on day j, where i is the client record (1to4) and j is the day list (1to5).
Objective Capability: Limit the all-out number of activities:
Minimize

D1 and D2 represents the number of operations for client one and client two

Therefore, objective function
Minimizing the overall number of operations

Constraints:
Every client's work should be finished within its handling time:
=Processing Time, for i=1,2,3,4

2. Task should be cleared once only:

3. Only one task is processed each day.
4. If task 2 onset on day k, task 3 must start one day later

Mathematical Formulation:

Number of Tasks ij

Subject to
Clarification:
The objective function intends to limit the complete number of tasks by adding the decision variables' (Xij) results and comparing the number of activities required.
Constraint 1 guarantees that every client's occupation is finished inside its predefined handling time.
Constraint 2 forces binary constraint requirements on the decision variables, demonstrating that the number of tasks cannot be negative and should be numbers.
Question 1(b)
Refer to Excel Solver.
Question 1(c)
To change the ILP model to incorporate that work 2 should begin no less than one day before work 3, you can acquaint a double choice variable to address the beginning time connection between occupations 2 and 3.
Therefore, present a paired variable Yi for every day i to such an extent that:

Decision Variables:
Xij for i in days 1, 2,3,4,5 and j in clients 1,2,3,4 Yi for i in days 1,2,…,5
Objective Function:
Minimize the entire figure of operations: