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I am currently working on a MILP formulation for optimizing AGV/AMR scheduling. The model aims to optimize task scheduling across multiple missions using a limited set of resources. Parameters such as the number of missions, resources, tasks, and segments define the problem space. Task-mission assignment is represented by the binary matrix M_T, while M_T_Resources and M_T_Segments indicate resource and segment usage for tasks in missions. Constraints ensure that each task is assigned exactly once, respecting mission-resource compatibility and task succession within missions. The objective is to minimize the makespan Cmax, representing the total time taken to complete all tasks across missions. The model's decision variables include binary indicators for task-resource assignment (X), resource assignment to missions (Y), resource occupation (Z), and task start/end times (St and C). I wanted to enforce X and M_T (which tell us which task belong to which mission) but whenever I tried that, my model does not converge to any solution. However, it does converge when I don't formulate the constraint between X and M_T. For example, I have 2 missions and 6 tasks in total. Each mission has a set of tasks, for this case, mission 1 has Task 1, Task 2 and Task 3 and Mission 2 has Task 4 Task 5 and Task 6 (which is indicated through M_T : 2D binary matrix consisting of missions and tasks). But for some reason, in the optimal solution, a resource can be assigned to task 5 or task 6 of mission 1 which is not true since Mission 1 has Task 1, Task 2 and Task 3. I've been stuck for a while now and I appreciate if someone bear with me and help me.

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    $\begingroup$ Converging to a solution is not what MIP solvers do. I suspect you mean that after you add the new constraint, the problem becomes infeasible. The easiest way to debug this is often to construct a tiny example with a known feasible solution and plug that in (e.g. by fixing). Cplex should tell you which constraint is (part of) the problem. $\endgroup$ Commented Apr 30 at 13:46
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    $\begingroup$ @Rami, Also it would be helpful to illustrate the math model you are trying to solve. $\endgroup$
    – A.Omidi
    Commented May 1 at 9:52

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