Optimizing manufacturing schedule with time-dependent energy cost

A non-transitory computer-readable storage medium comprising instructions stored thereon for optimizing a schedule to manufacture at least a first product and a second product with at least a first machine and a second machine at minimum cost in an environment in which a cost of energy used by the first machine and the second machine varies as a function of time, the instructions, when executed by at least one processor, being configured to cause a computing system to at least:

• generate multiple chromosomes, each chromosome including:
• a job sequence matrix describing an order of performing tasks to manufacture the first product and the second product using the first machine and the second machine;
• and
• an idle time matrix describing idle times before performing the tasks in the order described by the job sequence matrix;
• determine fitness scores of each of the chromosomes with the job sequence matrices and the idle time matrices, the fitness scores being based on energy costs at the times that the first and second machines perform the tasks;
• randomly generate, with probabilities based on the fitness scores, new chromosomes based on the chromosomes with the idle time matrices;
• determine fitness scores of the new chromosomes;
• select one of the new chromosomes with an optimal fitness score;
• and
• instruct the first machine and the second machine to manufacture at least the first product and the second product according to the schedule, the schedule being based on the selected new chromosome, the schedule determining when the first and second machines perform which tasks and when the first and second machines are idle.

A method of manufacturing at least a first product and a second product with at least a first machine and a second machine at minimum cost in an environment in which a cost of energy used by the first machine and the second machine varies as a function of time, the first product is associated with a first deadline and a first penalty cost per unit time for manufacturing the first product after the deadline, and the second product is associated with a second deadline and a second penalty cost per unit time for manufacturing the second product after the second deadline, the method comprising:

• generating multiple chromosomes, each chromosome including:
• a job sequence matrix describing an order of performing tasks to manufacture the first product and the second product using the first machine and the second machine;
• and
• an idle time matrix describing idle times before performing the tasks in the order described by the job sequence matrix;
• exchanging a first sequence of tasks from a first job sequence matrix from a first chromosome with a second sequence of tasks from a second job sequence matrix from a second chromosome, the first sequence of tasks and the second sequence of tasks including a subset of tasks from a same set of tasks and being performed on a same machine with the tasks being performed in a different order;
• swapping, within at least one of the job sequence matrices, an order of performing at least a first task for manufacturing the first product on the first machine with a second task for manufacturing the second product on the first machine;
• determining fitness scores of each of the chromosomes with the job sequence matrices and the idle time matrices, the fitness scores being based on a sum of energy costs at the times that the first and second machines perform the tasks according to the respective chromosomes and the penalty costs of manufacturing the first and second products after the associated deadlines;
• randomly generating, with probabilities based on the fitness scores, new chromosomes based on the chromosomes with the idle time matrices;
• determining fitness scores of the new chromosomes;
• selecting one of the new chromosomes with an optimal fitness score;
• and
• manufacturing at least the first product and the second product according to a schedule, the schedule being based on the selected new chromosome, the schedule determining when the first and second machines perform which tasks and when the first and second machines are idle,
• wherein the exchanging the first sequence of tasks, swapping the order of performing, determining fitness scores of each of the chromosomes, and randomly generating new chromosomes, are included in a process that is performed multiple times.