Kontrol Optimal Pengangguran Melalui Peningkatan Lapangan Kerja dan Program Pelatihan-Pendampingan

Azzukhruf, Vika Kumala (2025) Kontrol Optimal Pengangguran Melalui Peningkatan Lapangan Kerja dan Program Pelatihan-Pendampingan. Other thesis, Institut Teknologi Sepuluh Nopember.

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Abstract

Pengangguran di Indonesia pada tahun 2024 tercatat mencapai 7,47 juta orang (4,8% dari angkatan kerja), melebihi target pemerintah (4,0%–4,6%). Kondisi ini berpotensi menimbulkan ketidakstabilan sosial-ekonomi serta menghambat pertumbuhan ekonomi nasional. Oleh karena itu, strategi penurunan angka pengangguran perlu diterapkan. Salah satu pendekatan yang dapat digunakan adalah pemodelan matematika. Penelitian ini didasarkan pada suatu model matematika yang menggambarkan dinamika pengangguran. Model dimodifikasi dengan mengurangi parameter tingkat perpindahan pekerja informal ke pengusaha yang dipengaruhi oleh pengusaha, tingkat pekerja informal yang diberhentikan dan mencari pekerjaan di sektor lain, tingkat pekerja informal meninggalkan posisi karena mengundurkan diri, serta menambahkan parameter tingkat pengusaha yang gagal usahanya dan kembali menjadi pekerja, dan tingkat pengangguran yang beralih menjadi pengusaha. Selanjutnya, model direkonstruksi dengan menambahkan tiga variabel kontrol, yaitu u1 (peningkatan lowongan kerja), u2 (pelatihan dan pendampingan bagi pengangguran agar dapat bekerja), dan u3 (pelatihan dan pendampingan bagi pengangguran agar menjadi pengusaha). Model ini melibatkan empat variabel keadaan: pengangguran, pekerja, pengusaha, dan lowongan kerja, yang diformulasikan dalam sistem persamaan diferensial nonlinier. Analisis kestabilan menggunakan kriteria Routh-Hurwitz menunjukkan bahwa baik titik kesetimbangan eksterior maupun titik kesetimbangan interior keduanya bersifat stabil. Selain itu, sistem juga terbukti terkendali karena rank matriks keterkontrolan sama dengan jumlah variabel keadaan. Selanjutnya, hasil simulasi numerik menggunakan metode Runge-Kutta orde 4 menunjukkan bahwa ketiga kontrol bekerja secara sinergis dalam menurunkan jumlah pengangguran secara signifikan, sekaligus mendorong peningkatan jumlah pekerja, pengusaha, dan lowongan pekerjaan sepanjang periode simulasi.
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Unemployment in Indonesia in 2024 was recorded at 7.47 million people (4.8% of the labor force), exceeding the government’s target of 4.0%–4.6%. This condition has the potential to trigger socio-economic instability and hinder national economic growth. Therefore, strategies to reduce the unemployment rate need to be implemented. One possible approach is through mathematical modeling. This study is based on a mathematical model that describes the dynamics of unemployment. The model is modified by reducing the parameter representing the transition rate from informal workers to entrepreneurs, influenced by existing entrepreneurs, the rate of informal workers being laid off and seeking jobs in other sectors, and the rate of informal workers resigning from their positions. Additional parameters are introduced, including the rate of entrepreneurs whose businesses fail and return to the workforce, and the rate of unemployed individuals who transition into entrepreneurship. The model is then reconstructed by introducing three control variables: (u1) (job vacancy creation), (u2) (training and mentoring programs for the unemployed to become workers), and (u3) (training and mentoring programs for the unemployed to become entrepreneurs). The model comprises four state variables: unemployment, workers, entrepreneurs, and job vacancies, and is formulated as a system of nonlinear differential equations. Stability analysis using the Routh–Hurwitz criterion shows that both the exterior and interior equilibrium points are stable. Furthermore, the system is proven to be controllable, as the rank of the controllability matrix equals the number of state variables. Numerical simulations using the fourth-order Runge–Kutta method demonstrate that the three controls work synergistically to significantly reduce unemployment, while simultaneously increasing the number of workers, entrepreneurs, and job vacancies throughout the simulation period.

Item Type:	Thesis (Other)
Uncontrolled Keywords:	Pengangguran, Model Matematika, Kendali Optimal, Prinsip Minimum Pontryagin, Simulasi Numerik, Unemployment, Mathematical Model, Optimal Control, Pontryagin's Minimum Principle, Numerical Simulation.
Subjects:	Q Science Q Science > QA Mathematics Q Science > QA Mathematics > QA371 Differential equations--Numerical solutions Q Science > QA Mathematics > QA401 Mathematical models.
Divisions:	Faculty of Science and Data Analytics (SCIENTICS) > Mathematics > 44201-(S1) Undergraduate Thesis
Depositing User:	Vika Kumala Azzukhruf
Date Deposited:	30 Jul 2025 06:27
Last Modified:	30 Jul 2025 06:27
URI:	http://repository.its.ac.id/id/eprint/124268

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