Abstract
In this paper we discuss a mathematical model of inventory control policy based on local stability analysis using a system dynamics approach. It is assumed that the production capacity and the maximum production capacity has an upper limit but with sufficient availability of raw materials so that the production occurs continuously without stock out. The model is intended to meet the market equilibrium by determining the optimal number of agents in a team of salesman, the level of inventory, and the level of production capacity, so that thenet income is maximized. We use the Pontryagin Maximum Principle to find the optimal control of the system. Finally some numerical simulations are performed to give a sensitivity analysis of the inventory control policy to the parameters involved in the system.
Highlights
In this paper we discuss a mathematical model of inventory control policy based on local stability analysis using a system dynamics approach
It is assumed that the production capacity
We use the Pontryagin Maximum Principle to find the optimal control of the system
Summary
Penurunan model sistem dinamik yang dilakukan sama dengan yang telah dilakukan Sana [6, 7]. Jumlah persediaan masing-masing produk untuk tingkat permintaan dibatasi oleh pengaruh inisiatif tim sales bersama. Hal tersebut mengakibatkan tingkat permintaan pada akhirnya mengalami pertumbuhan yang terbatas dengan pengaruh proporsional antara suatu produk dan jumlah inisiatif tim sales bersama. Meninjau persamaan (7), (8), (11) serta (12) maka sistem dinamik untuk model pengendalian persediaan dua produk berbeda pada kapasitas produksi terbatas serta inisiatif tim sales bersama dari waktu ke waktu diberikan oleh;. . Fungsi–fungsi dan merupakan fungsi persediaan produk yang didapat dari selisih tingkat produksi dan tingkat permintaan untuk masing-masing produk dengan inisiatif tim sales bersama pada waktu. Sementara dan merupakan fungsi kapasitas produksi dari selisih hasil pengaruh pertumbuhan dan peluruhan bahan baku serta inisiatif tim sales bersama untuk masingmasing produk pada waktu
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