Lim, Xinru (2020) *An Inventory Model With Time-Varying Demand And Recycling.* Final Year Project, UTAR.

## Abstract

Inventory models are excellent examples to use mathematical models in order to solve real world problems. They are used frequently in any business to determine the optimal level of inventories, which are the stocks, so as to minimize the total inventory cost. In this project, the most general inventory model with time-varying demand and recycling has been built, which is the inventory model with multiple production and remanufacturing set-ups per cycle. The production set-ups produce new products from scratch, while the remanufacturing set-ups utilize returned items from the returned cycle to remanufacture them to produce products which are considered as good as new. All products are produced, remanufactured and returned at constant rates, while the demand rate is an arbitrary function of time. The goal is to formulate a total cost per unit time function to find the minimum cost of the model. Since the total cost per unit time function is a function of the acceptable returned quantity, it is plotted against the variable in order to prove the optimality of the total cost per unit time function. Other than that, comparisons between several policies with different production and remanufacturing set-ups per cycle have been done to observe the optimal policy that gives the minimum cost. Finally, sensitivity analysis has been performed to show that the inventory model built is robust. Python is used to compute all calculations and plot all visualizations in this report. Python is a high level programming language that is easily interpreted and understood by beginner programmers. It has various data science libraries that make the process of complex computations to be done effortlessly and effectively in a short time. The optimization function in the SciPy library is used to calculate the optimal value of the total cost per unit time and the Matplotlib library is used to plot the graphs.

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