Mathematical Inventory Management Modeling

Abstract

For inventory tracking strategies that specifically consider storage space capacity, this research entails creating new mathematical formulas to determine the reorder point and order quantity. The backlog and decreased demands during stock outs are taken into consideration, along with continuous and periodic evaluations. When inventory outnumbers storage space, the cost of over-warehousing at an outside warehouse is calculated on a per-unit basis. The goal is to reduce the entire cost, which includes the expenses associated with ordering, shortages, holding, and over ordering. Consumption and lead time have discontinuous, unpredictable characteristics. To ensure that the results are not dependent on assumptions about demand and lead time posterior distributions, demand is modelled using a likelihood function during periods of variable lead time. The challenges are tackled iteratively since the developed mathematical formulas are so complex. The approach is tested using examples of problems and actual business data. An extensive search is used to identify the challenge instance's optimal solutions. The suggested approach can identify near-optimal solutions for continuous review policies and ideal solutions for continuous review policies. A comparison of continuous review and periodic review methods, as well as a comparison of overstock and lost sales scenarios, reveals important inventory policy insights.