# The Bi-level Programming Approach to Improve the Inventory Control System with a Practical Application

## Authors

• Othman Atiya Wardil *
• Samera Khaleel Ibrahim

## Keywords:

The linear-quadratic bi-level programming (LQBP), Modified Simplex Algorithm, Karush-Kuhn-Tucker conditions (K.K.T), Multi-item production model (no shortage) With -Restriction ,The Classic method.

## Abstract

In this research, we investigated addressing the challenges associated with the seasonal allergic medical drug inventory system. The focus was on determining the optimal demand by calculating the Economic Order Quantity (EOQ) and achieving the lowest cost within the Pharmaceutical Industries and Medical Supplies company in Samarra. The primary objective was to efficiently meet the demand for seasonal allergy medications by identifying the optimal demand for medical drugs. The study encompassed two types of seasonal allergy medications, namely Samatifen drink and VALIAPAM 2 pills. The calculation of the lowest cost involved two methods: the multi-component production model without deficit, with restrictions, the solution was done using the classical method (normal) and mathematical analyses, utilizing tools such as QM and Win Qsb. Additionally, linear quadratic bilevel programming (LQBP) was employed. The LQBP model comprised an upper-level decision maker (leader) and a lower-level decision maker (follower). The transformation of the bilevel model into a single-level model was accomplished through the application of Karush-Kuhn-Tucker (KKT) conditions, and the solution was obtained using the modified simplex algorithm. The study's findings underscore the effectiveness of the LQBP method in identifying the optimal solution for the inventory problem by calculating the lowest cost. This approach significantly reduced medical drug inventory-related costs, with a value of 1,496,700,000 Iraqi Dinars (ID) and a production of 1200,700 ID. Notably, this cost was considerably lower than the total cost value obtained using the classical method, which was 1,719,166 ID/year, with a production of 2526,1773 ID. Therefore, bilevel programming (BLPP) demonstrates superior efficiency, providing more accurate and cost-effective solutions. This research emphasizes the potential of bilevel programming in optimizing medical drug inventory systems and contributes to the advancement of operational research in the healthcare sector.

Paper type: Research Paper

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2024-09-06

## Section

Statistical Researches

## How to Cite

“The Bi-level Programming Approach to Improve the Inventory Control System with a Practical Application” (2024) Journal of Economics and Administrative Sciences, 30(142), pp. 509–531. doi:10.33095/gd8dy062.

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