Application of Langrangian Theory in Inventory Cost Reduction of a Firm

Abstract

Current events confirm the vital and dynamic need for studies that embrace Economics, Engineering, Management, and many other disciplines to confront the difficulties encountered in converting raw inputs to manufacturing outputs. This paper presents the assessment of inventory control system in a typical steel construction firm in Ibadan, Nigeria, with a view to predicting how best the inventory cost can be reduced. Data were collected by interviewing appropriate respondents at the production, stores, transport, purchasing, accounts, and wages sections of the firm and relevant documents used between the year 2014 and 2019. These were tailored towards identifying the controllable variables that were later classified using ABC Pareto analysis; implementation of an inventory model (Langrangian Multiplier) by mathematically relating the variables to the total cost; and evaluating the optimal values of the variables and the optimal cost of the system. The raw materials of the outfit were found to involve 88 items; which were grouped into 5, 20 and 63 items for classes A, B, and C respectively in accordance to ABC Pareto analysis. The identified controllable variables involved premises rent, unit ordering cost, annual demand, unit space and unit holding cost. On implementing the model, the annual total inventory cost was found to be N307,446.25, N154,667.50, and N84,035.00 for quarterly, bi-annual and annual inventory policies respectively; while the annual Economic Order Quantity (EOQ) was found to be N45,110.65 per annum. This shows that the company’s inventory cost can be reduced by N262,335.60 (85%), if the Annual Economic Order Quantity (proposed model)is implemented. This study has revealed the effect of implementing a standard inventory model for cost reduction in the area of material management.Keywords—Economics, Engineering, EOQ model, Inventory cost reduction, Management.