Modeling and optimization of manufacturing lot size in Aggregate production planning under demand Uncertainty: a case study of movit Products (U) Limited

Abstract

Demand uncertainty is eminent in many manufacturing industries giving a task of establishing the optimum manufacturing lot sizes in the production planning, leading to overstocking or understocking of the finished products. Different methods can be used in the reduction of these complexities and among these is modelling demand uncertainty of the production planning problem. The main objective was to develop an optimization model that predicts optimal manufacturing lot size in production planning under demand uncertainty. Specific objectives were: to characterize the existing production planning system with respect to manufacturing lot sizes, to define & formulate the manufacturing lot size problem in production planning under demand uncertainty at Movit products (U) Ltd, and to develop the manufacturing lot-size model under demand uncertainty that predicts optimal manufacturing lot sizes and then validating it. Two approaches were applied: Markov chains to formulate the possible states of demand under the condition of uncertainty; and stochastic goal programming to determine the number of units to be produced considering the over- achievement or under-achievement of the manufacturing lot size priorities desired. Using a framework on quarterly basis, the study undertook a case study on a manufacturing facility that manufactures, distributes and sells skin care, hair & nail care products to apply the mathematical model developed and demonstrate the proposed decision-making framework. The priorities for the model were established, the objective function was defined and the goal constraints were formulated for each of the five products. The ‘stochastic goal programming’ model for ‘manufacturing lot size’ was then established for all the products. The developed model was solved using MATLABTM software where an optimal solution was obtained. Results from the study indicated optimal levels of manufacturing lot size as demand changes from one state to another as 0, 2.3729, 0, 104.0840 for product A, 6.7720, 0, 0, 109.6800 for B, 0, 1.7602, 0, 181.8117 for C, 0, 369.4800, 0, 4975.1000 for D and 0, 13.3956, 0.6835, 6286.3000 for E. The under achievement was established as 8137.7000, 4555.6000, 12103.0000, 5478.7000, 56.2688 for products A, B, C, D, and E respectively and there was no over-achievement for all the products in a quarter of the year. The model was validated giving optimal results for aggregate production planning of the products (manufacturing lot size as 0, 182.02, 0, and 2.8341 and under achievement 4546.38). All the objectives in this study were achieved and an optimization model that predicts optimal manufacturing lot size in production planning (PP) under demand uncertainty was developed. In conclusion, the production planning system was characterized as a batch and make-to-stock strategy with standardization of product and process sequence. The manufacturing lot size was defined and formulated as determining the optimal manufacturing lot size minimizing the total production cost. Varying demand was then modeled as a two-state Markov chain where the optimality was state-dependent and then validated. The study recommends the adoption of the stochastic goal programming model to assist manufacturing companies that operate under demand uncertainty to accurately project production levels in order to sustain demand.