Two-Stage Production Planning Under Stochastic Demand: Case Study of Fertilizer Manufacturing

Abstract

Agriculture is a key facilitator of economic prosperity and nourishes the huge global population. To achieve sustainable agriculture, several factors should be considered, such as increasing nutrient and water efficiency and/or improving soil health and quality. Using fertilizer is one of the fastest and easiest ways to improve the quality of nutrients inland and increase the effectiveness of crop yields. Fertilizer supplies most of the necessary nutrients for plants, and it is estimated that at least 30%-50% of crop yields is attributable to commercial fertilizer nutrient inputs. Fertilizer is always a major concern in achieving sustainable and efficient agriculture. Applying reasonable and customized fertilizers will require a significant increase in the number of formulae, involving increasing costs and the accurate forecasting of the right time to apply the suitable formulae. An alternative solution is given by two-stage production planning under stochastic demand, which divides a planning schedule into two stages. The primary stage has non-existing demand information, the inputs of which are the proportion of raw materials needed for producing fertilizer products, the cost for purchasing materials, and the production cost. The total quantity of purchased material and produced products to be used in the blending process must be defined to meet as small as possible a paid cost. At the second stage, demand appears under multiple scenarios and their respective possibilities. This stage will provide a solution for each occurring scenario to achieve the best profit. The two-stage approach is presented in this paper, the mathematical model of which is based on linear integer programming. Considering the diversity of fertilizer types, the mathematical model can advise manufacturers about which products will generate as much as profit as possible. Specifically, two objectives are taken into account. First, the paper's thesis focuses on minimizing overall system costs, e.g., including inventory cost, purchasing cost, unit cost, and ordering cost at Stage 1. Second, the thesis