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Two-Stage Production Planning Under Stochastic Demand: Case Study of Fertilizer Manufacturing
Two-Stage Production Planning Under Stochastic Demand: Case Study of Fertilizer Manufacturing
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Date
2022
Authors
Chia-Nan Wang
Shao-Dong Syu
Chien-Chang Chou
Viet Tinh Nguyen
Dang Van Thuy Cuc
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Research Projects
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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
fertilizerswill 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, themathematicalmodel 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.
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Keywords
"Two-stage stochastic programming,
demand uncertainty,
planning,
blending,
fertilizer"