An Optimization Model for Production Planning in the Synthetic Fertilizer Industry

Production planning plays a key role in manufacturing. Different industrial requirements impose different conditions, eventually leading to different and non-trivial production plans. In this work, a particular planning problem which arises in synthetic fertilizer manufacturing is considered, to which the industrial conditions in the process of making fertilizer are incorporated. As in standard industrial scheduling problems, we assume a situation where different types of synthetic fertilizer are produced by different mixers having different capacities, in order to fulfil the demand of each vehicle that receives fertilizer from the outlets of those mixers. Loading the fertilizer to vehicles that wait in a queue at the factory premises and cleaning costs when using some mixer to produce two fertilizer types makes our problem significantly different to existing scheduling problems in literature. We first survey related problems and attempt to find the venue of our problem among those standard planning problems. Then we attempt to generate a production plan, addressing the industry-specific conditions for fertilizer manufacturing by reformulating as a binary integer program aimed at minimizing the total waiting time of the vehicles to which the fertilizers are loaded and the machine cleaning cost, satisfying industrial constraints. Due to the non-linearity of the optimization model, we adopt optimization heuristics to generate solutions.