Automated planning tool (APT): A mixed integer non linear programming problem solver for workorder scheduling

Workorder scheduling is a type of Resource allocation problem which is NP-complete. Workorder scheduling related to maintenance work becomes more challenging because of the inherent complexity of e-commerce facilities owing to various local requirements and variety of equipments viz.electrical, mechanical and electro-mechanical etc. Hence, we formulated the problem by using multiple decision variables to accommodate all these requirements. Next, we decomposed the problem into two smaller sub-problems to ensure a fast yet accurate solution with load balancing of workorder hours as the main objective function. Through this objective function, we are addressing the business requirement of reducing overtime and ensuring uniformity in workorders to be executed across the planning horizon. We have a mix of continuous and binary decision variables with multiple linear constraints, hence, this problem has been formulated as a Mixed Integer Nonlinear programming problem (MINLP) with nonlinear objection function. Being a NP-hard hard problem the runtime increases as the problem size increases (problem size is proportional to number of planning days and number of workorders). However, through problem decomposition, code vectorization and use of AWS EC2 instances, we have achieved a run time in the range of 5-20 minutes. Through this article, we have covered the vital details of optimization model, cloud compute infrastructure used to solve this NP-hard problem and salient points of MINLP model formulation.