Mixed-Integer Linear Programming, Constraint Programming and a Novel Dedicated Heuristic for Production Scheduling in a Packaging Plant

Abstract

In this paper, we are discussing a research project aiming to optimize the scheduling of production orders within a real application in the packaging field. As a first approach, we model the problem as an extended version of the hybrid and flexible flowshop scheduling problem with precedence constraints, parallel machines, and sequence-dependent setups. The optimization objective considered is the minimization of the total tardiness. To tackle this problem, we use two methodologies: mixed-integer linear programming (MILP) and constraint programming (CP). These two models were further extended by adding resource calendar constraints named also availability constraints; this implies that the tasks should be scheduled only when the machine is available. The different proposed models were compared to each other on a set of generated benchmarks that reflect the specific properties of the industrial partner. Finally, as the studied configuration relies on practical real-world application, where thousands of orders are produced monthly, a novel dedicated heuristic was designed to address the need for quick solutions. The latter outperforms the other proposed algorithms for expected total tardiness minimization. The proposed problem can be readily modified to suit a wide range of real-world situations involving the scheduling of activities that share similar characteristics.

Model of Multi Criteria Decision-Making for Selection of Transportation Alternatives on the Base of Transport Needs Hierarchy Framework and Application of Petri Net

“…The paper [10] compares linear programming (LP) and mixed integer programming (MIP) models for managing seedling transportation. The LP model uses a linear objective function, while MIP bases costs on vehicle loads.…”

Optimal Volume Planning and Scheduling of Paper Production with Smooth Transitions by Product Grades

“…Paper [13] discusses the scheduling of production orders at a packaging mill with parallel machines and sequence-dependent setups aiming to minimize the total tardiness subject to precedence constraints, calendar constraints and also availability constraints. The authors note that for practical applications, the resulting constrained mixed-integer linear programming problem is NP-hard in the strong sense and propose a dedicated heuristic for quick solutions.…”

“…We will discuss the main methods for solving this problem and give a practical example of successful application of these methods in real production conditions. Similarly to [13], a novel dedicated heuristic is required to ensure quick solutions for this integer linear programming problem of large dimension.…”