Mathematical models for planning support

In this paper we describe how computer systems can provide planners with active planning support, when these planners are carrying out their daily planning activities. This means that computer systems actively participate in the planning process by automatically generating plans or partial plans. Active planning support by computer systems requires the application of mathematical models and solution techniques. In this paper we describe the modeling process in general terms, as well as several modeling and solution techniques. We also present some background information on computational complexity theory, since most practical planning problems are hard to solve. We also describe how several objective functions can be handled, since it is rare that solutions can be evaluated by just one single objective. Furthermore, we give an introduction into the use of mathematical modeling systems, which are useful tools in a modeling context, especially during the development phases of a mathematical model. We finish the paper with a real life example related to the planning process of the rolling stock circulation of a railway operator.optimization;mathematical models;modeling process;planning support;Planning

Mixed integer linear programming models for Flow Shop Scheduling with a demand plan of job types

This is a post-peer-review, pre-copyedit version of an article published in Central european journal of operations research. The final authenticated version is available online at: http://www.doi.org/10.1007/s10100-018-0553-8This paper presents two mixed integer linear programming (MILP) models that extend two basic Flow Shop Scheduling problems: Fm/prmu/Cmax and Fm/block/Cmax. This extension incorporates the concept of an overall demand plan for types of jobs or products. After using an example to illustrate the new problems under study, we evaluated the new models and analyzed their behaviors when applied to instances found in the literature and industrial instances of a case study from Nissan’s plant in Barcelona. CPLEX solver was used as a solution tool and obtained acceptable results, allowing us to conclude that MILP can be used as a method for solving Flow Shop Scheduling problems with an overall demand plan.Peer ReviewedPostprint (published version

Mathematical models for planning support

In this paper we describe how computer systems can provide planners with active planning support, when these planners are carrying out their daily planning activities. This means that computer systems actively participate in the planning process by automatically generating plans or partial plans. Active planning support by computer systems requires the application of mathematical models and solution techniques. In this paper we describe the modeling process in general terms, as well as several modeling and solution techniques. We also present some background information on computational complexity theory, since most practical planning problems are hard to solve. We also describe how several objective functions can be handled, since it is rare that solutions can be evaluated by just one single objective. Furthermore, we give an introduction into the use of mathematical modeling systems, which are useful tools in a modeling context, especially during the development phases of a mathematical model. We finish the paper with a real life example related to the planning process of the rolling stock circulation of a railway operator

A Constraint Programming Approach to Simultaneous Task Allocation and Motion Scheduling for Industrial Dual-Arm Manipulation Tasks

Modern lightweight dual-arm robots bring the physical capabilities to quickly take over tasks at typical industrial workplaces designed for workers. In times of mass-customization, low setup times including the instructing/specifying of new tasks are crucial to stay competitive. We propose a constraint programming approach to simultaneous task allocation and motion scheduling for such industrial manipulation and assembly tasks. The proposed approach covers dual-arm and even multi-arm robots as well as connected machines. The key concept are Ordered Visiting Constraints, a descriptive and extensible model to specify such tasks with their spatiotemporal requirements and task-specific combinatorial or ordering constraints. Our solver integrates such task models and robot motion models into constraint optimization problems and solves them efficiently using various heuristics to produce makespan-optimized robot programs. The proposed task model is robot independent and thus can easily be deployed to other robotic platforms. Flexibility and portability of our proposed model is validated through several experiments on different simulated robot platforms. We benchmarked our search strategy against a general-purpose heuristic. For large manipulation tasks with 200 objects, our solver implemented using Google's Operations Research tools and ROS requires less than a minute to compute usable plans.Comment: 8 pages, 8 figures, submitted to ICRA'1