Models of scheduling synchronized movement of many objects

The paper deals with the problem of determining movement schedule of many objects, used in many domains such as: routing in computer networks, movement planning of mobile robots, tasks processing in parallel or distributed computing systems, arms control of independent robots, planning and synchronization of the movement of many objects in computer simulation games (e.g., in Computer Generated Forces (CGF) systems or Semi-Automated Forces (SAF) systems). A lot of movement scheduling models are discussed. Two groups of criteria which are essential from the point of view of schedule estimation are described: a group connected with movement time of all objects and a group connected with “parallelization” of their movement (in the sense of location and times of reaching specified checkpoints). A nonlinear movement scheduling problem in order to minimize the sum of delays of all objects at checkpoints with some additional constraints is defined. Two equivalent formulations of two-criteria mathematical programming problems are also presented. It is proved that constraint coefficient matrices for both problems are totally unimodular and we can use effective algorithms for solving linear programming problems to find lexicographic solution of two-criteria problems. Similarities and differences between the defined problem and classical tasks scheduling problem before critical lines on parallel processors are discussed. Some extensions of the problem are presented, one of which is the scheduling movement problem of many objects according to a group pattern. Methods of solving formulated problems are indicated.movement scheduling and synchronization, shortest paths, disjoint paths, multicriteria shortest paths problems

A Constraint Programming Approach for Non-Preemptive Evacuation Scheduling

Large-scale controlled evacuations require emergency services to select evacuation routes, decide departure times, and mobilize resources to issue orders, all under strict time constraints. Existing algorithms almost always allow for preemptive evacuation schedules, which are less desirable in practice. This paper proposes, for the first time, a constraint-based scheduling model that optimizes the evacuation flow rate (number of vehicles sent at regular time intervals) and evacuation phasing of widely populated areas, while ensuring a nonpreemptive evacuation for each residential zone. Two optimization objectives are considered: (1) to maximize the number of evacuees reaching safety and (2) to minimize the overall duration of the evacuation. Preliminary results on a set of real-world instances show that the approach can produce, within a few seconds, a non-preemptive evacuation schedule which is either optimal or at most 6% away of the optimal preemptive solution.Comment: Submitted to the 21st International Conference on Principles and Practice of Constraint Programming (CP 2015). 15 pages + 1 reference pag

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The application of a stockpile stochastic model into long-term open pit mine production scheduling to improve the feed grade for the processing plant

This paper presents a chance-constrained integer programming approach based on the linear method to solve the long-term open pit mine production scheduling problem. Specifically, a single stockpile has been addressed for storing excess low-grade material based on the availability of processing capacity and for possible future processing. The proposed scheduling model maximizes the project NPV while respecting a series of physical and economic constraints. Differently from common practice, where deterministic models are used to calculate the average grade for material in the stockpiles, in this work a stochastic approach was performed, starting from the time of planning before the stockpile realization. By performing a probability analysis on two case studies (on iron and gold deposits), it was proven that the stockpile attributes can be treated as normally distributed random variables. Afterwards, the stochastic programming model was formulated in an open pit gold mine in order to determine the optimum amount of ore dispatched from different bench levels in the open pit and at the same time a low-grade stockpile to the mill. The chance-constrained programming was finally applied to obtain the equivalent deterministic solution of the primary model. The obtained results have shown a better feed grade for the processing plant with a higher NPV and probability of grade blending constraint satisfaction, with respect to using the traditional stockpile deterministic model.

Scheduling microCHPs in a group of houses

The increasing penetration of renewable energy sources, the demand for more energy efficient electricity production and the increase in distributed electricity generation causes a shift in the way electricity is produced and consumed. The downside of these changes in the electricity grid is that network stability and controllability become more difficult compared to the old situation. The new network has to accommodate various means of production, consumption and buffering and needs to offer control over the energy flows between these three elements.\ud In order to offer such a control mechanism we need to know more about the individual aspects. In this paper we focus on the modelling of distributed production. Especially, we look at the use of microCHP (Combined Heat and Power) appliances in a group of houses.\ud The problem of planning the production runs of the microCHP is modelled via an ILP formulation, both for a single house and for a group of houses.\u