Edward Kozłowski

Integer Linear Programming in Optimization of Waste After Cutting in the Furniture Manufacturing

The study was an attempt to develop the model of a decision controller allowing for simultaneous optimisation of the stock of semi-finished product generated during cutting and cut-out waste. The proposed decision controller was designed to select a suitable cut-out programme to account for such factors as: production orders, current stock of semi-finished product, minimum stock limits, the set limit of rejects. The elaboration concerns application of integer linear programming in multicriteria optimisation in constraint.

Application of survival function in robust scheduling of production jobs

Scheduling production jobs in the real production system requires considering a number of factors which may prove to exert a negative effect on the production processes. Hence the need for the identification and compensation of potential disruptions as early as at the production planning stage. The aim of this paper is to employ the survival and the hazard function to anticipate potential disruptions of the schedule so that they could be absorbed to produce a robust job schedule.

Optimal route determining for LQ problem with optimally stopped horizon

The routing problem with optimal stopping of linear system is investigated in this paper. The classical linear quadratic control problem was replaced by determining the optimal trajectory (way, track, path). The general aim of optimal stopping and route determining consists of minimization of composite cost function. To illustrate the optimal track a numerical example is included.

Optimal stopping of controlled linear stochastic systems

The optimal control problem with stopping for a discrete time linear stochastic system is investigated in this paper. Sometimes, in order to optimally realise the aim we need to know how long the system will be controlled. The traditional solutions with fixed terminal time are not enough to control the system optimally. The general aim of optimal control and stopping consists in minimization of a composite cost function. The paper presents two methods of solving this problem. A numerical example is included to illustrate the optimal control with stopping.

Binary Linear Programming as a Decision-Making Aid for Water Intake Operators

The cost of energy consumed in the course of pumping water from its sources constitutes a considerable share of the total operating costs borne by a water company. In order to optimize the operation of a water pumping station, it is essential to devise an appropriate pumps schedule. The aim of the work was to develop a smart tool which would facilitate decision-making by the operator of a water intake, including a group of wells, supplying actual municipal waterworks. The tool creates a real-time schedule for wells and pumps integrated with them, which constitutes a basis for a final decision made by the operator, related to the degree and period of their usage. The main criterion of facilitating the decision-making pertained to achieving the minimum energy consumption during pumping water from a well to a reservoir tank, while simultaneously keeping all the wells on full stand-by. The schedule was prepared by means of binary linear programming. In this method, both the function of the goal and the limiting functions are linear, whereas the particular variables belong to the set {0,1}.

The linear-quadratic stochastic optimal control problem with random horizon at the finite number of infinitesimal events

The aim of the article is to expand the results of the theory of Linear Quadratic Control (the state of the system is described with the help of stochastic linear equation while the quality coefficient is of a quadratic form) in the case of random horizon independent of the states of the system. As for the question under consideration the control system horizon is an independent variable with a discreet decomposition and has got a limited number of possible accomplishments. The above mentioned situation takes places when the number of controls is brought out by the outside factor (generally independent of the system).

Module for Prediction of Technological Operation Times in an Intelligent Job Scheduling System

This paper presents a model for the prediction of technological operation times in the framework of an intelligent job scheduling system. The developed prediction module implements ARMA/ARIMA time series models. In addition, the paper introduces the mathematical prediction model and its implementation to the particular test case. The scheduling made use of dispatching rules: LPT, SPT, FCFS and EDD. The validation of the model appears to confirm the effectiveness of the proposed solution and substantiate further research works in this direction.

Application of a Multidimensional Scaling Method to Identify the Factors Influencing on Reliability of Deep Wells

Elements of the water distribution systems (WDS) as removable objects can be repaired or replaced, however their failures are difficult for analysis. The impact of WDS failures can be reduced if preventive actions are taken based on their potential of occurrences or if a failure occurs and is detected within a minimum period of time after its occurrence. This requires the development of a forensic system for WDS failures. This is why in this paper we will present an analysis of reliability data from a water supply sources consisting of deep wells taking into consideration additional, potential failure reasons. The aim of the work was also application possibility analysis of a multidimensional scaling method to identify the factors influencing on reliability of deep wells.

Optimal stopping areas for discrete time linear quadratic control problem

The problem of determining the optimal stopping areas for a discrete time linear stochastic controlled system is investigated in this paper. Sometimes we have no information how long the system will be controlled. In this case we have a complex problem: the system should be controlled and stopped at the appropriate moment. Thus at each moment we make a decision about continuation of control and when the decision is positive, we need to determine the optimal control for stochastic system. To solve this problem the dynamic programming and the optimal stopping rules for stochastic processes were employed. The paper presents the method of determining the optimal stopping areas — sets of states where the system should be stopped. A numerical example is included and illustrates the behavior of these sets.

Intelligent Systems of Forecasting the Failure of Machinery Park and Supporting Fulfilment of Orders of Spare Parts

The article presents the possibility of forecasting failures of machinery park using IIOT (Industrial Internet of Things) that supports the range of activities concerning the collection of data using solutions that, by means of time series analysis and dynamic adjustment of the individual models, will allow to generate prognosis for failures of machinery park. Moreover, the use of the generated prognosis to control the storage of replacement parts and to support the area of orders fulfilment was proposed.