In this paper, we present a study of the robust (non-deterministic) job scheduling problem with interval release dates on unrelated machines. Robust optimization is a tractable alternative to stochastic optimization suited for problems in which parameter distributions are undetermined due to insufficient data. Our problem formulation involves minimizing the maximum regret, defined as the worst-case deviation from an optimal makespan, with the assumption that each release date belongs to a well-defined interval. Mathematical analysis is accomplished to investigate the properties of the robust scheduling problem examining the inapproximability, determination of the upper bound of a regret function, and selection of feasible scenarios. In order to solve the robust scheduling problem, we propose an algorithm that implements a greedy strategy and schedules jobs using only the deterministic criterion (the makespan) instead of assessing the worst-case regret value. We compare the quality of our schedules with the solutions obtained by the properly adapted and tuned simulated annealing algorithm. Additionally, the applicability of our robust approach (robust framework) in the Scheduling-Location problem (deterministic problem in which the parameters are precisely defined), which combines the facility location problem and job scheduling problem, is demonstrated. The numerical evaluation shows that including the uncertainty and regret-averse (the minimax regret criterion) can allow, in certain cases, to achieve optimal solutions for incomplete dataset.

In this paper, we propose novel algorithms for the Scheduling and Location problem (called ScheLoc problem) that combine fields of job scheduling with the makespan criterion on unrelated machines and machine deployment. This research’s fundamental aim and distinguishing feature is the application of robust (nondeterministic) optimization with interval data for the ScheLoc problem (deterministic problem with precisely defined input parameters). The minimax regret criterion is considered as the measure of robustness, and the release dates of jobs are represented as well-defined intervals. We show that the algorithms designed for the robust optimization problem with interval release dates determined based on the ScheLoc problem can achieve a lower makespan than a schedule obtained by the greedy algorithm intended for the deterministic ScheLoc problem.

This paper considers the job scheduling problem with varying release dates on unrelated parallel machines. Our model involves the machine-dependent release dates and the makespan criterion. The two developed and presented constructive deterministic algorithms use different decomposition strategies that result logically from exploiting the problem structure. The approximation factor of the greedy polynomial algorithm depends on the machines. An efficient adaptation of the well-known brute-force technique to solve $Rm\vert r_{i,j}\vert C_{\max}$ is also considered in this paper. A series of numerical experiments are conducted to compare the quality of schedules.

A new case of joint location and scheduling (ScheLoc) problem is considered. It deals with selecting a non-fixed number of locations for identical parallel executors (machines) from a given set of available sites. Simultaneously, a schedule for a set of tasks is sought. For every task, it comprises an executor carrying-out the task and the moment of time when the performance of the task is started. The locations for executors and the schedule are evaluated by two criteria: the sum of task completion times and investment costs incurred when locations for executors are selected and launched. It is justified that the joint optimization problem is strongly NP-hard. In consequence, a heuristic algorithm Alg_BC is proposed, which uses the general scheme of NSGA II provided for the multi-criteria optimization. The performance of Alg_BC is evaluated for small instances by exact solutions determined by the Matlab solver. The sensitivity analysis for bigger instances is also provided, which among others, allows examining the influence of both component criteria on results generated by the evaluated algorithm. A case study dealing with the evacuation of citizen groups from danger zones is provided as an example of the investigated bi-criteria ScheLoc problem. The usefulness of Alg_BC is confirmed as well.

This work considered a joint problem of train rescheduling and closure planning. The derivation of a new train run schedule and the determination of a closure plan not only must guarantee the satisfaction of all the given constraints but also must optimize the number of accepted closures, the number of approved train runs, and the total time shift between the resultant and the original schedule. Presented is a novel nonlinear mixed integer optimization problem which is valid for a broad class of railway networks. A multi-level hierarchical heuristic algorithm is introduced due to the NP-hardness of the considered optimization problem. The algorithm is able, on an iterative basis, to jointly select closures and train runs, along with the derivation of a train schedule. Results obtained by the algorithm, launched for the conducted experiments, confirm its ability to provide acceptable and feasible solutions in a reasonable amount of time.

This paper presents a profound analysis of the robust job scheduling problem with uncertain release dates on unrelated machines. Our model involves minimizing the worst-case makespan and interval uncertainty where each release date belongs to a well-defined interval. Robust optimization requires scenario-based decision-making. A finite subset of feasible scenarios to determine the worst-case regret (a deviation from the optimal makespan) for a particular schedule is indicated. We formulate a mixed-integer nonlinear programming model to solve the underlying problem via three (constructive) greedy algorithms. Polynomial-time solvable cases are also discussed in detail. The algorithms solve the robust combinatorial problem using the makespan criterion and its non-deterministic counterpart. Computational testing compares both robust solutions and different decomposition strategies. Finally, the results confirm that a decomposition strategy applied to the makespan criterion is enough to create a competitive robust schedule.

The chapter introduces a unified representation of decision-making and decision-support in the form of a decision system with a distinct decision-making plant and a distinct decision-making algorithm. The used systems approach is exemplified by such complex problems of decision-making or decision-support where the sought decisions are interconnected. The investigated cases concern the determination of optimal decisions in technological systems. The joint problem of scheduling the spatially deployed tasks, together with a collision-free control of executors to minimize the total execution time is the one most extensively presented. Proactive and reactive decision-making is considered with the use of an uncertain approach for the former case. The connection between this problem and that of multi-robot task allocation is indicated. Integrated planning of production as well as raw material and product transportation in a supply chain to minimize the total cost serves as an example of a complex decision-support problem. Joint admission control and rate allocation in computer networks is included as the last example of complex decision-making problems. Numerical examples appended to all of the considered problems confirm the advantage of the systems approach over methods assuming separate determination of component decisions.

We consider the robust version of single machine scheduling problem with the objective to minimize the weighted number of jobs completed after their due-dates. The jobs have uncertain processing times represented by intervals, and decision-maker must determine their execution sequence that minimizes the maximum regret. We develop an exact solution algorithm based on a specialized branch and bound method, using mixed-integer linear programming formulations for a common due-date and for job-dependent due-dates. Finally, we examine the solution algorithm in a series of computational experiments.

This research explores integrated and sequential approaches to a combined job scheduling and discrete facility location optimization problem (ScheLoc). The makespan is considered as a criterion for job scheduling. A Tabu Search based Memetic Algorithm (TSMA) has been developed and applied for the former approach due to the NP-hardness of ScheLoc. For the latter approach, the problem is decomposed into two sub-problems m-median and parallel job scheduling with unrelated machines. Extensive numerical tests have confirmed the advantage of the integrated optimization strategy ensured by TSMA in terms of the makespan and the computation time. Conducted computational experiments have also shown the improvement of results generated by TSMA in comparison with another algorithm known from the literature.

Purpose Rapid advancements in internet technology have made it possible to develop electronic commerce in general and internet shopping in particular. Easy access to a vast number of existing internet stores enables buyers to customize their shopping processes to minimize the total purchase cost. This paper aims to investigate a novel internet shopping problem, which consists of the diversification of a given list of products to buy among many stores and to use discounts offered by the stores. Design/methodology/approach The adequate discrete optimization problem referred to as internet shopping optimization problem with price sensitivity discounts (ISOPwD) is investigated, which turned out to be strongly nondeterministic polynomial (NS)-hard. Two heuristic solution algorithms have been derived using the tabu search (TS) and the simulated annealing (SA) metaheuristics for having a solution in a reasonable time. The algorithms have been assessed via computational experiments, and they have been compared with another algorithm known from the literature that has been elaborated for a simpler version of ISOPwD. Findings The conducted evaluation has shown the advantage of both heuristic algorithms on the algorithm known from the literature. Moreover, the TS-based algorithm outperformed the other one in terms of the total cost incurred by customers and the computational time. Research limitations/implications The special primary piecewise linear discounting function is only taken into account. Other possible discounts connected, for example, with bundles of products and (or) coupons are not considered. Practical implications The elaborated algorithms can be recommended for internet shopping providers who want to introduce the ability to search a cost-optimized set of products in their databases or for applications that combine offers from various online retailers, e.g. internet price comparison services and auction sites. Originality/value The novelty of considered ISOPwD, in comparison with similar problems discussed in the literature, deals with an arbitrary number of purchased products, the possibility to buy an identical product in different stores and the consideration of the weight, the amount and the availability of goods as parameters of ISOPwD.

An uncertain version of the permutation flow-shop with unlimited buffers and the makespan as a criterion is considered. The investigated parametric uncertainty is represented by given interval-valued processing times. The maximum regret is used for the evaluation of uncertainty. Consequently, the minmax regret discrete optimization problem is solved. Due to its high complexity, two relaxations are applied to simplify the optimization procedure. First of all, a greedy procedure is used for calculating the criterion’s value, as such calculation is NP-hard problem itself. Moreover, the lower bound is used instead of solving the internal deterministic flow-shop. The constructive heuristic algorithm is applied for the relaxed optimization problem. The algorithm is compared with previously elaborated other heuristic algorithms basing on the evolutionary and the middle interval approaches. The conducted computational experiments showed the advantage of the constructive heuristic algorithm with regards to both the criterion and the time of computations. The Wilcoxon paired-rank statistical test confirmed this conclusion.

Selected complex railway track maintenance problem, composed of train rescheduling and track closures planning, is considered. It is assumed that a set of obligatory and facultative planned track closures is given for a specified railway network with the operating railway traffic managed by a current timetable. A new timetable is derived including all obligatory closures as well as a sub-set of facultative closures to maximize a combined performance index evaluating not only a number of accepted facultative closures but also a traffic quality expressed by a similarity of current and new timetables. A proposed heuristic algorithm is based on the decomposition of the problem into several connected sub-problems solved by solvers together with greedy algorithms. The algorithm responsible for the generation of railway sub-networks on the basis of the railway network is described in detail. Other algorithms are characterized in a general way. An illustrative numerical experiment is also given.

A complex population-based solution algorithm for an uncertain decision making problem is presented. The uncertain version of a permutation flow-shop problem with interval execution times is considered. The worst-case regret based on the makespan is used for the evaluation of permutations of tasks. The resulting complex minmax combinatorial optimization problem is solved. The heuristic algorithm is proposed which is based on the decomposition of the problem into three sequential sub-problems and employs a paradigm of evolutionary computing. The proposed algorithm solves the sub-problems sequentially. It is compared with the fast middle point heuristic algorithm via computer simulation experiments. The results show the usefulness of this heuristic algorithm for instances up to five machines.

Purpose – The concept of utility was the first time applied in Economics. The purpose of this paper is to report its usefulness for the decision making in complex technological systems, in general and in computer networks, in particular. Three selected decision-making problems are considered, corresponding solution algorithms are explained and results of numerical experiments are presented for the selected real-world case study. Design/methodology/approach – Referring to similar decision-making problems in Economics, three problems of different time horizon are investigated: strategic investment planning, short-term network rate allocation and on-line network operating. Deterministic and uncertain versions are taken into account, and the latter one is handled more thoroughly. The formalism of uncertain variables is used to represent the parameter uncertainty which concerns users’ demands for services in computer networks as well as network links’ capacities. Corresponding optimization tasks are presented. Numerical experiments concerning a part of the computer network Pionier working in Poland confirmed the usefulness of the solution algorithms proposed. Findings – The carried out numerical experiments verified the importance and worth of the decision-making algorithms for the Pionier computer network. It particularly concerns the game theory-based algorithm solving the on-line network operating problem which enables calculating the rates for computer links distinctly, i.e., separately for every link. Research limitations/implications – More case studies should be considered to formulate more general corollaries. The application of utility concept for wireless sensor networks needs further studies on solution algorithms. Practical implications – The results can be directly applied to a class of modern computer networks, e.g., content delivery networks, self-managing networks, context aware networks, multilevel virtual networks. Originality/value – The paper presents the unified and systematic approach for individual results previously obtained, and it considers one case study.

The uncertain flow-shop is considered. It is assumed that processing times are not given a priori, but they belong to intervals of known bounds. The absolute regret (regret) is used to evaluate a solution (a schedule) which gives the minmax regret binary optimization problem. The evolutionary heuristic solution algorithm is experimentally compared with a simple middle interval heuristic algorithm for three machines instances. The conducted simulations confirmed the several percent advantage of the evolutionary approach.

This article extends the former results concerning the routing flow-shop problem to minimize the makespan on the case with buffers, non-zero ready times and different speeds of machines. The corresponding combinatorial optimization problem is formulated. The exact as well as four heuristic solution algorithms are presented. The branch and bound approach is applied for the former one. The heuristic algorithms employ known constructive idea proposed for the former version of the problem as well as the Tabu Search metaheuristics. Moreover, the improvement procedure is proposed to enhance the quality of both heuristic algorithms. The conducted simulation experiments allow evaluating all algorithms. Firstly, the heuristic algorithms are compared with the exact one for small instances of the problem in terms of the criterion and execution times. Then, for larger instances, the heuristic algorithms are mutually compared. The case study regarding the maintenance of software products, given in the final part of the paper, illustrates the possibility to apply the results for real-world manufacturing systems.

A new decision making problem for wireless sensor networks is considered in the paper. A coverage of data sources, the routing of measured data as well as a scheduling of working periods of sensors are assumed as the decision to be made. All decisions as interconnected are determined jointly. The energy consumption and execution time of sensors are used as criteria. The corresponding combinatorial NP-hard optimization problem is formulated. To solve it, two heuristic algorithms are proposed. Some initial analitical evaluations of algorithms are presented as well as the result of computational experiments are given.

An uncertain version of the task scheduling problem on unrelated machines to minimize the total flow time is considered. It is assumed that processing times are not known a priori, but they belong to intervals of known bounds. The absolute regret is applied to evaluate the uncertainty, and minmax regret task scheduling problem is solved. A simple 2-approximate middle intervals time efficient algorithm is proposed. More time consuming but better in terms of the quality of solutions scatter search based heuristic algorithm is described. Its usefulness is justified via computational experiments.

The data placement problem arises in the design and operation of Content Delivery Networks—computer systems used to efficiently distribute Internet traffic to the users by replicating data objects (media files, applications, database queries, etc.) and caching them at multiple locations in the network. This allows not only to reduce the processing load on the server hardware, but also helps eliminating transmission network congestion. Currently all major Internet content providers entrust their offered services to such systems. In this paper we formulate the data placement problem as quadratic binary programming problem, taking into account server processing time, storage capacity and communication bandwidth. Two decomposition-based solution approaches are proposed: the Lagrangian relaxation and randomized rounding. Computational experiments are conducted in order to evaluate and compare the performance of presented algorithms.

This paper deals with selected joint problem of location, coverage and routing in a class of wireless sensor networks. The minimization of the total cost of data collection and transmission as well as sensors and sinks location is considered. Its NP-hardness is justified and a heuristic solution algorithm based on the result of the circulation problem in a directed graph is proposed. The quality of the algorithm has been assessed during numerical experiments, and the examples of corresponding results are presented.