Constructing fair sports leagues schedules

A single round robin tournament (SRRT) consists of n teams and a set of periods. Matches between the teams have to be scheduled such that each team plays against each other team exactly once and each team plays at most once per period. In order to establish fairness among teams we consider a partition of the teams into strength groups. Then, the goal is to avoid that a team plays against extremely weak or extremely strong teams in consecutive periods. In this paper we pick up two concepts ensuring different degrees of fairness and adress several questions which remained open so far

Robust storage loading problems with stacking and payload constraints

We consider storage loading problems where items with uncertain weights have to be loaded into a storage area, taking into account stacking and payload constraints. Following the robust optimization paradigm, we propose strict and adjustable optimization models for finite and interval-based uncertainties. To solve these problems, exact decomposition and heuristic solution algorithms are developed. For strict robustness, we also propose a compact formulation based on a characterization of worst-case scenarios. Computational results for randomly generated data with up to 300 items are presented showing that the robustness concepts have different potential depending on the type of data being used

Shop-Scheduling Problems with Transportation

In this thesis scheduling problems with transportation aspects are studied. Classical scheduling models for problems with multiple operations are the so-called shop-scheduling models. In these models jobs consisting of different operations have to be planned on certain machines in such a way that a given objective function is minimized. Each machine may process at most one operation at a time and operations belonging to the same job cannot be processed simultaneously. We generalize these classical shop-scheduling problems by assuming that the jobs additionally have to be transported between the machines. This transportation has to be done by robots which can handle at most one job at a time. Besides transportation times which occur for the jobs during their transport, also empty moving times are considered which arise when a robot moves empty from one machine to another. Two types of problems are distinguished: on the one hand, problems without transportation conflicts (i.e. each transportation can be performed without delay), and on the other hand, problems where transportation conflicts may arise due to a limited capacity of transport robots. In the first part of this thesis several new complexity results are derived for flow-shop problems with a single robot. Since very special cases of these problems are already NP-hard, in the second part of this thesis some techniques are developed for dealing with these hard problems in practice. We concentrate on the job-shop problem with a single robot and the makespan objective. At first we study the subproblem which arises for the robot when some scheduling decisions for the machines have already been made. The resulting single-machine problem can be regarded as a generalization of the traveling salesman problem with time windows where additionally minimal time-lags between certain jobs have to be respected and the makespan has to be minimized. For this single-machine problem we adapt immediate selection techniques used for other scheduling problems and calculate lower bounds based on linear programming and the technique of column generation. On the other hand, to determine upper bounds for the single-machine problem we develop an efficient local search algorithm which finds good solutions in reasonable time. This algorithm is integrated into a local search algorithm for the job-shop problem with a single robot. Finally, the proposed algorithms are tested on different test data and computational results are presented

Optimality Conditions and Exact Neighborhoods for Sequencing Problems

Based on several scheduling examples some classes of polynomially solvable sequencing problems with and without precedence constraints are considered. Sufficient conditions for the existence of an adjacent pair interchange (API)-relation are derived in the case of sum- and bottleneck-objective functions. Furthermore, we obtain new conditions which are necessary and sufficient for the optimality of permutations. It is shown that exact neighborhoods exist for all considered problems. These are neighborhoods in which each local optimum is a global one. Additionally, the neighborhoods are polynomially bounded and optimal solutions can be found by Iterative Improvement procedures in a polynomial number of iterations. Keywords: exact neighborhood, sequencing problem, API-property, Iterative Improvement 1 Introduction In a sequencing problem we have to find a permutation which minimizes some objective function F : P n ! R, where P n denotes the set of all permutations of n elements. If th..

Scheduling non-professional table-tennis leagues

In this paper we consider a sports league scheduling problem which occurs in planning non-professional table-tennis leagues. The problem consists in finding a schedule for a time-relaxed double round robin tournament where different hard and soft constraints have to be taken into account. We model the problem as an integer linear program and a multi-mode resource-constrained project scheduling problem, respectively. Based on the second model a heuristic solution algorithm is proposed, which proceeds in two stages using local search and genetic algorithms. Computational results show the efficiency of the approaches.Scheduling Sports league Resource-constrained project scheduling problem Partially renewable resources Genetic algorithm

On Circular 2-Factorizations of the Complete Tripartite Graph

We consider 2-factorizations of the complete tripartite graph K{n;3) where each 2-factor consists of cycles with even length. An additional requirement is related to pairs of edges being consecutive in an arbitrary cycle. For all pairs of edges we require that the three nodes incident to these two edges must be from different partite sets of the tripartite graph. We show that such a 2-factorizations cannot exist if n = 2 or n is odd. Furthermore, we show how to construct such a 2-factorization for all even n with n{2,26,34,58,74}

Tabu search algorithms for job-shop problems with a single transport robot

We consider a generalized job-shop problem where the jobs additionally have to be transported between the machines by a single transport robot. Besides transportation times for the jobs, empty moving times for the robot are taken into account. The objective is to determine a schedule with minimal makespan. We present local search algorithms for this problem where appropriate neighborhood structures are defined using problem-specific properties. An one-stage procedure is compared with a two-stage approach and a combination of both. Computational results are presented for test data arising from job-shop benchmark instances enlarged by transportation and empty moving times

A tabu search algorithm for scheduling a single robot in a job-shop environment

We consider a single-machine scheduling problem which arises as a subproblem in a job-shop environment where the jobs have to be transported between the machines by a single transport robot. The robot scheduling problem may be regarded as a generalization of the travelling-salesman problem with time windows, where additionally generalized precedence constraints have to be respected. The objective is to determine a sequence of all nodes and corresponding starting times in the given time windows in such a way that all generalized precedence relations are respected and the sum of all travelling and waiting times is minimized. We present a local search algorithm for this problem where an appropriate neighborhood structure is defined using problem-specific properties. In order to make the search process more efficient, we apply some techniques which accelerate the evaluation of the solutions in the proposed neighbourhood considerably. Computational results are presented for test data arising from job-shop instances with a single transport robot. \u