Mixed integer programming in production planning with backlogging and setup carryover : modeling and algorithms

This paper proposes a mixed integer programming formulation for modeling the capacitated multi-level lot sizing problem with both backlogging and setup carryover. Based on the model formulation, a progressive time-oriented decomposition heuristic framework is then proposed, where improvement and construction heuristics are effectively combined, therefore efficiently avoiding the weaknesses associated with the one-time decisions made by other classical time-oriented decomposition algorithms. Computational results show that the proposed optimization framework provides competitive solutions within a reasonable time

Traveling Baseball Players' Problem in Korea

We study the so-called the traveling tournament problem (TTP), to find an optimal tournament schedule. Differently from the original TTP, in which the total travel distance of all the participants is the objective function to minimize, we instead seek to maximize the fairness of the round robin tournament schedule of the Korean Baseball League. The standard deviation of the travel distances of teams is defined as the energy function, and the Metropolis Monte-Carlo method combined with the simulated annealing technique is applied to find the ground state configuration. The resulting tournament schedule is found to satisfy all the constraint rules set by the Korean Baseball Organization, but with drastically increased fairness in traveling distances.Comment: 8 pages, 4 figure

A branching scheme for minimum cost tournaments with regard to real-world constraints

Single round robin tournaments are a well-known class of sports leagues schedules. We consider leagues with a set T of n teams where n is even. Costs are associated with each possible match. Moreover, stadium availability, fixed matches, and regions' capacities are taken into account. The goal is to find the minimum cost tournament among those having the minimum number of breaks and being feasible with regard to these additional constraints. A branching scheme is developed where branching is done by fixing a break for a team. Thus, the focus is on identifying breaks leading to an infeasible home away pattern set in order to avoid the resulting infeasible subtrees of a branch and bound tree. Journal of the Operational Research Society (2011) 62, 2133-2145. doi: 10.1057/jors.2010.185 Published online 2 March 201

A branching scheme for minimum cost tournaments with regard to real-world constraints

Single round robin tournaments are a well-known class of sports leagues schedules. We consider leagues with a set T of n teams where n is even. Costs are associated with each possible match. Moreover, stadium availability, fixed matches, and regions’ capacities are taken into account. The goal is to find the minimum cost tournament among those having the minimum number of breaks and being feasible with regard to these additional constraints. A branching scheme is developed where branching is done by fixing a break for a team. Thus, the focus is on identifying breaks leading to an infeasible home away pattern set in order to avoid the resulting infeasible subtrees of a branch and bound tree.

ReplenishmentProblemWithMultipleArticlesAndAnOrderThreshold

These are the raw data sets used in the computational study in "The replenishment problem with multiple articles and an order threshold" by Dirk Briskorn and Thomas Wensin

Evaluating the emission reduction potential of scheduling locks on inland waterways

Locks constitute a bottleneck along many inland waterways. We consider the problem of scheduling a system of multiple locks arranged in a sequence, a setting that occurs naturally along many inland waterways. We provide two alternative mathematical programming models and evaluate their performance. In particular, we show how ship speed can be included as a variable, which allows to consider the emissions of ships passing through the system. We then use the models to investigate the trade-off between total flow-time and emissions on instances based on realistic problem instances.status: publishe

ReplenishmentProblemWithMultipleArticlesAndAnOrderThreshold

These are the raw data sets used in the computational study in "The replenishment problem with multiple articles and an order threshold" by Dirk Briskorn and Thomas Wensin

Dynamic programming for scheduling locks in sequence

status: publishe

Round robin tournaments and three index assignment

Scheduling a sports league can be seen as a difficult combinatorial optimization problem. We study some variants of round robin tournaments and analyze the relationship with the planar three-index assignment problem. The complexity of scheduling a minimum cost round robin tournament is established by a reduction from the planar three-index assignment problem. Furthermore, we introduce integer programming models. We pick up a popular idea and decompose the overall problem in order to obtain two subproblems which can be solved sequentially. We show that the latter subproblem can be casted as a planar three-index assignment problem. This makes existing solution techniques for the planar three-index assignment problem amenable to sports league scheduling.status: publishe