A stopping rule while searching for optimal solution of facility-location

Solutions to combinatorial optimization, such as p-median problems of locating facilities, frequently rely on heuristics to minimize the objective function. The minimum is sought iteratively and a criterion is needed to decide when the procedure (almost) attains it. However, pre-setting the number of iterations dominates in OR applications, which implies that the quality of the solution cannot be ascertained. A small branch of the literature suggests using statistical principles to estimate the minimum and use the estimate for either stopping or evaluating the quality of the solution. In this paper we use test-problems taken from Baesley's OR-library and apply Simulated Annealing on these p-median problems. We do this for the purpose of comparing suggested methods of minimum estimation and, eventually, provide a recommendation for practioners. An illustration ends the paper being a problem of locating some 70 distribution centers of the Swedish Post in a region.

The Optimal trigger speed of vehicle activated signs

The thesis aims to elaborate on the optimum trigger speed for Vehicle Activated Signs (VAS) and to study the effectiveness of VAS trigger speed on drivers’ behaviour. Vehicle activated signs (VAS) are speed warning signs that are activated by individual vehicle when the driver exceeds a speed threshold. The threshold, which triggers the VAS, is commonly based on a driver speed, and accordingly, is called a trigger speed. At present, the trigger speed activating the VAS is usually set to a constant value and does not consider the fact that an optimal trigger speed might exist. The optimal trigger speed significantly impacts driver behaviour. In order to be able to fulfil the aims of this thesis, systematic vehicle speed data were collected from field experiments that utilized Doppler radar. Further calibration methods for the radar used in the experiment have been developed and evaluated to provide accurate data for the experiment. The calibration method was bidirectional; consisting of data cleaning and data reconstruction. The data cleaning calibration had a superior performance than the calibration based on the reconstructed data. To study the effectiveness of trigger speed on driver behaviour, the collected data were analysed by both descriptive and inferential statistics. Both descriptive and inferential statistics showed that the change in trigger speed had an effect on vehicle mean speed and on vehicle standard deviation of the mean speed. When the trigger speed was set near the speed limit, the standard deviation was high. Therefore, the choice of trigger speed cannot be based solely on the speed limit at the proposed VAS location. The optimal trigger speeds for VAS were not considered in previous studies. As well, the relationship between the trigger value and its consequences under different conditions were not clearly stated. The finding from this thesis is that the optimal trigger speed should be primarily based on lowering the standard deviation rather than lowering the mean speed of vehicles. Furthermore, the optimal trigger speed should be set near the 85th percentile speed, with the goal of lowering the standard deviation.

Optimal V. O2max-to-mass ratio for predicting 15 km performance among elite male cross-country skiers

The aim of this study was 1) to validate the 0.5 body-mass exponent for maximal oxygen uptake (V. O2max) as the optimal predictor of performance in a 15 km classical-technique skiing competition among elite male cross-country skiers and 2) to evaluate the influence of distance covered on the body-mass exponent for V. O2max among elite male skiers. Twenty-four elite male skiers (age: 21.4±3.3 years [mean ± standard deviation]) completed an incremental treadmill roller-skiing test to determine their V. O2max. Performance data were collected from a 15 km classicaltechnique cross-country skiing competition performed on a 5 km course. Power-function modeling (ie, an allometric scaling approach) was used to establish the optimal body-mass exponent for V . O2max to predict the skiing performance. The optimal power-function models were found to be race speed = 8.83⋅(V . O2max m-0.53) 0.66 and lap speed = 5.89⋅(V . O2max m-(0.49+0.018lap)) 0.43e0.010age, which explained 69% and 81% of the variance in skiing speed, respectively. All the variables contributed to the models. Based on the validation results, it may be recommended that V. O2max divided by the square root of body mass (mL⋅min−1 ⋅kg−0.5) should be used when elite male skiers’ performance capability in 15 km classical-technique races is evaluated. Moreover, the body-mass exponent for V . O2max was demonstrated to be influenced by the distance covered, indicating that heavier skiers have a more pronounced positive pacing profile (ie, race speed gradually decreasing throughout the race) compared to that of lighter skiers.