This paper presents a branch-and-cut-and-price algorithm for the vehicle-routing problem with time windows. The standard Dantzig-Wolfe decomposition of the arc flow formulation leads to a set-partitioning problem as the master problem and an elementary shortest-path problem with resource constraints as the pricing problem. We introduce the subset-row inequalities, which are Chvatal-Gomory rank-1 cuts based on a subset of the constraints in the master problem. Applying a subset-row inequality in the master problem increases the complexity of the label-setting algorithm used to solve the pricing problem because an additional resource is added for each inequality. We propose a modified dominance criterion that makes it possible to dominate more labels by exploiting the step-like structure of the objective function of the pricing problem. Computational experiments have been performed on the Solomon benchmarks where we were able to close several instances. The results show that applying subset-row inequalities in the master problem significantly improves the lower bound and, in many cases, makes it possible to prove optimality in the root node.

The purpose of the calibrated model determines how to approach a model calibration, e.g. which information is needed and to which level of detail the model should be calibrated. A systematic model calibration procedure was therefore defined and evaluated for a municipal–industrial wastewater treatment plant. In the case that was studied it was important to have a detailed description of the process dynamics, since the model was to be used as the basis for optimisation scenarios in a later phase. Therefore, a complete model calibration procedure was applied including: (1) a description of the hydraulics in the system via a tracer test, (2) an intensive measuring campaign and (3) supporting lab-scale experiments to obtain and confirm kinetic parameters for the model. In this paper the model calibration procedure for this case study is described step by step, and the importance of the different steps is discussed. The calibrated model was evaluated via a sensitivity analysis on the influence of model parameters and influent component concentrations on the model output. The sensitivity analysis confirmed that the model output was sensitive to the parameters that were modified from the default parameter values. The calibrated model was finally reduced from a 24 tanks-in-series configuration to a 12 tanks-in-series configuration, resulting in a 50% reduction of the simulation time.

Summary We present research on sunscreen use with possible pitfalls and discuss theory vs. reality. A literature review in PubMed was conducted using the terms ‘sunscreen application’, ‘sunscreen use’ and ‘sun protection factor’. The sun protection factor (SPF) of sunscreens are tested using a thickness of 2 mg/cm2, but investigations show that sunscreen under natural conditions is applied insufficiently with amounts about 0.39 to 1.0 mg/cm2, which decreases the protection factor considerably. It has been shown that early reapplication or use of very high SPF (70–100) may partly compensate for the discrepancy between the amounts of sunscreen applied during testing and in reality, and that sunscreen application can be improved by education of consumers. Missing areas and ultraviolet radiation exposure before sunscreen application are other pitfalls that reduce the protective effect of sunscreens considerably. Current sunscreen labelling overrates the protective effect of a given sunscreen when the reality of sunscreen use is taken into account. This may possibly mislead consumers to feel it is safe to extend sun exposure. Alternatively to educating people to use large amounts of sunscreen, we suggest a simple teaching strategy: (1) Apply before sun exposure and (2) Reapply once within 1 h.

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