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The Vehicle Routing Problem (VRP) has been thoroughly studied in the last decades. However, the main focus has been on the deterministic version where customer demands are fixed and known in advance. Uncertainty in demand has not received enough consideration. When demands are uncertain, several problems arise in the VRP. For example, there might be unmet customers' demands, which eventually lead to profit loss. A reliable plan and set of routes, after solving the VRP, can significantly reduce the unmet demand costs, helping in obtaining customer satisfaction. This paper investigates a variant of an uncertain VRP in which the customers' demands are supposed to be uncertain with unknown distributions. An advanced Particle Swarm Optimization (PSO) algorithm has been proposed to solve such a VRP. A novel decoding scheme has also been developed to increase the PSO efficiency. Comprehensive computational experiments, along with comparisons with other existing algorithms, have been provided to validate the proposed algorithms.

Recently, rare health events issue has motivated many researches in the field of control charting. Various methods such as g-type control chart, g-type CUSUM control chart, sets method, CUSCORE method, SHDA method and the Bernoulli CUSUM have been developed in this regard, in which each of them has a specific approach to the problem. As a relatively new approach, zero inflation in Poisson distribution, named ZIP distribution can be applied. In this paper, an exponentially weighted moving average (EWMA) control chart is developed for the ZIP random variable to monitor rare health-related events with a predefined performance measure value. Since the ZIP-EWMA plotted data are dependent, Markov chain approach is applied to calculate average run lengths (ARLs) as the control chart performance criteria. Based on the ARL measure, the ZIP-EWMA chart performs better in comparison with the methods available in the literature. As the main contribution of this paper is the development a control chart which performs better than the previously proposed charts. Also, a motivating real case study related to monitoring needle-stick rare occurrences in a hospital is investigated to show the applicability of the developed chart.

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