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This thesis studies two optimization problems: the optimization of a staffingpolicy assuming non stationary Poisson demand, and exponential travel and jobtimes, and the optimization of investment decisions with an investment lag.In the staffing policy optimization, we solve a novel time-dynamic Hamilton-Jacobi-Bellman equation that models jobs as a Poisson jump process. The modelgives the employer the flexibility to control the number of staff hired by two factors:the cost of hiring and the effect of delay.We have solved the optimal staffing policy problem using different approaches,which are compared. We produce accurate numerical results for different parameters,and discuss the advantages and disadvantages of each approach. Moreover,we have solved a staffing problem for a national utility company, using a standardlinear programming approach, which is compared with our methods. Inaddition to the Poisson jump process, we extend the model to treat a continuousjob model, and two locations model that is extendible to a larger network problem.In the investment lag problem, we use a mixture of numerical methods includingfinite difference and body fitted co-ordinates to form a robust and stablenumerical scheme which is applied to solve the investment lag problem for a geometricBrownian motion presented in the paper by Bar-Ilan and Strange (1996).The problem is to calculate the optimal price to invest in a project that havea time lag period between the decision to invest and production, and the optimalprice to mothball the project. The method presented in this thesis is moreflexible as we compare it with the previous results, and solves the problem fordifferent stochastic processes, such as Cox-Ingersoll-Ross model, which does nothave analytic solution.