Many‐server loss models with non‐poisson time‐varying arrivals

This article proposes an approximation for the blocking probability in a many‐server loss model with a non‐Poisson time‐varying arrival process and flexible staffing (number of servers) and shows that it can be used to set staffing levels to stabilize the time‐varying blocking probability at a target level. Because the blocking probabilities necessarily change dramatically after each staffing change, we randomize the time of each staffing change about the planned time. We apply simulation to show that (i) the blocking probabilities cannot be stabilized without some form of randomization, (ii) the new staffing algorithm with randomiation can stabilize blocking probabilities at target levels and (iii) the required staffing can be quite different when the Poisson assumption is dropped. © 2017 Wiley Periodicals, Inc. Naval Research Logistics 64: 177–202, 2017     

Bounded flexibility in days‐on and days‐off scheduling

This article presents a flexible days‐on and days‐off scheduling problem and develops an exact branch and price (B&P) algorithm to find solutions. The main objective is to minimize the size of the total workforce required to cover time‐varying demand over a planning horizon that may extend up to 12 weeks. A new aspect of the problem is the general restriction that the number of consecutive days on and the number of consecutive days off must each fall within a predefined range. Moreover, the total assignment of working days in the planning horizon cannot exceed some maximum value. In the B&P framework, the master problem is stated as a set covering‐type problem whose columns are generated iteratively by solving one of three different subproblems. The first is an implicit model, the second is a resource constrained shortest path problem, and the third is a dynamic program. Computational experiments using both real‐word and randomly generated data show that workforce reductions up to 66% are possible with highly flexible days‐on and days‐off patterns. When evaluating the performance of the three subproblems, it was found that each yielded equivalent solutions but the dynamic program proved to be significantly more efficient. © 2013 Wiley Periodicals, Inc. Naval Research Logistics 60: 678–701, 2013     

What you should know about queueing models to set staffing requirements in service systems

One traditional application of queueing models is to help set staffing requirements in service systems, but the way to do so is not entirely straightforward, largely because demand in service systems typically varies greatly by the time of day. This article discusses ways—old and new—to cope with that time‐varying demand. © 2007 Wiley Periodicals, Inc. Naval Research Logistics, 2007     

An efficient metaheuristic for integrated scheduling and staffing IT projects based on a generalized minimum cost flow network

Scheduling IT projects and assigning the project work to human resources are an important and common tasks in almost any IT service company. It is particularly complex because human resources usually have multiple skills. Up to now only little work has considered IT‐specific properties of the project structure and human resources. In this article, we present an optimization model that simultaneously schedules the activities of multiple IT projects with serial network structures and assigns the project work to multiskilled internal and external human resources with different efficiencies. The goal is to minimize costs. We introduce a metaheuristic that decomposes the problem into a binary scheduling problem and a continuous staffing problem where the latter is solved efficiently by exploiting its underlying network structure. For comparison, we solve the mixed–binary linear program with a state–of–the–art commercial solver. The impacts of problem parameters on computation time and solution gaps between the metaheuristic and the solver are assessed in an experimental study. Our results show that the metaheuristic provides very favorable results in considerable less time than the solver for midsize problems. For larger problems, it shows a similar performance while the solver fails to return feasible solutions. © 2012 Wiley Periodicals, Inc. Naval Research Logistics 59: 111–127, 2012