Andreas T. Ernst

Staff scheduling and rostering: A review of applications, methods and models

Abstract This paper presents a review of staff scheduling and rostering, an area that has become increasingly important as business becomes more service oriented and cost conscious in a global environment. Optimised staff schedules can provide enormous benefits, but require carefully implemented decision support systems if an organisation is to meet customer demands in a cost effective manner while satisfying requirements such as flexible workplace agreements, shift equity, staff preferences, and part-time work. In addition, each industry sector has its own set of issues and must be viewed in its own right. There are many computer software packages for staff scheduling, ranging from spreadsheet implementations of manual processes through to mathematical models using efficient optimal or heuristic algorithms. We do not review software packages in this paper. Rather, we review rostering problems in specific application areas, and the models and algorithms that have been reported in the literature for their solution. We also survey commonly used methods for solving rostering problems.

Efficient algorithms for the uncapacitated single allocation p-hub median problem

We present a new LP formulation for the single allocation p-hub median problem, which requires fewer variables and constraints than those traditionally used in the literature. We develop a good heuristic algorithm for its solution based on simulated annealing (SA). We use the SA upper bound to develop an LP-based branch-and-bound solution method. We present computational results for well-known problems from the literature which show that exact solutions can be found in a reasonable amount of computational time. We also benchmark our new solution approach on a new data set. This data set, which includes problems that are larger than those used in the literature, is based on a postal delivery network.

An Annotated Bibliography of Personnel Scheduling and Rostering

Computational methods for rostering and personnel scheduling has been a subject of continued research and commercial interest since the 1950s. This annotated bibliography puts together a comprehensive collection of some 700 references in this area, focusing mainly on algorithms for generating rosters and personnel schedules but also covering related areas such as workforce planning and estimating staffing requirements. We classify these papers according to the type of problem addressed, the application areas covered and the methods used. In addition, a short summary is provided for each paper.

ICE: a statistical approach to identifying endmembers in hyperspectral images

Several of the more important endmember-finding algorithms for hyperspectral data are discussed and some of their shortcomings highlighted. A new algorithm - iterated constrained endmembers (ICE) - which attempts to address these shortcomings is introduced. An example of its use is given. There is also a discussion of the advantages and disadvantages of normalizing spectra before the application of ICE or other endmember-finding algorithms.

SOLUTION ALGORITHMS FOR THE CAPACITATED SINGLE ALLOCATION HUB LOCATION PROBLEM

In this paper, we present an efficient approach for solving capacitated single allocationhub location problems. We use a modified version of a previous mixed integer linearprogramming formulation developed by us for p‐hub median problems. This formulationrequires fewer variables and constraints than those traditionally used in the literature. Wedevelop good heuristic algorithms for its solution based on simulated annealing (SA) andrandom descent (RDH). We use the upper bound to develop an LP‐based branch and boundsolution method. The problem, as we define it, finds applications in the design of postaldelivery networks, particularly in the location of capacitated mail sorting and distributioncentres. We test our algorithms on data obtained from this application. To the best of ourknowledge, this problem has not been solved in the literature. Computational results arepresented indicating the usefulness of our approach.

Exact and heuristic algorithms for the uncapacitated multiple allocation p-hub median problem

In this paper new MILP formulations for the multiple allocation p-hub median problem are presented. These require fewer variables and constraints than those traditionally used in the literature. An efficient heuristic algorithm, based on shortest paths, is described. LP based solution methods as well as an explicit enumeration algorithm are developed to obtain exact solutions. Computational results are presented for well known problems from the literature which show that exact solutions can be found in a reasonable amount of computational time. Our algorithms are also benchmarked on a different data set. This data set, which includes problems that are larger than those used in the literature, is based on a postal delivery network and has been treated by the authors in an earlier paper.

The capacitated multiple allocation hub location problem: Formulations and algorithms

In this paper we consider and present formulations and solution approaches for the capacitated multiple allocation hub location problem. We present a new mixed integer linear programming formulation for the problem. We also construct an efficient heuristic algorithm, using shortest paths. We incorporate the upper bound obtained from this heuristic in a linear-programming-based branch-and-bound solution procedure. We present the results of extensive computational experience with both the heuristic and the exact methods.

Hub Arc Location Problems: Part I-Introduction and Results

Hub networks play an important role in many transportation and telecommunications systems. This paper introduces a new model called the hub arc location model. Rather than locate discrete hub facilities, this model locates hub arcs, which have reduced unit flow costs. Four special cases of the general hub arc location model are examined in detail. We provide motivation for the new models, and present examples and optimal solutions, using data for U.S. air passenger traffic. Results are used to compare optimal costs, hub locations, and hub arc locations with corresponding hub median optimal solutions. The results reveal interesting spatial patterns and help identify promising cities and regions for hubs. A companion paper (Campbell et al. 2005) presents integer programming formulations and solution algorithms for the new hub arc problems. It also provides details and computation times for these solution algorithms.

An Exact Solution Approach Based on Shortest-Paths for P -Hub Median Problems

The problem of locating hub facilities arises in the design of transportation and telecommunications networks. The p-hub median problem belongs to a class of discrete location-allocation problems in which all the hubs are fully interconnected. Nonhub nodes may be either uniquely or multiply allocated to hubs. The hubs are uncapacitated and the total number of hubs, p is specified a priori. We describe a novel exact-solution approach for solving the multiple-allocation case of the p-hub median problem and show how a similar method can be adapted for solving the more difficult single-allocation case. The methods for both of these solve shortest-path problems to obtain lower bounds, which are used in a branch-and-bound scheme to obtain the exact solution. Numerical results show the superiority of this new approach over traditional LP-based methods.

Heuristic and exact algorithms for scheduling aircraft landings

The problem of scheduling aircraft landings on one or more runways is an interesting problem that is similar to a machine job scheduling problem with sequence-dependent processing times and with earliness and tardiness penalties. The aim is to optimally land a set of planes on one or several runways in such a way that separation criteria between all pairs of planes (not just successive ones) are satisfied. Each plane has an allowable time window as well as a target time. There are costs associated with landing either earlier or later than this target landing time. In this paper, we present a specialized simplex algorithm which evaluates the landing times very rapidly, based on some partial ordering information. This method is then used in a problem space search heuristic as well as a branch-and-bound method for both single-and multiple-runway problems. The effectiveness of our algorithms is tested using some standard test problems from the literature.