Solving the selective multi-category parallel-servicing problem

In this paper, we present a new scheduling problem and describe a shortest path-based heuristic as well as a dynamic programming-based exact optimization algorithm to solve it. The selective multi-category parallel-servicing problem arises when a set of jobs has to be scheduled on a server (machine) with limited capacity. Each job requests service in a prespecified time window and belongs to a certain category. Jobs may be serviced partially, incurring a penalty; however, only jobs of the same category can be processed simultaneously. One must identify the best subset of jobs to process in each time interval of a given planning horizon, while respecting the server capacity and scheduling requirements. We compare the proposed solution methods with a Mixed Integer Linear Programming (MILP) formulation and show that the dynamic programming approach is faster when the number of categories is large, whereas the MILP can be solved faster when the number of categories is small

A Benders Decomposition-Based Matheuristic for the Cardinality Constrained Shift Design Problem

The Shift Design Problem is an important optimization problem which arises when scheduling personnel in industries that require continuous operation. Based on the forecast, required staffing levels for a set of time periods, a set of shift types that best covers the demand must be determined. A shift type is a consecutive sequence of time periods that adheres to legal and union rules and can be assigned to an employee on any day. In this paper we introduce the Cardinality Constrained Shift Design Problem; a variant of the Shift Design Problem in which the number of permitted shift types is bounded by an upper limit. We present an integer programming model for this problem and show that its structure lends itself very naturally to Benders decomposition. Due to convergence issues with a conventional implementation, we propose a matheuristic based on Benders decomposition for solving the problem. Furthermore, we argue that an important step in this approach is finding dual alternative optimal solutions to the Benders subproblems and describe an approach to obtain a diverse set of these. Numerical tests show that the described methodology significantly outperforms a commercial mixed integer programming solver on instances with 1241 different shift types and remains competitive for larger cases with 2145 shift types. On all classes of problems the heuristic is able to quickly find good solutions.</p

Stochastic master surgery scheduling

The aim of the Master Surgery Scheduling Problem (MSSP) is to schedule the medical specialties to the different operating rooms available, such that surgeries may be performed efficiently. We consider a MSSP where elective and emergency patients can be treated in the same operating rooms. In addition to elective-dedicated operating room slots, flexible operating room slots are introduced to handle the fluctuating demand of emergency patients. To solve the MSSP, we propose a simulation-optimization approach consisting of a two-stage stochastic optimization model and a discrete-event simulation model. For the two-stage stochastic optimization model, uncertain arrivals of emergency patients are represented by discrete scenarios. The discrete-event simulation model is developed to address uncertainty related to the surgery duration and the length of stay at the hospital, and to test the Master Surgery Schedule (MSS) developed by the optimization model in a stochastic operational-level environment. In addition, the simulation model is used to generate scenarios for the optimization model. We present some general advice for surgery scheduling based on testing the optimization model in a numerical study. The simulation-optimization approach is applied to a case study from a hospital department that treats both elective and emergency patients. The optimized MSS outperforms the manually generated MSS, both in terms of emergency waiting time for surgery, and emergency interruptions to the flow of electives.acceptedVersio