A multilevel integrative approach to hospital case mix and capacity planning.

Hospital case mix and capacity planning involves the decision making both on patient volumes that can be taken care of at a hospital and on resource requirements and capacity management. In this research, to advance both the hospital resource efficiency and the health care service level, a multilevel integrative approach to the planning problem is proposed on the basis of mathematical programming modeling and simulation analysis. It consists of three stages, namely the case mix planning phase, the master surgery scheduling phase and the operational performance evaluation phase. At the case mix planning phase, a hospital is assumed to choose the optimal patient mix and volume that can bring the maximum overall financial contribution under the given resource capacity. Then, in order to improve the patient service level potentially, the total expected bed shortage due to the variable length of stay of patients is minimized through reallocating the bed capacity and building balanced master surgery schedules at the master surgery scheduling phase. After that, the performance evaluation is carried out at the operational stage through simulation analysis, and a few effective operational policies are suggested and analyzed to enhance the trade-offs between resource efficiency and service level. The three stages are interacting and are combined in an iterative way to make sound decisions both on the patient case mix and on the resource allocation.Health care; Case mix and capacity planning; Master surgery schedule; Multilevel; Resource efficiency; Service level;

Railway scheduling reduces the expected project makespan.

The Critical Chain Scheduling and Buffer Management (CC/BM) methodology, proposed by Goldratt (1997), introduced the concepts of feeding buffers, project buffers and resource buffers as well as the roadrunner mentality. This last concept, in which activities are started as soon as possible, was introduced in order to speed up projects by taking advantage of predecessors finishing early. Later on, the railway scheduling concept of never starting activities earlier than planned was introduced as a way to increase the stability of the project, typically at the cost of an increase in the expected project makespan. In this paper, we will indicate a realistic situation in which railway scheduling improves both the stability and the expected project makespan over roadrunner scheduling.Railway scheduling; Roadrunner scheduling; Feeding buffer; Priority list; Resource availability;

Heuristic branch-and-price for building long term trainee schedules.

Branch-and-price is an increasingly important technique for solving large integer programming models. Staff scheduling has been a particularly fruitful area since these problems typically exhibit a decomposable structure. Beside computational efficiency branch-and-price produces two other important advantages in comparison with pure integer programming. Firstly, it often allows for a more accurate problem statement since many constraints which are hard to formulate in the integer program could be easily incorporated in the column generator. Secondly, a branch-and-price algorithm can easily be turned into an effective heuristic when optimality is no major concern. We illustrate these advantages for a medical trainee scheduling problem encountered at Oogziekenhuis Gasthuisberg Leuven and present some computational results together with implementation issues.Advantages; Area; Branch-and-price; Constraint; Efficiency; Heuristic; Integer programming; Model; Models; Problems; Research; Scheduling; Staff scheduling; Structure;

A decision support system for surgery sequencing at UZ Leuven's day-care department.

In this paper, we test the applicability of a decision support system (DSS) that is developed to optimize the sequence of surgeries in the day-care center of the UZ Leuven Campus Gasthuisberg (Belgium). We introduce a multi-objective function in which children and prioritized patients are scheduled as early as possible on the day of surgery, recovery overtime is minimized and recovery workload is leveled throughout the day. This combinatorial optimization problem is solved by applying a pre-processed mixed integer linear programming model. We report on a 10-day case study to illustrate the performance of the DSS. In particular, we compare the schedules provided by the hospital with those that are suggested by the DSS. The results indicate that the DSS leads to both an increased probability of obtaining feasible schedules and an improved quality of the schedules in terms of the objective function value. We further highlight some of the major advantages of the application, such as its visualization and algorithmic performance, but also report on the difficulties that were encountered during the study and the shortcomings that currently delay its implementation in practice, as this information may contribute to the success rate of future software applications in hospitals.Decision support system; Optimization; Visualization; Health care application;

Resource-constrained project scheduling.

Abstract: Resource-constrained project scheduling involves the scheduling of project activities subject to precedence and resource constraints in order to meet the objective(s) in the best possible way. The area covers a wide variety of problem types. The objective of this paper is to provide a survey of what we believe are important recent in the area . Our main focus will be on the recent progress made in and the encouraging computational experience gained with the use of optimal solution procedures for the basic resource-constrained project scheduling problem (RCPSP) and important extensions. The RCPSP involves the scheduling of a project its duration subject to zero-lag finish-start precedence constraints of the PERT/CPM type and constant availability constraints on the required set of renewable resources. We discuss recent striking advances in dealing with this problem using a new depth-first branch-and-bound procedure, elaborating on the effective and efficient branching scheme, bounding calculations and dominance rules, and discuss the potential of using truncated branch-and-bound. We derive a set of conclusions from the research on optimal solution procedures for the basis RCPSP and subsequently illustrate how effective and efficient branching rules and several of the strong dominance and bounding arguments can be extended to a rich and realistic variety of related problems. The preemptive resource-constrained project scheduling problem (PRCPSP) relaxes the nonpreemption condition of the RCPSP, thus allowing activities to be interrupted at integer points in time and resumed later without additional penalty cost. The generalized resource-constrained project scheduling (GRCPSP) extends the RCPSP to the case of precedence diagramming type of precedence constraints (minimal finish-start, start-start, start-finish, finish-finish precedence relations), activity ready times, deadlines and variable resource availability's. The resource-constrained project scheduling problem with generalized precedence relations (RCPSP-GPR) allows for start-start, finish-start and finish-finish constraints with minimal and maximal time lags. The MAX-NPV problem aims at scheduling project activities in order to maximize the net present value of the project in the absence of resource constraints. The resource-constrained project scheduling problem with discounted cash flows (RCPSP-DC) aims at the same non-regular objective in the presence of resource constraints. The resource availability cost problem (RACP) aims at determining the cheapest resource availability amounts for which a feasible solution exists that does not violate the project deadline. In the discrete time/cost trade-off problem (DTCTP) the duration of an activity is a discrete, non-increasing function of the amount of a single nonrenewable resource committed to it. In the discrete time/resource trade-off problem (DTRTP) the duration of an activity is a discrete, non-increasing function of the amount of a single renewable resource. Each activity must then be scheduled in one of its possible execution modes. In addition to time/resource trade-offs, the multi-mode project scheduling problem (MRCPSP) allows for resource/resource trade-offs and constraints on renewable, nonrenewable and doubly-constrained resources. We report on recent computational results and end with overall conclusions and suggestions for future research.Scheduling; Optimal;

Integer programming for building robust surgery schedules.

This paper proposes and evaluates a number of models for building robust cyclic surgery schedules. The developed models involve two types of constraints. Demand constraints ensure that each surgeon (or surgical group) obtains a specific number of operating room (OR) blocks. Capacity con- straints limit the available OR blocks on each day. Furthermore, the number of operated patients per block and the length of stay (LOS) of each operated patient are dependent on the type of surgery. Both are considered stochas- tic, following a multinomial distribution. We develop a number of MIP-based heuristics and a metaheuristic to minimize the expected total bed shortage and present computational results.Constraint; Demand; Distribution; Expected; Heuristic; Integer programming; Model; Models; Resource leveling; Surgery scheduling;

Evaluating the capacity of clinical pathways through discrete-event simulation.

Organizing a medical facility efficiently is hard due to the numerous patient trajectories and their use of joint and scarce resources. Moreover, these trajectories tend to be complex and characterized by uncertain medical processes. In this paper, we will structure patient trajectories using clinical pathways and aggregate them in a discrete-event simulation model. This model enables the health manager to evaluate and improve important performance indicators, both for the patient and the hospital, by conducting a detailed sensitivity analysis. Two case studies, performed at large hospitals in Antwerp and Leuven (Belgium), will be introduced and briefly discussed in order to illustrate the generic nature of the model.Capacity management; Case studies; Discrete-event simulation; Health care operations; Processes; Structure; Simulation; Model; Performance; Indicators; Sensitivity; Studies; Hospitals; Belgium; Order;

On the trade-off between staff-decomposed and activity-decomposed column generation for a staff scheduling problem.

In this paper a comparison is made between two decomposition techniques to solve a staff scheduling problem with column generation. In the first approach, decomposition takes place on the staff members, whereas in the second approach decomposition takes place on the activities that have to be performed by the staff members. The resulting master LP is respectively a set partitioning problem and a capacitated multi-commodity flow problem. Both approaches have been implemented in a branch-and-price algorithm. We show a trade-off between modeling power and computation times of both techniques.decomposition; staff scheduling; set partitioning; multi-commodity flow; branch-and-price; branch-and-price; programs;

Integrating nurse and surgery scheduling.

Scheduling; Surgery scheduling; International; Theory; Applications; Euro; Researchers;