Improving operational effectiveness of tactical master plans for emergency and elective patients under stochastic demand and capacitated resources

This paper develops a two-stage planning procedure for master planning of elective and emergency patients while allocating at best the available hospital resources. Four types of resources are considered: operating theatre, beds in the medium and in the intensive care units, and nursing hours in the intensive care unit. A tactical plan is obtained by minimizing the deviations of the resources consumption to the target levels of resources utilization, following a goal programming approach. The MIP formulation to get this tactical plan is specifically designed to account for emergency care since it allows for the reservation of some capacity for emergency patients and possible capacity excess. To deal with the deviation between actually arriving elective patients and the average number of patients on which the tactical plan is based, we consider the possibility of planning a higher number of patients than the average to create operating slots in the tactical plan (slack planning). These operating slots are then filled in the operational plan following several flexibility rules. We consider three options for slack planning that lead to three different tactical plans on which we apply three flexibility rules to get finally nine alternative weekly schedules of elective patients. We then develop an algorithm to modify this schedule on a daily basis so as to account for emergency patients’ arrivals. Scheduled elective patients may be cancelled and emergency patients may be sent to other hospitals. Cancellation rules for both types of patients rely on the possibility to exceed the available capacities. Several performance indicators are defined to assess patient service and hospital efficiency. Simulation results show a trade-off between hospital efficiency and patient service.     

A bi-objective hierarchical program scheduling problem and its solution based on NSGA-III

In enterprise project management systems, a program at the tactical level coordinates and manages multiple projects at the operational level. There are close relationships between multiple projects in a program, which are typically manifested as shared resources and precedence relationships. Most research efforts have concentrated on the resource sharing by projects, while the precedence relationships between projects have yet to be comprehensively investigated. In this paper, a bi-objective hierarchical resource-constrained program scheduling problem proposed, where both resource sharing and precedence relationships between projects are considered in a distributed environment. The problem contains two different sub-problems at the operational level and the tactical level, and they are modeled in the same way as two bi-objective multi-mode scheduling problems. Shared resources are allocated from the tactical level to the operational level, and once they are allocated to a project, they can only be re-allocated to other projects once the current project is finished. Subsequently, a two-phase algorithm based on NSGA-III is developed. The algorithm runs at the operational level and the tactical level in turn. According to the Pareto fronts of projects that are submitted from the operational level, the bi-objective program planning at the tactical level is conducted under the constraints of precedence relationships and shared resources. The results of computational simulations demonstrate the satisfactory performance of the improved algorithm. By coordinating the local optimization of projects and the global optimization of the program in a hierarchical framework, the method proposed in this paper provides an effective integrated scheduling method for decision-makers at various levels of a program.

     

A queueing model for bed-occupancy management and planning of hospitals

The aim of this paper is, on the one hand, to describe the movement of patients through a hospital department by using classical queueing theory and, on the other hand, to present a way of optimising the use of hospital resources in order to improve hospital care. A queueing model is used to determine the main characteristics of the access of patients to hospital, such as mean bed occupancy and the probability that a demand for hospital care is lost because all beds are occupied. Moreover, we present a technique for optimising the number of beds in order to maintain an acceptable delay probability at a sufficiently low level and, finally, a way of optimising the average cost per day by balancing costs of empty beds against costs of delayed patients.     

Nursing care demand prediction based on a decomposed semi-markov population model

The semi-markovian population model introduced by Kao for the planning of progressive care hospitals is adapted to the prediction of nursing care demand at the level of a care unit in a general hospital. Assuming a feedback admission policy which refills the unit as soon as discharges occur, it is shown that the care unit can be decomposed into B independent subsystems corresponding to each of the B beds in the unit.For each bed the semi-Markov model permits the computation of the expected care demand and its variance for each of the seven forthcoming days. The model permits also the prediction of admissions of new patients. A prediction formula can thus be obtained where the expected care demand is expressed as a linear function of the expected number of admissions in the forthcoming days.Finally this methodology is illustrated on real data obtained in the gynaecology department of the Montreal Jewish General Hospital.     

Scheduling the hospital-wide flow of elective patients

In this paper, we address the problem of planning the patient flow in hospitals subject to scarce medical resources with the objective of maximizing the contribution margin. We assume that we can classify a large enough percentage of elective patients according to their diagnosis-related group (DRG) and clinical pathway. The clinical pathway defines the procedures (such as different types of diagnostic activities and surgery) as well as the sequence in which they have to be applied to the patient. The decision is then on which day each procedure of each patient’s clinical pathway should be done, taking into account the sequence of procedures as well as scarce clinical resources, such that the contribution margin of all patients is maximized. We develop two mixed-integer programs (MIP) for this problem which are embedded in a static and a rolling horizon planning approach. Computational results on real-world data show that employing the MIPs leads to a significant improvement of the contribution margin compared to the contribution margin obtained by employing the planning approach currently practiced. Furthermore, we show that the time between admission and surgery is significantly reduced by applying our models.     

Introducing cost-plus-loss analysis into a hierarchical forestry planning environment

Cost-plus-loss analysis of data for forestry planning has often been carried out for highly simplified planning situations. In this study, we suggest an advance in the cost-plus-loss methodology that aims to capture the hierarchical structure and iterative nature of planning by the large forest owner. The simulation system that is developed to simulate the planning process of the forest owner includes the tactical and operational levels of a continuous planning process. The system is characterized by annual re-planning of the tactical plan with a planning horizon of ten year and with the option to reassess data for selected stands before operational planning. Operational planning is done with a planning horizon of two years and the first year of the plan is considered to have been executed before moving the planning process one year forward. The annual cycle is repeated 10 times, simulating decisions made over a ten-year time horizon. The optimizing planning models of the system consider wood flow requirements, available harvest resources, seasonal variation of ground conditions and spatiality. The data used are evaluated according to standard procedures in cost-plus-loss analysis. Results from a test case indicate high decision losses when planning at both levels is based on the type of data prevalent in the stand databases of Swedish companies. The losses can be reduced substantially if higher-quality data are introduced before operational planning. In summary, the results indicate that the method makes it possible to analyze where in the planning process one needs better data and their value.     

Forest planning at the tactical level

Forest management and planning can involve large tracts of land involving numerous areal units. One approach to plan activities for a forested region over decades involves breaking down decision making into three components: strategic, tactical, and operational. Each level of the management hierarchy can involve the development and application of optimization models. These models typically aid in exploring management alternatives as well as multi-objective tradeoffs. Even though a strategic model can provide support for long term management at a broad scale, solutions may not be feasible at an operational level. Tactical level modeling helps to bridge solutions reached at a strategic level using operational planning information. This paper presents several tactical level planning models that have been developed as a part of a research effort supported by the US Forest Service. These models have been utilized in land use management and planning by the US Forest Service through a specially developed spatial decision support system.     

Modelling the size and skill-mix of hospital nursing teams

Previously published work has described the development of a hospital capacity simulation tool, PROMPT. PROMPT has now been adopted by a number of hospitals in the UK and is used for both strategic and operational planning and management of key hospital resources. The work, as presented here, extends the PROMPT functionality to consider in more detail workforce issues. In particular, working with some of the current hospital users, the research has focussed on detailed planning for calculating the size and skill-mix of inpatient nursing teams. The chosen methodology utilizes both simulation and optimization. Outputs from the PROMPT three-phase discrete event simulation are fed into a stochastic programme which suggests the optimal number of nurses to employ (whole time equivalents) by skill-mix and the corresponding numbers by shift. A novel feature of the tool is the ability to predict and compare nursing needs based on different methods of capturing patient-to-nurse ratios as currently adopted across the UK National Health Service. Illustrative results from one hospital demonstrate that although the overall sizes of nursing teams on different wards are of an acceptable level and comparable to the outputs from the simulation phase of the work, often the number of nurses employed at different grades is not well matched to patient needs and the skill-mix should be reconsidered. Results from the optimization phase of the work suggest that it is cost beneficial to increase the number of permanently employed nurses to account for fluctuations in demand and corresponding high costs of temporary (agency) nurses. The scenario functionality of the tool permits for the study of changing size and skill-mix as a consequence of changes in patient volumes, patient case-mix, numbers of beds and length of stay.     

Planning Activities in a Network of Logistic Platforms with Shared Resources

This paper has been motivated by the study of a real application, the transshipment container terminal of Gioia Tauro in Italy. The activities in a container terminal concern with the movement of containers from/to mother vessels and feeders and with the handling and storage of containers in the yard. For such type of applications both operational (e.g., scheduling) and tactical (e.g., planning) models, currently available in the literature, are not useful in terms of operations management and resources optimization. Indeed, the former models are too detailed for the complexity of the systems, while the latter are not able to capture the operational constraints in representing those activities which limit the nominal capacity. Herein, the container terminal, or more in general a service or production system, is represented as a network of complex substructures or platforms. The idea is to formalize the concept of platform capacity, which is used to represent the operational aspects of the container terminal in a mathematical model for the tactical planning. The problem, which consists in finding an allocation of resources in each platform in order to minimize the total delay on the overall network and on the time horizon, is modelled by a mathematical programming formulation for which we carry out a computational analysis using CPLEX-MIP solver. Moreover, we present a dynamic programming based heuristic to solve larger instances in short computational time. On all but one of the smaller instances, the heuristic solutions are also optimal. On the larger instances, the maximum gap, i.e. the percentage deviation, between the heuristic solutions and the best solutions computed by CPLEX-MIP within the time limit of 3600 s, has been 6.3%.     

Furniture supply chain tactical planning optimization using a time decomposition approach

We study the supply chain tactical planning problem of an integrated furniture company located in the Province of Québec, Canada. The paper presents a mathematical model for tactical planning of a subset of the supply chain. The decisions concern procurement, inventory, outsourcing and demand allocation policies. The goal is to define manufacturing and logistics policies that will allow the furniture company to have a competitive level of service at minimum cost. We consider planning horizon of 1 year and the time periods are based on weeks. We assume that customer’s demand is known and dynamic over the planning horizon. Supply chain planning is formulated as a large mixed integer programming model. We developed a heuristic using a time decomposition approach in order to obtain good solutions within reasonable time limit for large size problems. Computational results of the heuristic are reported. We also present the quantitative and qualitative results of the application of the mathematical model to a real industrial case.     

Column generation based heuristic for tactical planning in multi-period vehicle routing

The periodic vehicle routing problem (PVRP) consists in establishing a planning of visits to clients over a given time horizon so as to satisfy some service level while optimizing the routes used in each time period. The tactical planning model considered here restricts its attention to scheduling visits and assigning them to vehicles while leaving sequencing decisions for an underlying operational model. The objective is twofold: to optimize regional compactness of the routes in a desire to specialize routes to restricted geographical area and to balance the workload evenly between vehicles. Approximate solutions are constructed using a truncated column generation procedure followed by a rounding heuristic. This mathematical programming based procedure can deal with problems with 50–80 customers over five working days which is the range of size of most PVRP instances treated in the literature with meta-heuristics. The paper highlights the importance of alternative optimization criteria not accounted for in standard operational models and provides insights on the implementation of a column generation based rounding heuristic.     

Tactical store delivery planning

We describe a system for tactical planning of store deliveries that has been developed for a major US retailer. The retailer operates several distribution centres (DCs) and has over one thousand stores. The system is used for planning weekly fixed truck routes for store deliveries at minimal cost, where each route visits several stores, taking into account tight daily workload constraints in the DCs, limited daily transportation capacity, and store requirements. Initial results show a saving potential of 1–5%, amounting to several million US dollars annually, and truncation of the planning process from weeks to hours.     

Harvest planning in the Brazilian sugar cane industry via mixed integer programming

This work addresses harvest planning problems that arise in the production of sugar and alcohol from sugar cane in Brazil. The planning is performed for two planning horizons, tactical and operational planning, such that the total sugar content in the harvested cane is maximized. The tactical planning comprises the entire harvest season that averages seven months. The operational planning considers a horizon from seven to thirty days. Both problems are solved by mixed integer programming. The tactical planning is well handled. The model for the operational planning extends the one for the tactical planning and is presented in detail. Valid inequalities are introduced and three techniques are proposed to speed up finding quality solutions. These include pre-processing by grouping and filtering the distance matrix between fields, hot starting with construction heuristic solutions, and dividing and sequentially solving the resulting MIP program. Experiments are run over a set of real world and artificial instances. A case study illustrates the benefits of the proposed planning.     

Erlang loss bounds for OT–ICU systems

In hospitals, patients can be rejected at both the operating theater (OT) and the intensive care unit (ICU) due to limited ICU capacity. The corresponding ICU rejection probability is an important service factor for hospitals. Rejection of an ICU request may lead to health deterioration for patients, and for hospitals to costly actions and a loss of precious capacity when an operation is canceled. There is no simple expression available for this ICU rejection probability that takes the interaction with the OT into account. With c the ICU capacity (number of ICU beds), this paper proves and numerically illustrates a lower bound by an M|G|c|c system and an upper bound by an M|G|c-1|c-1 system, hence by simple Erlang loss expressions. The result is based on a product form modification for a special OT–ICU tandem formulation and proved by a technically complicated Markov reward comparison approach. The upper bound result is of particular practical interest for dimensioning an ICU to secure a prespecified service quality. The numerical results include a case study.     

Managing the overflow of intensive care patients

Many hospitals in the Netherlands are confronted with capacity problems at their intensive care units (ICUs) resulting in cancelling operations, overloading the staff with extra patients, or rejecting emergency patients. In practice, the last option is a common choice because for legal reasons, as well as for hospital logistics, rejecting emergency patients has minimal consequences for the hospital. As a result, emergency patients occasionally have to be transported to hospitals far away. In this work, we propose a cooperative solution for the ICU capacity problem. In our model, several hospitals in a region jointly reserve a small number of beds for regional emergency patients. We present a mathematical method for computing the number of regional beds for any given acceptance rate. The analytic approach is inspired by overflow models in telecommunication systems with multiple streams of telephone calls. Simulation studies show that our model is quite accurate. We conclude that cooperation between hospitals helps to achieve a high acceptance level with a smaller number of beds resulting in improved service for all patients.     

An integrated simulation-optimization framework for the operational planning of seaport container terminals

In this article the operational planning of seaport container terminals is considered by defining a suitable integrated framework in which simulation and optimization interact. The proposed tool is a simulation environment (implemented by using the Arena software) representing the dynamics of a container terminal. When the system faces some particular conditions (critical events), an optimization procedure integrated in the simulation tool is called. This means that the simulation is paused, an optimization problem is solved and the relative solution is an input for the simulation environment where some system parameters are modified (generally, the handling rates of some resources are changed). For this reason, in the present article we consider two modelling and planning levels about container terminals. The simulation framework, based on an appropriate discrete-event model, represents the dynamic behaviour of the terminal, thus it needs to be quite detailed and it is used as an operational planning tool. On the other hand, the optimization approach is devised in order to define some system parameters such as the resource handling rates; in this sense, it can be considered as a tool for tactical planning. The optimization procedure is based on an aggregate representation of the terminal where the dynamics is modelled by means of discrete-time equations.     

Tactical supply chain planning models with inherent flexibility: definition and review

Supply chains (SCs) can be managed at many levels. The use of tactical SC planning models with multiple flexibility options can help manage the usual operations efficiently and effectively, whilst improve the SC resiliency in response to inherent environmental uncertainties. This paper defines tactical SC flexibility and identifies tactical flexibility measures and options for development of flexible SC planning models. A classification of the existing literature of SC planning is introduced that highlights the characteristics of published flexibility inclusive models. Additional classifications from the reviewed literature are presented based on the integration of flexibility options used, solution methods utilized, and real world applications presented. These classifications are helpful for identifying research gaps in the current literature and provide insights for future modeling and research efforts in the field.     

Tactical Planning for a Cutting Stock System

Wood processing on a centralized conversion site can be considered as a cutting stock problem. The multiperiod optimization of the production system is a very hard problem to solve. A balance has to be made between value recovery optimization and service rate maximization. In this research a decision support system was designed and built to support production planning. Strategic, tactical and operational planning are covered, but here the focus is primarily on tactical planning.     

医疗资源影响下具有潜伏期的一类传染病模型建立及性态分析

建立了医疗资源影响下的考虑疾病具有潜伏期的一类传染病模型,并分析了模型的动力学性态.发现疾病流行与否由基本再生数和医院病床数共同决定,并得到了病床数的阈值条件.当基本再生数R_0大于1时,系统只存在惟一正平衡点,且通过构造Dulac函数证明了正平衡点只要存在一定是全局渐近稳定的;当R_01,我们得到系统存在两个正平衡点及无正平衡点的条件,且只有当医院的病床数小于阈值时,系统会经历后向分支.因此,可根据实际情况使医院病床的投入量不低于阈值条件,不仅有利于疾病的控制而且不会出现医疗资源过剩的现象.     

A task and resource scheduling system for automated planning

Planning is done at both the strategic and tactical levels. This paper classifies some previous planning techniques into these different levels, and details of some of their problems. A planning technique known as heuristic task scheduling is then presented along with a planner architecture that integrates task-scheduling with more traditional techniques to form a system that bridges the strategic/tactical division