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The aim of this constructive study was to develop model-based principles to provide guidance to managers and policy makers when making decisions about team size and composition in the context of home healthcare. Six model-based principles were developed based on extensive data analysis and in close interaction with practice. In particular, the principles involve insights in capacity planning, travel time, available effective capacity, contract types, and team manageability. The principles are formalized in terms of elementary mathematical models that capture the essence of decision-making. Numerical results based on real-life scenarios reveal that efficiency improves with team size, albeit more prominently for smaller teams due to diminishing returns. Moreover, it is demonstrated that the complexity of managing and coordinating a team becomes increasingly more difficult as team size grows. An estimate for travel time is provided given the size and territory of a team, as well as an upper bound for the fraction of full-time contracts, if split shifts are to be avoided. Overall, it can be concluded that an ideally sized team should serve (at least) around a few hundreds care hours per week. [ABSTRACT FROM AUTHOR]

Let HT ht denote the virtual queue length at the start of period I n i , where a period typically represents a single day. Hence, HT ht should be able to capture the impact of the (non-work-conserving) allocation policy. Assume for the moment that HT ht is i.i.d. and HT ht . [Extracted from the article]

The design of container terminal operations is complex because multiple factors affect operational performance. These factors include numerous choices for handling technology, terminal topology, and design parameters and stochastic interactions between the quayside, stackside, and vehicle transport processes. In this research, we propose new integrated queuing network models for rapid design evaluation of container terminals with automated lift vehicles and automated guided vehicles. These models offer the flexibility to analyze alternate design variations and develop insights. For instance, the effect of different vehicle dwell point policies and efficient terminal layouts are analyzed. We show the relation among the dwell point–dependent waiting times and also show their asymptotic equivalence at heavy traffic conditions. These models form the building blocks for design and analysis of large-scale terminal operations. We test the model efficacy using detailed simulation experiments and real-terminal validation. The design of container terminal operations is complex because multiple factors affect operational performance. These factors include numerous choices for handling technology, terminal topology, and design parameters and stochastic interactions between the quayside, stackside, and vehicle transport processes. In this research, we propose new integrated queuing network models for rapid design evaluation of container terminals with automated lift vehicles and automated guided vehicles. These models offer the flexibility to analyze alternate design variations and develop insights. For instance, the effect of different vehicle dwell point policies is analyzed using state-dependent queues, whereas the efficient terminal layout is determined using variation in the service time expressions at the stations. We show the relation among the dwell point–dependent waiting times and also show their asymptotic equivalence at heavy traffic conditions. These models form the building blocks for design and analysis of large-scale terminal operations. We test the model efficacy using detailed in-house simulation experiments and real-terminal validation by partnering with an external party. [ABSTRACT FROM AUTHOR]

Nursing homes are challenged to develop staffing strategies that enable them to efficiently meet the healthcare demand of their residents. In this study, we investigate how demand for care and support fluctuates over time and during the course of a day, using demand data from three independent nursing home departments of a single Dutch nursing home. This demand data is used as input for an optimization model that provides optimal staffing patterns across the day. For the optimization we use a Lindley-type equation and techniques from stochastic optimization to formulate a Mixed-Integer Linear Programming (MILP) model. The impact of both the current and proposed staffing patterns, in terms of waiting time and service level, are investigated. The results show substantial improvements for all three departments both in terms of average waiting time as well as in 15 minutes service level. Especially waiting during rush hours is significantly reduced, whereas there is only a slight increase in waiting time during non-rush hours. [ABSTRACT FROM AUTHOR]

Nursing homes face ever-tightening healthcare budgets and are searching for ways to increase the efficiency of their healthcare processes without losing sight of the needs of their residents. Optimizing the allocation of care workers plays a key role in this search as care workers are responsible for the daily care of the residents and account for a significant proportion of the total labor expenses. In practice, the lack of reliable data makes it difficult for nursing home managers to make informed staffing decisions. The focus of this study lies on the 'care on demand' process in a Belgian nursing home. Based on the analysis of real-life 'call button' data, a queueing model is presented which can be used by nursing home managers to determine the number of care workers required to meet a specific service level. Based on numerical experiments an 80/10 service level is proposed for this nursing home, meaning that at least 80 percent of the clients should receive care within 10 minutes after a call button request. To the best of our knowledge, this is the first attempt to develop a quantitative model for the 'care on demand' process in a nursing home. [ABSTRACT FROM AUTHOR]

This paper considers a population process on a dynamically evolving graph, which can be alternatively interpreted as a queueing network. The queues are of infinite-server type, entailing that at each node all customers present are served in parallel. The links that connect the queues have the special feature that they are unreliable, in the sense that their status alternates between ‘up’ and ‘down’. If a link between two nodes is down, with a fixed probability each of the clients attempting to use that link is lost; otherwise the client remains at the origin node and reattempts using the link (and jumps to the destination node when it finds the link restored). For these networks we present the following results: (a) a system of coupled partial differential equations that describes the joint probability generating function corresponding to the queues’ time-dependent behavior (and a system of ordinary differential equations for its stationary counterpart), (b) an algorithm to evaluate the (time-dependent and stationary) moments, and procedures to compute user-perceived performance measures which facilitate the quantification of the impact of the links’ outages, (c) a diffusion limit for the joint queue length process. We include explicit results for a series relevant special cases, such as tandem networks and symmetric fully connected networks. [ABSTRACT FROM AUTHOR]

Flexibility in the usage of clinical beds is considered to be a key element to efficiently organize critical capacity. However, full flexibility can have some major drawbacks as large systems are more difficult to manage, lack effective care delivery due to absence of focus and require multi-skilled medical teams. In this paper, we identify practical guidelines on how beds should be allocated to provide both flexibility and utilize specialization. Specifically, small scale systems can often benefit from full flexibility. Threshold type of control is then effective to prioritize patient types and to cope with patients having diverse lengths of stay. For large scale systems, we assert that a little flexibility is generally sufficient to take advantage of most of the economies of scale. Bed reservation (earmarking) or, equivalently, organizing a shared ward of overflow, then performs well. The theoretical models and guidelines are illustrated with numerical examples. Moreover, we address a key question stemming from practice: how to distribute a fixed number of hospital beds over the different units? [ABSTRACT FROM AUTHOR]

Variability in admissions and lengths of stay inherently leads to variability in bed occupancy. The aim of this paper is to analyse the impact of these sources of variability on the required amount of capacity and to determine admission quota for scheduled admissions to regulate the occupancy pattern. For the impact of variability on the required number of beds, we use a heavy-traffic limit theorem for the G/G/∞ queue yielding an intuitively appealing approximation in case the arrival process is not Poisson. Also, given a structural weekly admission pattern, we apply a time-dependent analysis to determine the mean offered load per day. This time-dependent analysis is combined with a Quadratic Programming model to determine the optimal number of elective admissions per day, such that an average desired daily occupancy is achieved. From the mathematical results, practical scenarios and guidelines are derived that can be used by hospital managers and support the method of quota scheduling. In practice, the results can be implemented by providing admission quota prescribing the target number of admissions for each patient group. [ABSTRACT FROM AUTHOR]