A systematic approach for the location of hand sanitizer dispensers in hospitals

Abstract

Compliance with hand hygiene practices is directly affected by the accessibility and availability of cleaning agents. Nevertheless, the decision of where to locate these dispensers is often not explicitly or fully addressed in the literature. In this paper, we study the problem of selecting the locations to install alcohol-based hand sanitizer dispensers throughout a hospital unit as an indirect approach to maximize compliance with hand hygiene practices. We investigate the relevant criteria in selecting dispenser locations that promote hand hygiene compliance, propose metrics for the evaluation of various location configurations, and formulate a dispenser location optimization model that systematically incorporates such criteria. A complete methodology to collect data and obtain the model parameters is described. We illustrate the proposed approach using data from a general care unit at a collaborating hospital. A cost analysis was performed to study the trade-offs between usability and cost. The proposed methodology can help in evaluating the current location configuration, determining the need for change, and establishing the best possible configuration. It can be adapted to incorporate alternative metrics, tailored to different institutions and updated as needed with new internal policies or safety regulation.

Appendices

Appendix 1: Determining the weights of usability characteristics

From the human factors engineering and hand hygiene compliance literature perspectives, the usability characteristics used in this manuscript are equally important. Thus, we used equal weights. Nevertheless, different healthcare settings with different workflows may have specific preferences as to which of these characteristics have prevalence in the decision. The weights allow for incorporating these preferences.

To determine the appropriate weights that a specific decision-maker should use, we suggest rating each usability characteristic according to a meaningful rating scale. Table 7 shows a suggested scale.

Table 7 Suggested rating scale to determine weights for usability characteristics

The weight of each characteristic k ∈ K can be determined by:

$$ \omega_{k} = \frac{Rating_{k}} {\sum_{k \in K}{Rating_{k}}} \qquad\qquad\qquad \forall k \in K $$

(13)

Appendix 2: Reconfiguration cost formulation

The cost associated with changing a dispenser configuration depends on the following parameters:

• ψ _ℓ ∈ {0, 1} indicates if there is a dispenser currently installed at location ℓ

• θ ₁ cost of removing an existing dispenser from its location

• θ ₂ cost of installing a new dispenser in a specific location

• θ ₃ difference in cost between installing a newly purchased and an old dispenser in a specific location

We define the cost function Θ in terms of the decision variable y _ℓ defined in the dispenser location model (Section 3.2):

$$ \Theta = \sum\limits_{\ell \in L}[\theta_{1}\psi_{\ell}(1-y_{\ell})+\theta_{2}(1-\psi_{\ell})y_{\ell}]-\theta_3r $$

(14)

The cost function includes the cost of removing an existing dispenser from its original location, the cost of installing a new dispenser and the savings from reusing existing dispensers. r is an auxiliary integer decision variable that denotes the number of existing dispensers that should be relocated in order to obtain the configuration determined by y _ℓ , ∀ ℓ ∈ L. r is the minimum value between the number of existing dispensers not indicated by y _ℓ , ℓ ∈ L and the number of locations without existing dispensers indicated by y _ℓ , ℓ ∈ L:

$$ r = \min{\left\{\sum\limits_{\ell \in L}{\psi_{\ell}(1-y_{\ell})}, \sum\limits_{\ell \in L}{(1-\psi_{\ell})y_{\ell}} \right\}} $$

(15)

The cost-usability analysis is done by solving the following bi-criteria model:

$$ \max{\left\{\Gamma, -\Theta\right\}} $$

(16)

s.t.

Equations (4)–(9)

Equation (15)

To approximate the set of Pareto optimal solutions, the 𝜖 -constraint method [15] was used. The cost function, Λ, was transformed into a budget constraint with an upper bound of 𝜖. Then, a family of usability maximization problems was solved with 𝜖 changing between $0 and the cost of implementing the configuration with optimal usability ($1,569). The resulting Pareto optimal solutions (and weak Pareto optimal solutions) are shown in Fig. 4.