A multiple-drawer medication layout problem in automated dispensing cabinets

Abstract

In this paper we investigate the problem of locating medications in automated dispensing cabinets (ADCs) to minimize human selection errors. We formulate the multiple-drawer medication layout problem and show that the problem can be formulated as a quadratic assignment problem. As a way to evaluate various medication layouts, we develop a similarity rating for medication pairs. To solve industry-sized problem instances, we develop a heuristic approach. We use hospital ADC transaction data to conduct a computational experiment to test the performance of our developed heuristics, to demonstrate how our approach can aid in ADC design trade-offs, and to illustrate the potential improvements that can be made when applying an analytical process to the multiple-drawer medication layout problem. Finally, we present conclusions and future research directions.

Appendix: A drawer assignment model formulation

We provide a non-linear integer programming formulation that uses the notation from Section 3 for the assignment of medications to drawers. To minimize the potential of a nurse having access to a drawer of medications that are similar, medications with high similarity ratings should be located in different drawers.

Drawer assignment model:

$$ \min \displaystyle\sum\limits_{d}\displaystyle\sum\limits_{i}\displaystyle\sum\limits_{j>i} \quad s_{ij} \; x_{id} \; x_{jd} $$

(13)

$$s.t. \displaystyle\sum\limits_{i} x_{id} \leq |C| \quad\forall d \in D, $$

(14)

$$ \displaystyle\sum\limits_{d} x_{id} = 1 \quad\forall i \in M $$

(15)

$$ x_{id} \in \{ 0,1 \} \quad \forall i \in M, \quad \forall d \in D $$

(16)

The objective, Eq. 13, is to minimize the similarity ratings of medications that are assigned to the same drawer, which has the impact of minimizing the likelihood of a similar medication being assigned to the same drawer. In Eq. 14, an upper bound on the number of medications to assign to each drawer is the total number of compartments in that drawer. Each medication must be assigned to exactly one drawer as enforced in Eq. 15. Finally, the x _id variables are restricted to be binary in Eq. 16.