Facility Location Problem Adapted to a Medication Dispensing Systems Location Problem in a Network of Hospitals

Facility Location Problem adapted to a Medication Dispensing Systems Location Problem in a Network of Hospitals

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Abstract

        This paper is concerned with adapting the facility location problem to a location problem of automated dispensing systems in a network of hospitals. The problem’s objective is to determine the locations of the unit dose production equipment and the dispensation machines while minimizing the costs and making sure the demand from each hospital in medicine is met. The classic steps of the facility location problem Plant – Distribution Centre – Customer have been modified to Over-conditioning– Dispensation Production – Patients. The model has also been extended by introducing constraints about utilization rates, stock levels and to take into consideration the machines characteristics – production capacity, storage capacity and price -.

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Introduction

The rise of automation in hospitalization environment is to provide gain in efficiency and accuracy but also represents important challenges in terms of adaptations, investments and optimization.  The technology of automated dispensing systems is an essential driver of increase quality in the dispensation of drugs in hospitals.

According to the ENEIS in 2009, there are between 60 and 130 000 Serious Adverse Events (SAE) related to drugs per year in France and between 15 and 60 000 could be prevented. The automated dispensing systems have for main objective to decrease the number of SAE related to medication. In the five-step process of drug use Prescription – Dispensation – Administration – Management of Endowment – Therapeutical Monitoring, those machines would be operating the dispensations preparations. In other words, it is the action of gathering the correct medicine to match the doctors’ prescriptions. Currently, two kinds of automated dispensing systems are available in the French marked, reconditioning machines and over-conditioning machines. The first one is taking the drugs out of its blister – drugs are never distributed loose in France compared to the USA for instance – and the dispensing system is then conditioning the drug in an individual blister. On the other hand, the over-conditioning system is keeping the original blister but cutting the medicine strip in order to create individual doses and to create a unit dose packaging with a unique ID number.

This paper is the result of a collaboration with the territorial grouping of Hospital; they are planning to purchase dispensing systems and are currently working on determining the optimal locations of such robots. They have pre-determined the scope of the project by focusing on over-conditioning systems of oral dry forms– excluding therefore all liquids or unusual shaped medications –. The reasons of those choices are practical, economical and pharmaceutical; those decisions will not be discussed in further details in this paper.

The process of the over-conditioning dispensing systems can be divided into three steps: over-conditioning, storage and dispensing (see below).

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  Those are exactly the three core functionalities of the over-conditioning systems. However, the options can highly vary depending on the manufacturers and the model considered. For instance, one model proposes the three functionalities integrated contrary to another that can be limited to one functionality – each step could therefore be in theory located in a different hospital -. For each model, the following characteristics have been determined as influential in their purchase or not.

The Unit Dose Production Rate is the number of doses a machine can cut from its original blister and the number of individual doses that can be produced per hour.

The dispensing rate is the number of doses that can be prepared per hour to build a given prescription. On average, a prescription is made of 10 individual doses.

Link with Facility Location Problem

The facility location problem is used particularly in Supply Chain Management to determine the locations of the production plants and the distribution centres depending on the locations of the suppliers, the customers’ locations and demands, the plants characteristics (costs, capacity etc.) as well as the logistics costs.

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In the case of the Dispensing System Location Problem, the Over-Conditioning machines replace the Plants, the Dispensing Systems are associated to the Distribution Centres while the Customers are the Patients. 

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Therefore, the optimization model used for the Facility Location Problem can be adapted to this problem with the particularity that one location –i.e. one hospital- can have over-conditioning systems, Dispensing systems and will always have patients. The problem must be seen as a flow of materials that is transformed and delivered to the patients. In the scope of this project, we do not consider locations that are not hospitals; the machines will always be located in the pharmacies of a hospital part of the network.

Material and Methods

Equipment data

All the data relative to the machinery (price, production rates, storage capacity, floor space etc.) were directly received from the manufacturers. Because of the innovative aspect of such equipment - only a few hospitals in France use dispensing systems-, the accuracy of the data provided could not be confirmed nor tested in practice.

Logistics costs

The yearly transportation costs have been estimated using the weekly delivery frequency, which differs between each hospital depending on the services of each hospital – emergency services will require deliveries twice a day while EHPAD (long-term care) would only require weekly deliveries for instance – and using an estimate of the cost of the delivery between two locations. Those costs have been divided into three components.