Last update: 28 September 2018

Problem description

Appointment scheduling systems represent a method to manage patient's waiting lists effectively. This work advances an innovative quantitative approach, based on an optimization model, to manage outpatient Day Service operations. 

Our work acknowledges online scheduling in a multidisciplinary setting, where a case manager, i.e. a physician who coordinates and shares the responsibility for patient care with other specialists. We focus on indirect waiting, and we see the amount of time a patient waits to be admitted as a factor affecting utilization of healthcare services.

We advance our earlier work [ielpa-guido-conforti_HCSE2017], that models HDS with the aim to explore the declarative approach of ASP, to represent knowledge related to the problem and to solve it.

Patients - Patients waiting to be scheduled for clinical test or exams.

Prescriptions - Each patient is characterised by a priority, according to severity of the disease, a number of days the patient has already waited, since a baseline visit, a list of prescriptions of clinical tests or exams. Priorities and prescriptions are determined by a case manager, during the baseline visit. 

Clinical Services - Clinical tests or exams listed in a Package specified for the diagnosis (or therapy) of a disease. For the sake of this work the Ankylosing Spondylitis Day Service Standard Package wase taken as reference.

Time Slot - Time slot is the unit time for patient's clinical service execution. Time slot lasts 1 hour, and it is identified by working hour, working day, week in a scheduling horizon of one working month. The working month consists of 160 time slots, according to a working calendar, specified in input.

Availability Calendar - The calendar specifies which clinical services are available at a given time slot in the scheduling period. The calendar is due to hospital resource management and policies. Some slots may result always unavailable for service maintenance or hospital organization reasons (e.g. no Hospital Day Service is available in the weekends).

Patient  Centered requirements - A number of soft requirements helps to keep the number of patient accesses to the hospital as the smaller as possible. We try to group the services, prescribed to a patient, by the same day, whenever this is not possible, for some reason, we try to group the exams by the same week. The advantage of this requirement is twofold: on the patient side, this contributes to shorten the waiting period, on the resource management side we try to maximize the utilization of hospital resources, according to service capacity.

All patients prescriptions are possibly scheduled in the scheduling month, possibly honouring patient requirements.

Patients are scheduled according to their priority.

If requirements are not met, and/or some exams cannot be scheduled (for a lack of service capacity), a penalty is given.

Clinical Services capacity - The number of clinical service prescriptions that can be scheduled in a day, or week or month. Some services have a very limited capacity, some others, such like blood counts, are highly available.

Priority Queues - Priorities devise priority queues, one for each priority level. Patient requirements are honoured according to their priority level.

Objective Function - Takes into account of the cost deriving from the violation of patient requirements. If admissible solutions are found, the optimal combinations are taken into account according to the value of the objective function.



Instances are available by following this link.

Results on the instances

The following table summarizes the main outcomes of the results download

Table Keys:P=Patient, D=distance between the beginning of the scheduling horizon and the schedule of the clinical service prescription,T=Prescribed clinical service (Test or Exam),W=week,D=day,H=hour of the scheduled clinical service, Weight=cost incurred to schedule the clinical service in the schedule slot (W,D,H), according to patient priority and requirements. A dash symbol in slot cells ('-', '-', '-') means that the clinical service was not scheduled.

Table Sorting: Results are sorted by 












Publication (under review)

Scheduling Outpatient Day Service Operations for Rheumatology Diseases. Giuseppe Ielpa, Rosita Guido, and Domenico Conforti.