PSNRPTW_ts ing-inf

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Ingénierie

UNIVERSITÀ DEGLI STUDI DI TRIESTE
Dipartimento di Ingegneria e Architettura
Corso di Studi in Ingegneria Elettronica e Informatica
SOME CONSIDERATIONS ABOUT:
PSNRP-TW
Patient Satisfaction-Oriented Nurse Routing Problem with Time Window
A.A. 2019/2020

PROBLEMA
A
Nurse Routing Problem:
-per cosa viene usato?
-cosa significa?
Caratterizzazione:
-Patient Satisfaction-oriented
-Time Window
-Altre tipologie

TRATTAZIONE PROBLEMA
A
PERCHE' E' IMPORTANTE TRATTARE QUESTO TIPO DI PROBLEMI?
- ridimensionamento ospedali
- case di riposo
- qualità di vita
- supporto indiretto alle famiglie dei malati
- es. COVID-19:
-Lombardia vs Veneto
-centralizzazione vs Domicilializzazione

MODELLIZZAZIONE
A
VARIABILI IN GIOCO:
-M insieme dei pazienti
-F insieme degli infermieri
-K insieme dei tipi di servizio
-N insieme di ogni possibile servizio richiesto da ogni singolo paziente
-Time Window tempo entro il quale il servizio deve iniziare
-Pi profitto positivo assegnato a ogni servizio i∈N
-Ah ricompensa fornita a ciascun sottoinsieme Nh se TUTTI i nodi in Nh sono stati serviti
-Wi vale 1 se il nodo i∈ N è stato visitato
-Xij vale 1 se l' arco (i,j) è stato percorso
-Yh vale 1 se tutti i nodi in Nh sono visitati
-Zij indica il tempo di arrivo a j quando si arriva da i.

MASSIMIZZAZIONE E VINCOLI
A
Funzione obiettivo: max Σi∈N Pi Wi + Σh∈M Ah Yh
Vincoli:
-condizione di parità
-N° itinerari<=F
-no subtours e controllo delle tempistiche
-limite di tempo per arrivare al 1° nodo
-limiti sup e inf per arrivare ad un nodo qualsiasi
-obbligo di svolgere il servizio entro la finestra di tempo
-condizioni di non negatività

0
P1
P3
N+1
P2
P4
P5
Pn
P6
F1F1F1
F3F2
F4F1F1F1F1
F3F3F3
F3
F3
F3F3
F3
F3
N
1
N
2
N
1
N
4
N
3
N
2
N
1
N
1
6
5
4
3
2
7
13
12
11 10 9
8
1
17
16
15
14
RAPPRESENTAZIONE
A
RAPPRESENTAZIONERAPPRESENTAZIONERAPPRESENTAZIONERAPPRESENTAZIONE

METODO RISOLUTIVO
A
IKS vs GUROBI:
-euristiche
-Kernel Search
-Bucket
IPOTESI PER LA SIMULAZIONE:
-40 istanze
-superficie campione
-velocità media
-tipi di servizi richiesti
-Tmax

RISULTATI
A
fattore moltiplicativo di ricompensa è 0.5
numero di servizi possibili è 5
obj: valore della funzione obiettivo
sat% : percentuale di pazienti totalmente soddisfatti
M: 'insieme dei malati F: insieme delle infermiere Ɵ: numero di servizi da prestare alla seconda metà di pazienti.
obj
sat%

CONCLUSIONI
A
MIGLIORAMENTO SERVIZIO SANITARIO A DOMICILIO
PROPOSTE:
-DAGLI AUTORI:
-MULTIPERIDO
-CO2 EMESSA
-SKILLS INFERMIERE
-DA PARAMETRI A INCOGNITE
-DA ME:
-TEMPO TRA ARRIVO E SERVIZIO
-DIVISIONE INSIEME F
GRAZIE PER L' ATTENZIONE

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PSNRPTW_ts ing-inf

1. UNIVERSITÀ DEGLI STUDI DI TRIESTE Dipartimento di Ingegneria e Architettura Corso di Studi in Ingegneria Elettronica e Informatica SOME CONSIDERATIONS ABOUT: PSNRP-TW Patient Satisfaction-Oriented Nurse Routing Problem with Time Window A.A. 2019/2020

2. PROBLEMA A Nurse Routing Problem: -per cosa viene usato? -cosa significa? Caratterizzazione: -Patient Satisfaction-oriented -Time Window -Altre tipologie

3. TRATTAZIONE PROBLEMA A PERCHE' E' IMPORTANTE TRATTARE QUESTO TIPO DI PROBLEMI? - ridimensionamento ospedali - case di riposo - qualità di vita - supporto indiretto alle famiglie dei malati - es. COVID-19: -Lombardia vs Veneto -centralizzazione vs Domicilializzazione

4. MODELLIZZAZIONE A VARIABILI IN GIOCO: -M insieme dei pazienti -F insieme degli infermieri -K insieme dei tipi di servizio -N insieme di ogni possibile servizio richiesto da ogni singolo paziente -Time Window tempo entro il quale il servizio deve iniziare -Pi profitto positivo assegnato a ogni servizio i∈N -Ah ricompensa fornita a ciascun sottoinsieme Nh se TUTTI i nodi in Nh sono stati serviti -Wi vale 1 se il nodo i∈ N è stato visitato -Xij vale 1 se l' arco (i,j) è stato percorso -Yh vale 1 se tutti i nodi in Nh sono visitati -Zij indica il tempo di arrivo a j quando si arriva da i.

5. MASSIMIZZAZIONE E VINCOLI A Funzione obiettivo: max Σi∈N Pi Wi + Σh∈M Ah Yh Vincoli: -condizione di parità -N° itinerari<=F -no subtours e controllo delle tempistiche -limite di tempo per arrivare al 1° nodo -limiti sup e inf per arrivare ad un nodo qualsiasi -obbligo di svolgere il servizio entro la finestra di tempo -condizioni di non negatività

6. 0 P1 P3 N+1 P2 P4 P5 Pn P6 F1F1F1 F3F2 F4F1F1F1F1 F3F3F3 F3 F3 F3F3 F3 F3 N 1 N 2 N 1 N 4 N 3 N 2 N 1 N 1 6 5 4 3 2 7 13 12 11 10 9 8 1 17 16 15 14 RAPPRESENTAZIONE A RAPPRESENTAZIONERAPPRESENTAZIONERAPPRESENTAZIONERAPPRESENTAZIONE

7. METODO RISOLUTIVO A IKS vs GUROBI: -euristiche -Kernel Search -Bucket IPOTESI PER LA SIMULAZIONE: -40 istanze -superficie campione -velocità media -tipi di servizi richiesti -Tmax

8. RISULTATI A fattore moltiplicativo di ricompensa è 0.5 numero di servizi possibili è 5 obj: valore della funzione obiettivo sat% : percentuale di pazienti totalmente soddisfatti M: 'insieme dei malati F: insieme delle infermiere Ɵ: numero di servizi da prestare alla seconda metà di pazienti. obj sat%

9. CONCLUSIONI A MIGLIORAMENTO SERVIZIO SANITARIO A DOMICILIO PROPOSTE: -DAGLI AUTORI: -MULTIPERIDO -CO2 EMESSA -SKILLS INFERMIERE -DA PARAMETRI A INCOGNITE -DA ME: -TEMPO TRA ARRIVO E SERVIZIO -DIVISIONE INSIEME F GRAZIE PER L' ATTENZIONE

PSNRPTW_ts ing-inf

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PSNRPTW_ts ing-inf