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In a target region, several Community Elderly Care Centers (CECCs) are going to be built for the

needs of the elderly people. Part of elderly require daytime care (DC) services, i.e., they have to

travel from the community he/she lived to the allocated CECC, and the rest elderly with limited

mobility have to stay at home waiting for caregivers from the allocated CECC providing home care

(HC) services. Let M = {1, 2, . . ., m} be the set of candidate locations, which can be selected to

build CECCs. The number of CECCs is limited as P. Let N = {1, 2, ... , n} be the set of communities

in which the elderly are distributed. There are two types of CECC, the first type of CECCs only

provide DC services, while the latter can provide both DC and HC services. All the CECCs are same

in DC service capacity Q

1

, and all the second type of CECCs have the same service capacity Q

2

in

terms of HC service. For t-type of CECC, the corresponding construction costs is C

k

. Let D

ij

be the

distance between two nodes (community or CECC location) i and j. The problem aims to decide the

location of different types of CECC and the allocation relation between elderly in each community

and the CECC, and the problem aims to minimize the total cost involving total constructed costs of

CECCs and total travel cost (i.e., total travel cost of elderly requiring DC services and doctors

providing HC services during the life cycle of the CECC).

The assumptions of this problem are as follows:

(1) The elderly in each community can only be allocated to (DC services) or served by (HC services)

one CECC;

(2) HC caregiver serves HC demands of one community at a time, and then returns to the CECC;

(3) The distance between any two CECCs must exceed a threshold d to avoid the selecting sites too

close;

(4) There is a maximum accessible distance L

1

and L

2

for DC and HC services, respectively. That

is to say, the elderly cannot be allocated to the CECC whose distance to the community is larger

than L

1

, and the maximum travel distance for HC caregivers is L

2

. Note that L

1

<L

2

since the

mobility range of the HC caregiver is larger than that of elderly people.

(5) Elderly in the same community cannot be allocated to different CECCs for DC services to avoid

dissatisfaction of elderly.

(6) HC demands in the same community can be served by caregivers from different CECCs.

(7) The travel distance equals the corresponding travel cost.

2

3

4

6

5

1

7

C

D

B

Candidate location

Selected location for

type 1 CECC

The travel route of HC

caregivers

The travel route of elderly

requiring outpatient services

8

A

Selected location for

type 2 CECC

The community without

HC demands

The community existing

HC demands

Figure 1 An example of CECC location problem

Set:

M: set of candidate CECC locations.

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