Location-distribution of cruise ship supply logistics distribution centre considering time window

Figures & data

Figure 1. Typical turnaround day at a port.

Figure 2. Network diagram of cruise ship supply distribution.

Table 1. Symbols and definitions of various parameters and variables.

Var	Type	Definition
$I$	Set	Ship supplier i
$J$	Set	Candidate logistics distribution center j
$\text{K}$	Set	Cruise port k
${\text{s}}_i$	Parameter	Ship supplier supply capacity
$d_k$	Parameter	cruise ship supplies demand
$c_y$	Parameter	Distribution cost of ship supplier i to candidate logistics distribution center j
$l_{jk}$	Parameter	Distribution cost of candidate logistics distribution center j to cruise port k
$x_{ij}$	Variable	Distribution quantity from ship supplier i to candidate logistics distribution center j
$y_{jk}$	Variable	Distribution quantity of candidate logistics distribution center j to cruise port k
$h_{jk}$	Parameter	Distribution time between candidate logistics distribution center j and cruise port k
$f_j$	Parameter	Monthly rental fee of candidate logistics distribution center j
$m_j$	Parameter	Monthly management expenses of candidate logistics distribution center j
$v_j$	Parameter	Turnover costs of handling goods in logistics distribution center j
$u_j$	Parameter	Capacity constraint of candidate logistics distribution center j
$T_1$	Parameter	The earliest time of delivery to cruise
$T_2$	Parameter	The latest time of delivery to cruise
$w_1$	Parameter	Penalty coefficient
$w_2$	Parameter	Penalty coefficient
$z_j$	Variable	0-1 variable, choosing logistics distribution center j, then it is 1; Otherwise 0

Figure 3. Flow chart of Benders decomposition algorithm.

Table 2. Unit delivery freight of ship suppliers to candidate logistics distribution centre (Unit: yuan).

	D1	D2	D3	D4	D5
S1	48	50	48	48	50
S2	50	55	55	50	48
S3	50	50	55	55	48
S4	55	50	50	46	55

Table 3. Unit distribution freight/time from candidate logistics distribution centres to cruise ports (Unit: yuan per Hour).

	K1	K2	K3
D1	32/10	35/8	35/8
D2	38/8	38/6	38/8
D3	35/8	42/8	38/8
D4	35/8	35/8	38/10
D5	36/8	35/15	38/10

Table 4. Data of candidate logistics distribution centres.

Candidate	D1	D2	D3	D4	D5
Monthly capacity (tons)	3000	3000	3000	3500	3500
Monthly rental fee (yuan)	300,000	257,000	236,000	248,000	278,000
Monthly management fee (yuan)	145,000	118,000	110,000	150,000	148,000
Unit turnover cost (yuan/ton)	28	26	28	26	26

Table 5. Supply ability of ship suppliers (Unit: tons).

Ship supplier	S1	S2	S3	S4
Supply ability	2000	1800	2200	2800

Table 6. Cruise ships demand (Unit: tons).

Cruise port of call	K1	K2	K3
Monthly demand	2100	1800	1500

Table 7. Distribution quantities of candidate logistics distribution centres to cruise home ports (Unit:tons).

	K1	K2	K3
D1	1200	0	1800
D2	0	0	0
D3	0	0	0
D4	300	2100	0
D5	0	0	0

Table 8. Values of candidate logistics distribution centres.

Candidate	D1	D2	D3	D4	D5
Value	1	0	0	1	0

Table 9. Distribution quantity from ship suppliers to logistics distribution centres (Unit: tons).

	D1	D2
S1	2000	0
S2	1000	0
S3	0	0
S4	0	2400

Table 10. Results of 10 APSO independent calculations.

Number	1	2	3	4	5	6	7	8	9	10
Results (yuan)	267,585	270,022	275,209	266,900	277,931	268,309	279,671	272,857	272,867	274,198
Time (s)	4.054	4.160	5.341	5.998	6.206	6.609	7.554	7.678	8.794	9.311