Arcadia deliveries¶

Problem definition¶

Arcadia Deliveries wants to determine the best location for their warehouses to supply the different retail regions of their best customer. There are 5 possible warehouse locations and 10 different retail regions. The following table shows the capacity and operation costs of the possible warehouse locations:

Data	warehouse 1	warehouse 2	warehouse 3	warehouse 4	warehouse 5
capacity	1000	2000	3000	4000	5000
Operation costs	50	60	70	80	90

The following table contains the demand at each region:

Region	Demand
Region 1	100
Region 2	200
Region 3	300
Region 4	400
Region 5	500
Region 6	600
Region 7	700
Region 8	800
Region 9	900
Region 10	1000

And the following cost contains the transportation costs from warehouses to regions:

Region	Warehouse 1	Warehouse 2	Warehouse 3	Warehouse 4	Warehouse 5
1	42	36	58	47	32
2	73	56	73	78	38
3	38	41	80	88	69
4	59	70	77	94	51
5	51	92	79	88	80
6	38	98	57	64	96
7	86	53	86	58	44
8	48	92	40	100	71
9	62	60	30	31	63
10	43	43	48	63	55

Find the optimal location for warehouses and determine which warehouses are going to deliver to every retail location, knowing that the customer requires that a region is supplied from only one source

[ ]:

Region	Warehouse 1	Warehouse 2	Warehouse 3	Warehouse 4	Warehouse 5
1	42	36	58	47	32
2	73	56	73	78	38
3	38	41	80	88	69
4	59	70	77	94	51
5	51	92	79	88	80
6	38	98	57	64	96
7	86	53	86	58	44
8	48	92	40	100	71
9	62	60	30	31	63
10	43	43	48	63	55

Region	Warehouse 1	Warehouse 2	Warehouse 3	Warehouse 4	Warehouse 5
1	42	36	58	47	32
2	73	56	73	78	38
3	38	41	80	88	69
4	59	70	77	94	51
5	51	92	79	88	80
6	38	98	57	64	96
7	86	53	86	58	44
8	48	92	40	100	71
9	62	60	30	31	63
10	43	43	48	63	55

Region	Warehouse 1	Warehouse 2	Warehouse 3	Warehouse 4	Warehouse 5
1	42	36	58	47	32
2	73	56	73	78	38
3	38	41	80	88	69
4	59	70	77	94	51
5	51	92	79	88	80
6	38	98	57	64	96
7	86	53	86	58	44
8	48	92	40	100	71
9	62	60	30	31	63
10	43	43	48	63	55