Question

Ekin Shoes is coordinating the shipments that happen across its supply chain and determining where to build new distribution centers. The chain starts with shoe factories outside of the United States. The shoes are then put on ships for transfer to one the US ports. From the ports the shoes are shipped to one regional distribution center. The distribution centers then disburse the shoes to smaller warehouses for distribution to the retailers. Ekin has determined that the factories, ports and warehouses will remain the same for the next year, but the locations of the distribution centers will be newly decided by choosing between five possible locations. The five locations have different lease amounts for next month.

Shoe Factories	Ports	Possible Distribution Center Locations	Warehouses
Brazil	Los Angeles	Atlanta	Chattanooga
Argentina	San Diego	Las Vegas	Denver
China	Baltimore	St. Louis	Minneapolis
Mexico	New Orleans	Indianapolis	Seattle
Ukraine		Philadelphia	Boston
			Dallas

The file “Ekin Shoes” contains the costs breakdowns for producing the shoes at the factories and transferring them across each part of the supply chain. The transfer costs are given in $1000s per container. The distribution center lease costs are in $1000s. The demands at each warehouse and the capacities of all other facilities are also given. Find the minimum total cost solution for transporting the shoes from factories to warehouses.

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Production and transfer costs for shoe factories and ports per intermodal container ($1000s)
	Los Angeles	San Diego	Baltimore	New Orleans		Capacity
Brazil	$          23.00	$    21.00	$         15.00	$          16.00		170
Argentina	$          24.00	$    25.00	$         19.00	$          19.00		570
China	$          19.00	$    21.00	$         27.00	$          29.00		410
Mexico	$          27.00	$    24.00	$         11.00	$            5.00		480
Ukraine	$          32.00	$    32.00	$           9.00	$          13.00		250
Transfer costs for ports and DCs per intermodal container ($1000s)
	Atlanta	Las Vegas	St. Louis	Indianapolis	Philadelphia		Capacity
Los Angeles	$          10.00	$      6.00	$           7.50	$            9.00	$         12.00		500
San Diego	$          11.00	$      5.00	$           8.50	$          10.00	$         11.00		500
Baltimore	$            8.00	$    13.00	$         10.00	$            7.00	$           3.00		500
New Orleans	$            4.00	$      9.00	$           6.60	$            5.00	$           8.00		700
Transfer costs for DCs and warehouses per intermodal container ($1000s)
	Chattanooga	Denver	Minneapolis	Seattle	Boston	Dallas		Capacity	Lease Cost ($1000s)
Atlanta	$            1.50	$      5.60	$           5.80	$            8.70	$           7.90	$    4.30		1000	$                 4,413.00
Las Vegas	$            4.80	$      2.20	$           4.00	$            4.30	$         10.10	$    6.50		1000	$                 6,430.00
St. Louis	$            2.40	$      2.50	$           2.70	$            7.70	$           8.20	$    3.90		1000	$                 4,808.00
Indianapolis	$            2.20	$      5.00	$           3.10	$          10.30	$           6.30	$    4.70		1000	$                 5,388.00
Philadelphia	$            4.60	$      9.60	$           7.00	$          12.90	$           1.40	$    5.30		1000	$                 4,881.00
Demand	225	195	640	310	185	290

Answer 1

Formulation in Excel

Final Result

From/ To	L' Angeles	San Diego	Baltimore	N'Orleans	Totals	Capacity		$26,475
Brazil	0	0	170	0	170	170		$11,586
Argentina	90	145	80	220	535	570		$17,746
China	410	0	0	0	410	410	Total Cost	$55,807
Mexico	0	0	0	480	480	480
Ukraine	0	0	250	0	250	250
Total IN	500	145	500	700
Total OUT	500	145	500	700
From/ To	Atlanta	Las Vegas	St. Louis	In'polis	Phil'hia	Totals	Capacity
L' Angeles	0	0	500	0	0	500	500
San Diego	0	0	145	0	0	145	500
Baltimore	0	0	0	0	500	500	500
N'Orleans	0	0	355	0	345	700	700
Totals IN	0	0	1000	0	845
Totals OUT	0	0	1000	0	845
From/ To	Chat'oga	Denver	Min'polis	Seattle	Boston	Dallas	Select (Yi)	Totals (Xi)
Atlanta	0	0	0	0	0	0	0	0
Las Vegas	0	0	0	0	0	0	0	0
St. Louis	0	195	495	310	0	0	1	1000
In'polis	0	0	0	0	0	0	0	0
Phil'hia	225	0	145	0	185	290	1	845
Totals	225	195	640	310	185	290
Demand	225	195	640	310	185	290

As per the solution, the DC's at St. Louis and Philadelphia should be selected and operated only.