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| : unit purchasing price of product p given by supplier k to hub distributor j at period t |
| : transaction costs of providing product p via supplier k to hub distributor j at period t |
| : unit transportation price of product p from supplier k to hub distributor j at period t |
| : unit transportation price of product p from hub distributor j to nonhub distributor h at period t |
| : unit transportation price of product p from nonhub distributer h to node distributor n at period t |
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| β: rate of discount for the transference of products from hub distributors to nonhub distributors |
| : binary parameter (equal to one if product p can be supplied by supplier k at period t; otherwise, zero) |
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| : percentage of returned product p to hub distributor j at period t |
| : percentage of returned product p to nonhub distributor h at period t |
| : percentage of returned product p to node distributor n at period t |
| : percentage of late delivered product p by hub distributor j at period t |
| : percentage of late delivered product p by nonhub distributor h at period t |
| : percentage of late delivered product p by node distributor n at period t |
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| : distance from hub distributor j to nonhub distributor h |
| : distance from nonhub distributor h to node distributor n |
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| : binary parameter (equal to one if the trade from supplier k to hub distributor j at period t is set; otherwise, zero) |
| : binary parameter (equal to one if the trade from hub distributor j to nonhub distributor h at period t is set; otherwise, zero) |
| : binary parameter (equal to one if the trade from nonhub distributor h to node distributor n at period t is set; otherwise, zero) |
| : binary parameter (equal to one if the trade from node distributor n to customer i at period t is set; otherwise, zero) |
| : binary parameter (equal to one if the hub distributor j is established; otherwise, zero) |
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| optimal order of product p from supplier k to hub distributor j at period t |
| optimal order of product p from hub distributor j to nonhub distributor h at period t |
| optimal order of product p from nonhub distributor h to node distributor n at period t |
| optimal order of product p from node distributor n to customer i at period t |
| : binary parameter (equal to one if the nonhub distributor h is established; otherwise, zero) |
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