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| | Notations | Definitions |
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| Sets | STj | Set of stages of production j є {1, 2, …, N} |
| I | Set of plants indexed by i є {1, 2, …, n} |
| SUCCi | Set of production plants that are direct successors of the plant i, i є {2, …, n} |
| P | Set of products indexed by p є {1, 2, …, P} |
| T | Set of periods indexed by t є {1, 2, …, T} |
| M | Set of transportation modes m є M = {m = 1: ship, m = 2: airplane} |
| S | Scenario set s є {1, 2, …, S} |
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| Stochastic parameters | | Occurrence probability of the scenario s where |
| Random replenishment order of the customer k for the product p in the period t over the scenario s |
| Uncertain regular production capacity of the plant i in the period t under the scenario s |
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| Deterministic parameters | | Deterministic demand of the customer k for the product p in the period t |
| Unit regular production cost of the product p by the plant i |
| Unit overtime production cost of the product p by the plant i |
| Unit shipping cost of the product p from the plant i to the plant i′, i′ є SUCCi |
| Unit distribution cost of the product p from the plant i, i є Sj=N, to the customer k using the transportation mode m |
| Unit backorder cost of the product p in supplying the demand of the customer k |
| Unit inventory-holding cost of the product p in the plant i |
| Maximum storage capacity of the plant i in the period t |
| Distribution capacity of the transportation mode m in the period t |
| Shipping capacity between the plant i and its successor i′ in the period t |
| Overtime production capacity of the plant i in the period t |
| β | Maximum fraction of backorder variation allowed in the period t, β є [0…1] |
| Production lead time of the product p in the plant i |
| Distribution lead time using the transportation mode m |
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| First-stage decision variables | | Quantity of the product p produced by the plant i in regular time period t ≤ t1 |
| Quantity of the product p produced by the plant i in overtime period t ≤ t1 |
| Number of product units p shipped from the plant i to the plant i′ in the period t ≤ t1, i′ є SUCCi |
| Amount of products p received by the plant i in the period t ≤ t1 |
| Inventory level of the end product p at the plant i at the end of the period t ≤ t1 |
| Inventory level of the semifinished product p at the plant i at the end of the period t ≤ t1 |
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| Second-stage decision variables | | Quantity of the product p produced by the plant i in regular time period t > t1 under the scenario s |
| Quantity of the product p produced by the plant i in overtime period t > t1 |
| Number of product units p shipped from the plant i to the plant i′ in the period t > t1 under the scenario s, i′ є SUCCi |
| Amount of products p received by the plant i in the period t > t1 under the scenario s |
| Inventory level of the end product p at the plant i at the end of the period t > t1 under the scenario s |
| Inventory level of the semifinished product p at the plant i at the end of the period t > t1 under the scenario s |
| Amount of finished products p transported from i є STj=N to the customer k in the period t using the transportation mode m under the scenario s |
| Backorder level of the product p incurred by the customer k at the end of the period t under the scenario s |
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