Network Optimization Models Supply City Demand City Production and Transportation Cost per Thousand Units (Thousand $) Monthly Capacity (Thousand Units) K Monthly Fixed Cost (Thousand $) f AtlantaBostonChicagoDenverOmahaPortland Baltimore1,6754009851,6301,1602,800187,650 Cheyenne1,4601,9409701004951,200243,500 Salt Lake City 1,9252,4001,450500950800275,000 Memphis3801,3555431,0456652,321224,100 Wichita9221,6467005083111,797312,200 Monthly demand (thousand units) D j 108146711 TelecomOne & HighOptic Case
Allocating demand to production facilities =number of factory locations =number of markets or demand points =annual demand from market j =capacity of factory i =cost of producing and shipping one unit from factory i to market j x ij =quantity shipped from factory i to market j subject to Case1: TelecomOne & HighOptic are two independent companies.
5-4 生產設施的需求分配 市場由哪個工廠服務？ 工廠使用哪個供應來源？ x ij = 每年自工廠 i 至市場 j 之裝運數量 受限於：
Optimal demand allocation AtlantaBostonChicagoDenverOmahaPort land TelecomOneBaltimore082 Memphis10012 Wichita000 HighOpticSalt Lake0011 Cheyenne670 Case1: TelecomOne & HighOptic are two independent companies.
Capacitated Plant Location Model =quantity shipped from plant i to market j =1 if plant i is open, 0 otherwise subject to Decision variables Case2: TelecomOne & HighOptic are merged into one company TelecomOptic.
Capacitated Model With Single Sourcing Market supplied by only one factory Modify decision variables y i =1 if factory i is open, 0 otherwise x ij =1 if market j is supplied by factory i, 0 otherwise subject to
5-12 單一供應來源的最適工廠位址模型 y i = 1 如果工廠 設於 i 地，否則為 0 x ij = 1 如果市場 j 是由工廠 i 供貨， 否則為 0 受限於：
Model inputs m =number of markets or demand points n =number of potential factory locations l =number of suppliers t =number of potential warehouse locations D j =annual demand from customer j K i =potential capacity of factory at site i S h =supply capacity at supplier h W e =potential warehouse capacity at site e f i =fixed cost of locating a plant at site i f e =fixed cost of locating a warehouse at site e c hi =cost of shipping one unit from supply source h to factory i c ie =cost of producing and shipping one unit from factory i to warehouse e c ej =cost of shipping one unit from warehouse e to customer j
Locating Plants and Warehouses Simultaneously Y i =1 if factory is located at site i, 0 otherwise Y e =1 if warehouse is located at site e, 0 otherwise x ej =quantity shipped from warehouse e to market j x ie =quantity shipped from factory at site i to warehouse e x hi =quantity shipped from supplier h to factory at site i Decision variables Objective Function:
Locating Plants and Warehouses Simultaneously subject to Constraints:
Accounting for Taxes, Tariffs, and Customer Requirements A supply chain network should maximize profits after tariffs and taxes while meeting customer service requirements Modified objective and constraint
Making Network Design Decisions In Practice Do not underestimate the life span of facilities Do not gloss over the cultural implications Do not ignore quality-of-life issues Focus on tariffs and tax incentives when locating facilities
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