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Consider a supply chain network for a product with n supplier, m manufacturer, and p warehouse nodes. The unit shipment costs from supplier i to plant j are represented by cij and plant j to warehouse k are represented by cjk. Assume that the product flow is from suppliers to plants to warehouses. In addition, the same part is sourced from all suppliers and there is a one to one relationship between the sourced part and the final product produced at the manufacturing plants.
Given the capacities at suppliers and plants, and demands at warehouses, formulate a mixed-integer programming model that minimizes the total cost in satisfying demand based on the following requirements:
(i) Assume that suppliers and plants are possible choice nodes with fixed costs fi and fj associated in selecting supplier i and plant j, respectively
(ii) Assume that the total supply is greater than total demand
(iii) The optimization model needs to minimize both transportation/transhipment and fixed costs in satisfying demand. Clearly define the decision variables and express the objective function and constraints in general mathematical form.
what are some theories that would support on my research study?
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