Please help with this optimization problem. I need a full mathematical model (Task 1) and a spreadsheet setup using Excel Solver (Task 2).
A company is planning its production and distribution network to serve five customer regions at the minimum total cost. The cost to be minimized includes:
the fixed cost of opening plants,
the variable transportation cost of shipping units from plants to demand regions, and
a shortage penalty cost of $200 per unit for any unmet demand.
Note: Unlike your previous assignment, this model includes shortage (unmet demand) penalties. Demand does not need to be fully satisfied. Instead, you must model and penalize any unmet demand. Pay close attention to this change when writing your model and setting up Solver.
Four cities labeled A, B, C, and D are considered for setting up production plants. Each city can host only one plant. The objective of this problem is to determine which plants to open and how much to ship to each customer region in order to minimize total cost, which includes the cost of building production plants, the cost of shipping goods from plants to regions, and the unmet demand (shortage) penalty cost for any unmet customer demand.
Note: The total production capacity across all four plants is 800 units, while the total customer demand is 700 units. However, opening all plants may not be cost-effective. Therefore, the model should evaluate whether meeting all demand is cost-effective, and allow for unmet demand when it minimizes total cost.
Task 1: Model Formulation
Write the complete optimization model for this problem, using the following structure:
Write a complete mathematical model using Microsoft Word.
You must typeset all equations using Insert → Equaton (do not paste images or handwritten work).
Clearly define decision variables and parameters in a table
State the objective function (minimize total cost)
List all constraints:
Demand constraints
Capacity constraints
Non-negativity and binary constraints
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