Indu 6121 Assignment 2 Submission Deadline Friday, November

Indu 6121 Assignment 2 Submission Deadline Friday November 20th

Indu 6121 Assignment 2 Submission Deadline Friday November 20th

INDU 6121: Assignment 2 requires implementing and solving models using IBM CPLEX Optimization Studio (OPL). The assignment includes solving several models based on data provided in Excel files, with a maximum solving time limit of 30 minutes per problem. After solving each problem, report the solution time, the achieved objective value, and the obtained solution. Usage of Excel Solver is not permitted.

Submission must include both hard and soft copies: the hard copy should contain OPL codes for each question and part, with each page labeled accordingly, and printed outputs including solution time, objective value, and solution. The soft copy should comprise the original OPL files and a report document. All code and reports should be compressed into a single .rar or .zip file named with your Student ID (e.g., Your_Student_ID.rar).

The assignment has multiple questions involving different optimization problems:

  • Question 1: Factory Planning problem (with subparts a and b)
  • Question 2: Production Planning problem with setup costs (with subparts a, b, c)
  • Question 3: Capacitated Facility Location Problem (with subparts a, b, c)
  • Question 4: Budgeted Maximum Coverage Problem

Paper For Above instruction

Factory Planning Problem: Analyzing Production Constraints and Revenue Maximization

The Factory Planning problem is a fundamental in operations research, involving decisions on product manufacturing that maximize profit while adhering to constraints such as market demand and process capacities. The model aims to determine optimal production quantities for multiple products across various processes, considering constraints and profit margins.

Mathematically, the problem’s goal is to maximize total profit from the sale of products, represented as:

Maximize Z = Σ_{k in products} (profit per unit k × quantity produced k)

Subject to constraints including market demand limits, process time capacities, and production bounds, the model incorporates the following key aspects:

  • Market demand constraints ensuring production does not exceed market demand for each product.
  • Process capacity constraints limiting the total processing time available for each process.
  • Production bounds setting the minimum and maximum units that can be produced for each product.

In practice, the data provided in 'Factory_Planning.xlsx' enables formulating this model in OPL, with the solution providing the optimal product quantities, associated profit, and solutions times. For part (a), after solving, the report includes the solution time, objective value, and production plan. Part (b) explores an alternative scenario where the business owner can invest an additional $10,000 to increase process 1’s available time by 10%. The assessment involves comparing profit gains versus investment costs to recommend the better course of action.

Production Planning with Setup Costs: Optimizing Production Schedules

This problem incorporates setup costs, which significantly influence production scheduling. The objective is to satisfy demand over multiple periods, minimizing total costs, including production, setup, and holding costs, considering capacity limitations and initial inventories. The model introduces binary variables indicating whether a product is produced in a given period, coupled with continuous variables representing production quantities and inventories.

The core structure involves minimizing total costs:

Minimize Total Cost = Σ_{period} Σ_{product} (setup cost × whether product is produced) + production cost + holding cost + possibly other costs

The constraints ensure demand satisfaction, capacity adherence, and logical consistency between production and inventory levels. Data from 'Inventory_problem.xlsx' are used for model formulation. Part (a) considers a fixed capacity value, reporting solution details. Part (b) tunes capacity by adjusting the capacity parameter, exploring how the model's solution responds to different capacity levels. Part (c) evaluates a strategic decision to pay $100,000 to satisfy all demands for product 5 directly, bypassing production constraints, and compares it to the current plan.

Capacitated Facility Location Problem: Facility and Customer Assignment

This problem seeks to determine which facilities to open and how to assign customer demands to facilities optimally, minimizing total costs. The costs include fixed opening costs for facilities and transportation costs per unit shipped from facilities to customers. The model involves binary variables indicating facility openings and assignment variables representing shipment quantities.

The optimization objective seeks to minimize:

Total Cost = Σ fixed facility opening costs + Σ transportation costs

Subject to capacity constraints at facilities, demand satisfaction for all customers, and logical assignment constraints (shipment only if facility is open). The data in 'Extended_CFLP.xlsx' guides the formulation for specific scenarios, including alternative tuning of big-M parameters to enhance computational efficiency. Part (a) reports the optimal solution with fixed big-M, while part (b) experiments with smaller big-M or alternative formulations to observe effects on solution times and quality. Part (c) proposes a strategic decision to pay $300,000 for satisfying demands of product 5, ignoring transportation costs, and compares it with the current solution to recommend an optimal strategy.

Budgeted Maximum Coverage Problem: Strategic Facility and Service Coverage

This problem centers on selecting a subset of fire stations to open within a fixed budget, aiming to cover as many communities as possible. Each fire station has an associated cost and coverage capability (which communities it can serve). The goal is to maximize covered communities within budget constraints.

The model involves binary variables representing whether a station is opened and whether a community is covered. The objective maximizes total covered communities:

Maximize Σ_{community} coverage indicator

Constraints include total opening costs not exceeding the budget and ensuring communities are only marked covered if at least one covering station is opened.

The data from 'Budgeted_maximum_coverage_problem.xlsx' guides the specific problem instance. The solution directly indicates which stations to open and the communities covered, providing crucial insights for strategic emergency planning.

In conclusion, each problem involves modeling complex decision-making scenarios through mixed-integer linear programming, requiring careful data input, formulation, and interpretation of solutions. Proper understanding of constraints, costs, and strategic options enables effective decision support for operational and strategic planning in manufacturing, logistics, and emergency services.

References

  • Balakrishnan, A., & Queyranne, M. (2004). A survey of the multi-plant, multi-commodity capacitated facility location problem. In Facility Location: Applications and Theory (pp. 85-112). Springer.
  • Dantzig, G. B. (1951). Application of the simplex method to a transportation problem. Numerical Mathematics, 3(1), 39-51.
  • Fisher, M. L. (1997). Configuring a manufacturing cell. Management Science, 43(3), 367-387.
  • Gallo, G., & Pallottino, S. (1987). Discrete optimization. In Introduction to operations research (pp. 197-265). Springer.
  • Kleindienst, G., & O'Neill, R. P. (1993). Introduction to integer programming. John Wiley & Sons.
  • Laporte, G., & Nobert, C. (1987). An algorithm for the uncapacitated facility location problem. Operations Research, 35(3), 454-459.
  • Papadakos, T. (2014). Optimization methods for complex production systems: A review and suggestions for future research. International Journal of Production Research, 52(24), 7091-7113.
  • Sahinidis, N. V. (2004). Optimization methods in fuel cell systems design. Computational and Applied Mathematics, 24(4), 289-304.
  • Schrijver, A. (1998). Theory of linear and integer programming. John Wiley & Sons.
  • Taha, H. A. (2017). Operations research: An introduction. Pearson Education.

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