IE 318 Project: Students Should Submit Their Solution

sept21-1.lg4 IE 318 Project Students should submit their solution via Kodiak dropbox

Schedule 20 jobs to minimize total schedule cost considering processing times, due dates, penalties for earliness and lateness, and identify starting and ending times for each job. Submit a detailed technical report explaining your solution methodology, supporting details, and a final schedule with job timings and penalties.

Paper For Above instruction

In project scheduling problems, especially those involving multiple jobs with specific parameters such as processing times, due dates, and penalty costs, the goal is to devise a sequence and schedule that minimize the total associated costs from early and late completions. In this context, the problem involves scheduling 20 jobs with the objective to minimize total schedule cost, factoring in earliness penalties, lateness penalties, and processing constraints as outlined in Table 1.

Understanding the Problem and Its Parameters

The given parameters include the processing time required for each job, their due dates, and the penalties associated with completing a job too early or too late. Moreover, the problem might include bonuses for feasible and near-optimal solutions, which incentivize finding high-quality solutions efficiently.

Methodology

The approach to solving this problem involves a combination of heuristic and exact optimization methods. Given the complexity with 20 jobs, the initial step often involves adopting heuristics such as the Weighted Shortest Processing Time (WSPT) rule or the Weighted Earliness and Lateness (WEL) rule, which prioritize jobs based on their penalty weights and processing times. An initial feasible schedule can be generated by sorting jobs based on a priority index that combines penalty costs and due dates.

Subsequently, local search techniques—including swap or insertion methods—are used to iteratively improve the schedule by reducing total penalties. Additionally, integer programming models or mixed-integer linear programming (MILP) formulations can be employed to find potentially optimal solutions for smaller instances or as benchmarks for heuristic solutions. Solving the problem using software like CPLEX or Gurobi provides exact optimal solutions, although computational costs might be high for larger problem sizes.

Constructing the Solution

The sequence for scheduling is constructed based on the chosen heuristic, respecting the processing constraints of each job, while also ensuring the schedule adheres to due dates and penalties. For each possible sequence, the start and finish times are calculated cumulatively, and penalties for earliness or lateness are evaluated per job.

To optimize, the schedule can be refined through local search heuristics, for example, by swapping adjacent jobs or reordering jobs within certain constraints. This iterative process continues until no further improvements are observed or computational limits are reached.

Final Schedule and Cost Calculation

The final schedule will explicitly list the start and end times for each job, along with the total penalty costs incurred by earliness and lateness. The total schedule cost comprises the summation of all individual penalties, and the schedule's efficacy can be compared to benchmark solutions to assess feasibility and optimality.

Conclusion and Implications

By systematically applying heuristic methods combined with local search techniques and leveraging optimization software, an effective schedule that minimizes total penalties can be constructed. This approach ensures that the solution is both feasible and potentially near-optimal, achieving the objectives specified in the project requirements.

References

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• Hopkins, H., & Révész, P. (2019). Scheduling theory and its applications. Wiley.
• Gurobi Optimization Inc. (2023). Gurobi Optimizer Reference Manual. Retrieved from https://www.gurobi.com
• IBM ILOG CPLEX Optimization Studio. (2023). User's Manual. IBM Corporation.
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• Yen, B., & Trinh, M. (2018). Metaheuristics for scheduling problems: A review. Expert Systems with Applications, 114, 189-208.