Journal of Industrial Engineering and Management Studies

Abstract Time is one of the most valuable assets in industry, and cost is another highly regarded factor. Optimal utilization of these resources can increase efficiency and profit. The parallel machine scheduling problem is a fundamental issue in industry and services. This research proposes a two-objective mathematical model for parallel machine scheduling. The first objective function is defined as the makespan, which is the completion time of the last job. The second objective function is defined as the maximum cost incurred by any single machine, which is a function of the sum of the processing costs of each operation and the fixed cost of purchasing and maintaining the machines. Each job consists of multiple operations, and all operations must be completed to finish the job. Additionally, it is assumed that jobs have priorities, and precedence constraints between operations must be satisfied. Due to the model's non-linearity and the problem's complexity, a metaheuristic algorithm based on the particle swarm optimization (PSO) approach is developed to solve the proposed model by aggregating the objective functions. The proposed method is simulated in MATLAB on three sample instances in small, medium, and large scales. The computational results demonstrate the robustness and efficiency of the proposed method.

Abstract Perishable food supply chains (PFSCs), particularly in the dairy sector, face significant challenges due to product deterioration, quality degradation, and financial risks associated with distribution delays. Despite extensive research on supply chain optimization, a critical gap remains in accurately modeling the dynamic relationship between product shelf-life and selling price—a factor that significantly impacts revenue and risk assessment in real-world operations. This study addresses this gap by developing a multi-objective optimization model for the dairy supply chain in Iran that incorporates: (1) a novel stepwise pricing mechanism based on remaining shelf-life, capturing revenue loss due to spoilage; (2) financial risk assessment of purchase and distribution operations; (3) transportation planning with vehicle routing; and (4) discount sales policies aligned with product freshness. Given the NP-Hard nature of the problem, NSGA-II and MOPSO algorithms with a modified priority-based encoding-decoding method were employed. Algorithm parameters were systematically tuned using the Taguchi method. The model was validated through a numerical example solved via the LP-metric method, followed by 15 larger test problems to evaluate algorithm performance. Comparative analysis using multiple evaluation metrics—including the number of Pareto-efficient solutions (NPF), maximum spread index (MSI), spacing metric (SM), and computational time—was conducted. The TOPSIS technique was applied to rank algorithm performance, revealing that NSGA-II (weight = 0.6945) significantly outperforms MOPSO (weight = 0.3055) across all problem sizes. The key contributions of this research include: (i) introducing a realistic stepwise pricing function linked to perishability, (ii) integrating financial risk into PFSC optimization, and (iii) providing a robust algorithmic framework for large-scale dairy supply chain problems. These findings offer practical guidance for managers seeking cost-effective, risk-aware, and quality-conscious management of perishable food supply chains.