Permutation Flow Shop Scheduling Optimization Method Based on Cooperative Games

Abstract

This paper proposes a cooperative games model for the permutation flow shop scheduling problem (PFSP) with multiple customer tasks. Here, customers create alliances through cooperation in the case of delayed and early delivery penalty constraints, and tasks in the alliance are rescheduled to seek maximum cost savings. A new β rule allocation method is proposed considering the variability in the delay penalty factor of different ordered tasks. Additionally, it is proven that the cost-saving allocation resulting from this allocation method is a core allocation of the PFSP cooperative games. A hybrid particle swarm optimization algorithm is proposed to obtain the optimal scheduling of each coalition. The algorithm uses a particle swarm as the main body, maintains the advantage of fast convergence of particle swarm optimization, increases the diversity among the population, and improves the optimization performance of the algorithm. Finally, the effectiveness of the algorithm, model, and allocation method is verified via experiments. The total cost for all customers under the optimal scheduling sequence is 5595.8, compared to 6689.8 for the initial scheduling order. The proposed cooperative games model can be applied to various enterprises to better satisfy the diverse needs of the market and customers.

Market Maestro: A Smart E-commerce Application

“…The values of the added products can still be modified even after the receipt is generated. When the quantity is modified to the products that are already added to the cart the changes are reflected in the cost and stock features also ensuring smooth inventory management [7].…”

An Estimation of Distribution Algorithm for Permutation Flow-Shop Scheduling Problem

“…The PFSP involves scheduling a set of jobs on a set of machines to minimize a specific performance measure. The most used objective function in the studies is makespan [22,23], which refers to the total time necessary to perform all of the jobs on all of the machines. The PFSP is a well-studied problem that has been widely used as a benchmark for various optimization algorithms [19,22].…”

“…These assumptions simplify the problem and allow for a focused analysis of scheduling strategies. However, it is important to recognize that real-world scenarios may deviate from these idealized conditions [22]. For example, variants of the PFSP may include considering machine breakdowns, job release dates, or setup times between operations [41].…”