Rapid changes in production environments have motivated researchers and industrial manufacturers to coordinate the production and distribution in supply chain management. This paper aims to address the permutation flow shop scheduling problem with batch delivery to multiple customers. In this problem, products are first manufactured in a permutation flow shop, and subsequently delivered to multiple customers in batches. To optimize the tradeoff between customer service and distribution cost, the objective of this paper is to minimize the total cost of tardiness and batch delivery. To deal with such optimization problem, two simple heuristics and a novel meta-heuristic (GA-TVNS) are developed to determine integrated production and distribution schedules. GA-TVNS hybridizes genetic algorithm and variable neighborhood search (VNS) to provide better exploration and exploitation in the search space. Moreover, to improve the local search of VNS, two new learning-based neighborhood structures are designed based on the classical school learning process of teaching-learning-based optimization. Computation experiments on both small-sized and large-sized test problems indicate that GA-TVNS performs the best among all the compared scheduling algorithms.

The estimation of distribution algorithm (EDA) has recently emerged as a promising alternative to traditional evolutionary algorithms for solving combinatorial optimisation problems. This paper presents a novel two-phase simulation-based EDA (TPSB-EDA) for minimising the makespan of a hybrid flow shop under stochastic processing times. To address the stochastic scheduling problem efficiently, the proposed TPSB-EDA incorporates a two-phase simulation model to estimate the performance of candidate solutions. In this model, an optimal back propagation network is firstly applied to identify a set of roughly good solutions, and then the selected solutions are further evaluated by a discrete-event simulation algorithm. Moreover, an annealing selection mechanism (ASM) is adopted to preserve the population diversity of EDA. Different from the selection operators of common EDAs, the ASM uses Boltzmann probability in the annealing algorithm to select part of population to establish the probabilistic model. Computation results indicate that the TPSB-EDA provides good solutions in the aspects of solution quality and computational efficiency.