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This paper studies the preemptive scheduling problem of independent jobs on identical machines. The purpose of this paper is to minimize the makespan under the imposed constraints, namely, the ones that relate the transportation delays which are required to transport a preempted job from one machine to another. This study considers the case when the transportation delays are variable.

The contribution is twofold. First, this study proposes a new linear programming formulation in real and binary decision variables. Then, this study proposes and implements a solution strategy, which consists of two stages. The goal of the first stage is to obtain the best machines order using a local search strategy. For the second stage, the objective is to determine the best possible sequence of jobs. To solve the preemptive scheduling problem with transportation delays, this study proposes a heuristic and two metaheuristics (simulated annealing and variable neighborhood search), each with two modes of evaluation.

Computational experiments are presented and discussed on randomly generated instances.

The study has implications in various industrial environments when the preemption of jobs is allowed.

This study proposes a new linear programming formulation for the problem with variable transportation delays as well as a corresponding heuristic and metaheuristics.

The decision-making to outsource and select the most suitable global manufacturing outsourcing partner (MOP) is complex and uncertain due to multiple conflicting qualitative and quantitative criteria as well as multiple alternatives. Vagueness and variability exist in ratings of criteria and alternatives by group of decision-makers (DMs). The paper provides a novel Stochastic Fuzzy (SF) method for evaluation and selection of agile and sustainable global MOP in uncertain and volatile business environment.

Four main selection criteria for global MOP selection were identified such as economic, agile, environmental and social criteria. Total 16 sub-criteria were selected. To consider the vagueness and variability in ratings by group of DMs, SF method using t-distribution or z-distribution was adopted. The criteria weights were determined using the Stochastic Fuzzy-CRiteria Importance Through Intercriteria Correlation (SF-CRITIC), while MOP selection was carried out using Stochastic Fuzzy-VIseKriterijumskaOptimizacija I KompromisnoResenje (SF-VIKOR) in the case study of footwear industry. Sensitivity analysis was performed to test the robustness of the proposed model. A comparative analysis of SF-VIKOR and VIKOR was made.

The worker’s wages and welfare, product price, product quality, green manufacturing process and collaboration with partners are the most important criteria for MOP selection. The MOP3 was found to be the best agile and sustainable global MOP for the footwear company. In sensitivity analysis, significance level is found to have important role in MOP ranking. Hence, the study concluded that integrated SF-CRITIC and SF-VIKOR is an improved method for MOP selection problem.

In a group decision-making, ambiguity, impreciseness and variability are found in relative ratings. Fuzzy variant Multi-Criteria Decision-Making methods cover impreciseness in ratings but not the variability. On the other hand, deterministic models do not cover either. Hence, the stochastic method based on the probability theory combining fuzzy theory is proposed to deal with decision-making problems in imprecise and uncertain environments. Most notably, the proposed model has novelty as it captures and reveals both the stochastic perspective and the fuzziness perspective in rating by group of DMs.

The proposed multi-criteria group decision-making model contributes to the sustainable and agile footwear supply chain management and will help the policymakers in selecting the best global MOP.

To the best of the authors’ knowledge, SF method has not been used to select MOP in the existing literature. For the first time, integrated SF-CRITIC and SF-VIKOR method were applied to select the best agile and sustainable MOP under uncertainty. Unlike other studies, this study considered agile criteria along with triple bottom line sustainable criteria for MOP selection. The novel method of SF assessment contributes to the literature and put forward the managerial implication for improving agility and sustainability of global manufacturing outsourcing in footwear industry.