During the past two decades, there have been increasing interests on permutation flow shop with different types of objective functions such as minimizing the makespan, the weighted mean flow-time etc. The permutation flow shop is formulated as a mixed integer programming and it is classified as NP-Hard problem. Therefore, a direct solution is not available and metaheuristic approaches need to be used to find the near-optimal solutions. In this paper, we present a new discrete firefly meta-heuristic to minimize the makespan for the permutation flow shop scheduling problem. The results of implementation of the proposed method are compared with other existing ant colony optimization technique. The preliminary results indicate that the new proposed method performs better than the ant colony for some well known benchmark problems.

PurposeThis paper aims to present a closed-loop supply chain (CLSC) optimization problem for a perishable agricultural product to achieve three pillars of sustainability, including minimizing total network costs and carbon dioxide emissions from different network activities and maximizing responsiveness to demands simultaneously.Design/methodology/approachThe research problem is formulated as a multi-objective mixed-integer linear programming model, and classical approaches, including the LP-Metric and weighted Tchebycheff method, have been applied to solve the optimization model. A set of test problems has been proposed to validate the model, and the results are presented.FindingsComputational time to find Pareto optimal solutions by using the weighted Tchebycheff method was twice as much as that of the LP-Metric method. Also, the result of the study is a mathematical model that can be applied to other products that are close to the fruit, such as vegetables.Research limitations/implicationsThe present study is limited to fruits supply chains and the inventory is considered at the distribution centers only. The study also considers only one type of transport.Practical implicationsThe paper can assist supply chain managers to define strategies to achieve a sustainable CLSC network configuration for the fruits.Originality/valueThis study is one of the early studies to consider environmental indicators in fruits supply chain design along with two other indicators of sustainability, namely, economic and social indicators. Therefore, this can help supply chain managers to achieve sustainability by optimizing location decisions, inventory quantities and flow between facilities.

The hub location problem (HLP) is a special type of the facility location problem with numerous applications in the airline industry, postal services, and computer and telecommunications networks. This paper addresses two basic variants of the HLP, namely the uncapacitated single allocation hub location problem (USAHLP) and the uncapacitated single allocation p-hub median problem (USApHMP). Exact solution procedures based on Benders decomposition algorithm are proposed to tackle large sized instances of these problems. The standard Benders decomposition algorithm is enhanced through implementation of several algorithmic refinements such as using a new cut disaggregation scheme, generating strong optimality cuts, and an efficient algorithm to solve the dual subproblems. Furthermore, a modern implementation of the algorithm is used where a single search tree is established for the problem and Benders cuts are successively added within a branch-and-cut framework. Extensive computational experiments are conducted to examine the efficiency of the proposed algorithms. We have been able to solve all the instances of the problems from all three main data sets of the HLP to optimality in reasonable computational times.

Hub location problems (HLPs) constitute an important class of problems in logistics with numerous applications in passenger/cargo transportation, postal services, telecommunications, etc. This paper addresses the competitive single and multiple allocation HLPs where the market is assumed to be a duopoly. Two firms (decision makers) sequentially decide on the configuration of their hub networks trying to maximize their own market shares. The customers choose one firm based on the cost of service provided by these firms. Mathematical formulations are presented for the problems of the first and second firms (the leader and the follower, respectively) and Simulated Annealing (SA) based solution algorithms are proposed for solving these problems both in single and multiple allocation settings. Extensive computational experiments show the capability of the proposed solution algorithms to obtain the optimal solutions in short computational times. Some managerial insights are also derived based on the obtained results.

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