An integer-valued data envelopment analysis model with bounded outputs

Integer-valued data envelopment analysis (DEA) with alternative returns to scale technology has been introduced and developed recently by Kuosmanen and Kazemi Matin. The proportionality assumption of their introduced "natural augmentability" axiom in constant and nondecreasing returns to scale technologies makes it possible to achieve feasible decision-making units (DMUs) of arbitrary large size. In many real world applications it is not possible to achieve such production plans since some of the input and output variables are bounded above. In this paper, we extend the axiomatic foundation of integer-valuedDEAmodels for including bounded output variables. Some model variants are achieved by introducing a new axiom of "boundedness" over the selected output variables. A mixed integer linear programming (MILP) formulation is also introduced for computing efficiency scores in the associated production set. © 2011 The Authors. International Transactions in Operational Research © 2011 International Federation of Operational Research Societies.

A fuzzy AHP based integer linear programming model for the multi-criteria transshipment problem

Purpose – The purpose of this research is to develop a holistic approach to maximize the customer service level while minimizing the logistics cost by using an integrated multiple criteria decision making (MCDM) method for the contemporary transshipment problem. Unlike the prevalent optimization techniques, this paper proposes an integrated approach which considers both quantitative and qualitative factors in order to maximize the benefits of service deliverers and customers under uncertain environments. Design/methodology/approach – This paper proposes a fuzzy-based integer linear programming model, based on the existing literature and validated with an example case. The model integrates the developed fuzzy modification of the analytic hierarchy process (FAHP), and solves the multi-criteria transshipment problem. Findings – This paper provides several novel insights about how to transform a company from a cost-based model to a service-dominated model by using an integrated MCDM method. It suggests that the contemporary customer-driven supply chain remains and increases its competitiveness from two aspects: optimizing the cost and providing the best service simultaneously. Research limitations/implications – This research used one illustrative industry case to exemplify the developed method. Considering the generalization of the research findings and the complexity of the transshipment service network, more cases across multiple industries are necessary to further enhance the validity of the research output. Practical implications – The paper includes implications for the evaluation and selection of transshipment service suppliers, the construction of optimal transshipment network as well as managing the network. Originality/value – The major advantages of this generic approach are that both quantitative and qualitative factors under fuzzy environment are considered simultaneously and also the viewpoints of service deliverers and customers are focused. Therefore, it is believed that it is useful and applicable for the transshipment service network design.