Abstract
Data envelopment analysis (DEA) measures the efficiency score of a set of homogeneous decision-making units (DMUs) based on observed input and output. Considering input-oriented, the inverse DEA models find the required input level for producing a given amount of production in the current efficiency level. This article proposes a new form of the inverse DEA model considering income (for planning) and budget (for finance and budgeting) constraints. In contrast with the classical inverse model, both input and output levels are variable in proposed models to meet income (or budget) constraints. Proposed models help decision-makers (DMs) to find the required value of each input and each output’s income share to meet the income or budget constraint. We apply the proposed model in the efficiency analysis of 58 supermarkets belonging to the same chain. However, these methods are general and can be used in the budgeting and planning process of any production system, including business sectors and firms that provide services.
Highlights
Data Envelopment Analysis (DEA) is a linear programming technique-based for evaluating the relative efficiency of a decision-making unit (DMU) by comparing it with other decision-making units (DMUs) that first time as proposed by Charnes et al [4], known as the CCR model
Wei et al [25] proposed the inverse DEA models that aim to answer this question: if among a group of DMUs, we increase certain inputs to a particular unit and assume that the DMU maintains its current efficiency level with respect to other units, how much more outputs could the unit produce? If the outputs need to be increased to a certain level and the unit’s efficiency remains unchanged, how much more inputs should be provided to the unit? These types of questions are answered using Multiple Objectives Linear Programming (MOLP) in general in the inverse DEA literature
This paper proposes two inverse DEA-based models to assist DMs on the budgeting and planning issue
Summary
Data Envelopment Analysis (DEA) is a linear programming technique-based for evaluating the relative efficiency of a decision-making unit (DMU) by comparing it with other DMUs that first time as proposed by Charnes et al [4], known as the CCR model. Gattoufi et al [8] proposed an application of the inverse DEA models in merger and acquisition in banking They developed an approach to realize the required level of the merged bank’s inputs and outputs to reach a predetermined efficiency target. The current article proposes a new class of inverse DEA to the literature It considers the budget constraint in the inverse DEA models and instead of increasing inputs and seeking for producible output with the same measure of efficiency. This paper considers a specific and limited budget that can be spent for buying different inputs (material vs service or equipment vs manpower), and the aim is estimating producible output with current efficiency measures.
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