Optimal system design and optimal budget models in the presence of interval data

Abstract

This paper develops an interval data envelopment analysis (DEA) framework for optimal system design (OSD) and optimal budget determination. Classical OSD DEA models generally assume that input and output data are known precisely. In many applications, however, production data are affected by measurement error, incomplete records, forecasting uncertainty, or managerial judgment and are therefore more realistically represented by lower and upper bounds. To address this issue, the present study extends profit-maximizing OSD DEA models to the case of interval input and output data. The proposed formulation enables a decision-making unit (DMU) to determine an economically desirable input-output configuration under a given budget when benchmark data are imprecise. The study also develops a complementary procedure for determining the optimal budget and for identifying budget congestion in the interval-data setting. In this framework, budget congestion occurs when forcing a DMU to consume a budget above the optimal level reduces profit rather than improving performance. The models are formulated as deterministic linear programming problems and can therefore be solved using standard optimization software. A numerical example with ten DMUs, three inputs, and two outputs is used to illustrate the applicability of the proposed approach. The results show that the interval OSD framework provides a practical decision-support tool for profit-oriented resource allocation when production data are not exactly known.