Yaakov Roll

Controlling Factor Weights in Data Envelopment Analysis

Abstract Data Envelopment Analysis (DEA) is a mathematical programming approach to assessing relative efficiencies within a group of Decision Making Units (DMUs). An important outcome of such an analysis is a set of virtual multipliers or weights accorded to each (input or output) factor taken into account. These sets of weights are, typically, different for each of the participating DMUs. A version of the DEA model is offered where bounds are imposed on weights, thus reducing the variation in the importance accorded to the same factor by the various DMUs. Techniques for locating appropriate bounds are suggested and the notion of a common set of weights is examined. Possible interpretations to differences in efficiency ratings obtained with the various models developed are discussed.

Alternate methods of treating factor weights in DEA

Provisions for controlling factor weights constitute a significant extension of the data envelopment analysis (DEA) methodology, as an effective tool for measuring efficiency. This paper suggests a conceptual framework for the treatment of factor weights in DEA. First, the paper proposes general guidelines for setting bounds on factor weights. Then, it develops and presents alternative methods to limit the range within which these factor weights are allowed to vary. All of these methods involve additional information which is entered into the analysis in the form of constraints, bounds or different objective functions. Finally, the implications of the various approaches is discussed.

A Dea Model For Measuring The Relative Eeficiency Of Highway Maintenance Patrols

AbstractA pilot application of Data Envelopment Analysis (DEA) for the measurement of the efficiency of highway maintenance patrols is demonstrated. Selection of pertinent factors is discussed and the potential benefits of the analysis listed. A bounded DEA model is constructed and results are compared to those obtained from a conventional DEA model. The effects of secondary factors on the relative efficiencies of patrols are examined by analyses of sub-groups of Decision Making Units (DMUs), differing in the intensities of the respective factors.

Internal Layout Design of a Warehouse

Abstract Two configurations of shelves, in a homogeneous or a zoned warehouse, are compared. Handling costs as well as costs associated with the warehouse area and perimeter are taken into consideration. From these, expressions for optimal design parameters are developed. It is shown that, depending on ratios between the relevant costs, some general preference rules for the two layouts examined can be laid down.

Warehouse design with storage policy considerations

A search procedure for finding a global optimal solution for a, specific formulation of the warehouse design problem is presented. In this formulation three types of costs are considered: costs associated with the initial investment (construction and handling facilities), a shortage cost and costs associated with the storage policy. The search procedure for finding the optimal storage design is developed, comprising analytical optimization and simulation techniques.

A combined optimization and simulation approach for designing automated storage/retrieval systems

The study of Automated Storage/Retrieval Systems (AS/RS) in warehouses has developed along two main lines: One seeks to minimize total cost of an AS/RS, while the other explores the dynamic behavior of such a system. This study addressing the two issues simultaneously, obtains design parameters for a system that complies with desired levels of performance. To this end, a heuristic recursive optimization/simulation procedure is developed. It is also assumed that the number of stacker cranes (an important cost component of AS/RS) can be less than or equal to the number of aisles. The proposed procedure was applied to several situations, and converged within a few iterations.

Some Extensions of Techniques to Handle Non- Discretionary Factors in Data Envelopment Analysis*

Data Envelopment Analysis (DEA) assumes, in most cases, that all inputs and outputs are controlled by the Decision Making Unit (DMU). Inputs and/or outputs that do not conform to this assumption are denoted in DEA asnon-discretionary (ND) factors. Banker and Morey [1986] formulated several variants of DEA models which incorporated ND with ordinary factors. This article extends the Banker and Morey approach for treating nondiscretionary factors in two ways. First, the model is extended to allow for thesimultaneous presence of ND factors in both the input and the output sets. Second, a generalization is offered which, for the first time, enables a quantitative evaluation ofpartially controlled factors. A numerical example is given to illustrate the different models.

A Heuristic Algorithm for the Multi-Item Lot-Sizing Problem with Capacity Constraints

Abstract A heuristic algorithm is presented for solving the scheduling of several items in parallel under capacity constraints with setup and carrying costs. The method is based upon finding a lower bound solution for these costs, securing the feasibility of the solution, and improving the feasible solution so obtained until no further improvements can be made. Comparison of the performance of the proposed heuristic algorithm to that of an exact mixed-integer programming model showed that best solution costs found by the heuristic deviated on an average by 1% from the optimal values, while the computing time was on an average 1/140 of that required by the exact method.

Productivity measurement at the plant level

A system of productivity indices, suitable for the plant level, is developed. The productivity of each input factor is measured separately against standard, input per unit of output, figures. This system enables the decomposition of comparative indices into components, whereby the contribution of each component to productivity differentials can be determined. A model is proposed for aggregating the single factor (physical) productivities into an overall (economic) index.

Warehouse capacity in a stochastic environment

In this study we examine the elements that affect the required capacity of a warehouse in a stochastic environment. The required capacity is measured in terms of its deviation from the nominal capacity requirement (NCR). A simulation model was developed to measure the relationship between warehouse capacity and the various pertinent parameters. From a set of simulated experiments, it is seen that the deviation in the required capacity is mainly affected by the number of items stored, the ordering quantity and the average issues of items per day.