Shanling Li

Sensitivity and Stability Analysis in DEA: Some Recent Developments

This papersurveys recently developed analytical methods for studying thesensitivity of DEA results to variations in the data. The focusis on the stability of classification of DMUs (Decision MakingUnits) into efficient and inefficient performers. Early workon this topic concentrated on developing solution methods andalgorithms for conducting such analyses after it was noted thatstandard approaches for conducting sensitivity analyses in linearprogramming could not be used in DEA. However, some of the recentwork we cover has bypassed the need for such algorithms. Evolvingfrom early work that was confined to studying data variationsin only one input or output for only one DMU at a time, the newermethods described in this paper make it possible to determineranges within which all data may be varied for any DMU beforea reclassification from efficient to inefficient status (or vice versa) occurs. Other coverage involves recent extensionswhich include methods for determining ranges of data variationthat can be allowed when all data are varied simultaneously for all DMUs. An initial section delimits the topics to be covered.A final section suggests topics for further research.

Structural Properties of Buyback Contracts for Price-Setting Newsvendors

This paper studies a buyback contract in the Stackelberg framework of a manufacturer (leader) selling to a price-setting newsvendor retailer (follower). Using an analytical model that focuses on a multiplicative demand form, we generalize previous results and produce new structural insights. A novel transformation technique first enables us to establish the unimodality of the profit functions for both channel partners, under relatively mild assumptions. Further analysis identifies the necessary and sufficient condition under which the optimal contract for the manufacturer (wholesale and buyback prices) is distribution free, i.e., independent of the uncertainty in customer demand. A specific instance of the above condition is also necessary and sufficient for a no-buyback contract to be optimal from the manufacturers perspective. We then prove that the optimal performance of the decentralized channel for distribution-free buyback contracts depends only on the curvature of the deterministic demand part. In addition, some of the optimal decisions and relevant profit ratios for buyback contracts in our setting are shown to be identical to those for their deterministic price-only counterparts.

Operational design of a supply chain system using the Taguchi method, response surface methodology, simulation, and optimization

Managing a supply chain to meet an organizations objectives is a challenge to many firms. It involves collaboration in multiple dimensions, such as cooperation, information sharing, and capacity planning. In this research, we focus on identifying the ‘best’ operating conditions for a supply chain. We propose a hybrid approach that incorporates simulation, Taguchi techniques, and response surface methodology to examine the interactions among the factors, and to search for the combination of factor levels throughout the supply chain to achieve the ‘optimal’ performance. This study makes it possible for firms to understand the dynamic relations among various factors, and provides guidelines for management to minimize the impact of demand uncertainty on the performance of the supply chain. The results help the manufacturer determine the proper plant capacity and adopt the right level of delayed differentiation strategy for its products. We also quantify the potential gains of cooperation among different members of the supply chain. Using such knowledge, a manufacturer can develop an appropriate incentive plan to motivate the retailers and suppliers to collaborate, and to realize the potential of the entire supply chain.

Comparisons and evaluations of alternative approaches to the treatment of congestion in DEA

Abstract This paper examines the two approaches that are presently available in the data envelopment analysis (DEA) literature for use in identifying and analyzing congestion. The first approach, due to Fare et al. (Fare, R., Grosskopf, S., Lovell, C.A.K., 1985. The Measurement of Efficiency of Production. Kluwer-Nijhoff, Boston) has been extensively employed to identify congestion in areas such as the provision of health services. The latter approach, due to Cooper et al. (Cooper, W.W., Thompson, R.G., Thrall, R.M., 1996. Annals of Operations Research 66, 3–45) was subsequently extended by Brockett et al. (Brockett, P.L., Cooper, W.W., Shin, H.C., Wang, Y., 1998. Socio-Economic Planning Sciences 32, 1–20) to treat tradeoff possibilities between employment and output in Chinese production when congestion is present. In contrast with Cooper et al., examples are provided in this paper which show that the Fare et al. approach can fail in both modes: It can show congestion to be present when this is not consistent with the observed behavior. It can also fail to exhibit congestion when the data show it to be present. Suggestions are offered both for (i) taking precautions before using the FGL approach and for (ii) overcoming these shortcomings.

Using DEA to improve the management of congestion in Chinese industries (1981-1997)

Abstract Congestion is said to be present when increases in inputs result in output reductions. An “iron rice bowl” policy instituted in China shortly after the revolution led by Mao Tze Tung resulted in congestion that ultimately led to bankruptcy in the textile industry, and near bankruptcy in other industries. A major policy shift away from the “iron rice bowl policy” in 1990 led to massive layoffs and increasing social tensions. Were these massive layoffs necessary? Extensions of data envelopment analysis models effected in the present paper identified inefficiencies in the management of congestion. Using textiles and automobiles for illustration, it is shown how elimination of such managerial inefficiencies could have led to output augmentation without reducing employment. Thus, even in the presence of congestion, it proved to be possible to identify additional (managerial) inefficiencies that provided opportunities for improvement. In the heavily congested textile industry, these output augmentations could have been accompanied by reductions in the amounts of capital used (as an added bonus). In any case, we show how to identify and evaluate new types of efficiency—viz., the efficiency with which needed (or desired) inefficiencies are managed.

Tailored Supply Chain Decision Making Under Price-Sensitive Stochastic Demand and Delivery Uncertainty

In this paper, we study a serial two-echelon supply chain selling a procure-to-stock product in a price-sensitive market. Our analytical modelling framework incorporates optimal pricing and stocking decisions for both echelons in the presence of stochastic demand and random delivery times. We focus on understanding how these decisions for the chain are affected by its management paradigm (centralized or decentralized), and its business characteristics-price sensitivity, demand uncertainty, and delivery time variability. A novel combination of transformations enables us to analyze the framework and determine the unique optimal choices for centralized and wholesale price-based decentralized supply chains. More detailed investigation reveals that, in general, the business characteristics influence both the behavior and the optimal values of the decision variables, while the management paradigm primarily governs the optimal values. We illustrate the significance of these results in terms of how managers should tailor their decisions to align with their business requirements. Subsequently, comparison of the optimal profits between the channel partners and the management paradigms provides implications for decentralization strategy. A decentralized chain is most inefficient for moderately price-sensitive customers and uncertain environments, but is relatively more effective when dealing with mature products. We propose a contracting scheme that can improve the decentralized chain profit in reliable delivery time settings. The salient modelling insight of this paper is that ignoring the randomness of delivery time trivializes the interaction between pricing and stocking decisions. On the other hand, from a managerial viewpoint, we establish that optimal pricing policies provide the means to increase revenue and also act as strategic tools for tackling uncertainty.

Selection of contract suppliers under price and demand uncertainty in a dynamic market

In this paper, we consider a supply contracting problem in which the buyer firm faces non-stationary stochastic price and demand. First, we derive analytical results to compare two pure strategies: (i) periodically purchasing from the spot market; and (ii) signing a long-term contract with a single supplier. The results from the pure strategies show that the selection of suppliers can be complicated by many parameters, and is particularly affected by price uncertainty. We then develop a stochastic dynamic programming model to incorporate mixed strategies, purchasing commitments and contract cancellations. Computational results show that increases in price (demand) uncertainty favor long-term (short-term) suppliers. By examining the two-way interactions of contract factors (price, demand, purchasing bounds, learning and technology effect, salvage values and contract cancellation), both intuitive and non-intuitive managerial insights in outsourcing strategies are derived.

Using DEA To evaluate 29 Canadian textile companies — Considering returns to scale

In this paper we analyse the performance of some Canadian textile firms by using Data Envelopment Analysis (DEA). Using DEA we develop efficiency scores, efficiency frontiers and returns-to-scale for three segments of the sector, i.e., spinning, weaving and dyeing. Finally we develop models to solve optimal expansion or vertical integration related problems for firms with increasing and decreasing returns respectively.

A hybrid two-stage flowshop with part family, batch production, major and minor set-ups

In this paper, we consider a two-stage hybrid flowshop with a single machine at stage 1 and multiple identical machines at stage 2. The flowshop is characterized by major and minor setups, part families and batch production allowing split and no split at stage 2. The parts within a family share a major setup and the parts in a batch share a minor setup. The objective of our problem is to minimize the makespan. We develop two allocation policies with one as a traditional way (called Forward Heuristic) and the other as a non-traditional way (called Backward Heuristic). We also develop several effective sequence rules to further improve the makespan. The computational results show that the Backward Heuristic, in general, is superior to the Forward Heuristic. The sequence rules developed in this paper also perform better than the traditional sequence rules such as SPT and LPT.

Note: Alternative treatments of congestion in DEA – a response to the Cherchye, Kuosmanen and Post critique

Abstract As its title suggests, this paper constitutes a response to the critique by Cherchye, Kuosmanen and Post which is leveled at the paper “Comparisons and evaluations of alternative approaches to the treatment of congestion in DEA” by Cooper, Gu and Li. All three papers are in this same issue of the European Journal of Operational Research where the just-cited paper by Cooper, Gu and Li appears.