Business-to-business Collaboration in a Softgoods E-supply Chain I01-s01 I. Background and Project Objectives

The effort in this project has been directed to studying the state-of-the-art of Data Envelopment Analysis, cooperative games, and auctions and developing corresponding models to capture vague and uncertain factors and demonstrate their potential for establishing collaboration and contracts in the increasingly global softgoods supply chain. Prototype software packages have also been developed. I. BACKGROUND AND PROJECT OBJECTIVES With the recent advances in e-commerce technology, supply chain design and management is being rapidly drawn into the “e-era.” An internet platform allows easier communication and collaboration among all business entities in the softgoods chain. A cross-industry subcommittee of VICS, which includes a number of participants from the softgoods industry, has been developing and documenting a process (protocol) for collaborative planning, forecasting, and replenishment (CPFR) between buyers and sellers in a supply chain. Software vendors such as Logility, Syncra Systems, i2 Technologies, and Manugistics have begun to provide proprietary solutions to support web-based collaboration. However, there is a need for scholarly research on fundamental issues such as building useful models and developing practical methods and strategies for all entities in the softgoods supply chain and with the results being broadly shared. The issues of partner selection, contract negotiation, and dynamic pricing and cost allocation have been identified as critical for success in CPFR implementations. Successful resolution of such issues involves the simultaneous consideration of a number of possibly conflicting measures including both quantitative factors such as cost and lead-time and vague qualitative factors such as “quality”, “reliability” and “reputation." NTC Project: S01-NS01 (formerly I01-S01) 2 National Textile Center Annual Report: November 2002 In many businesses performance data is collected and used in evaluating potential trading partners. Unfortunately, grading and comparing candidates based on this data is not straightforward owing to the presence of numerous and possibly conflicting evaluation criteria. For example, if one candidate outperforms all others according to one performance criterion but fails to achieve satisfactory levels on other criteria, comparison becomes difficult. The traditional approach is to assign a fixed weight to each criterion to form an aggregated, weighted score for each candidate. Usually weights are chosen to support specific business rules (i.e., weighting quality measures more heavily than financial measures to reflect their greater importance). Several problems can arise with the traditional approach, including: (1) Weights are subjective, difficult to agree on, and have a tremendous effect on the final scoring; (2) It is difficult to balance relatively strong and relatively weak performance for different criteria; (3) Differences in units of measurement for criteria can distort the influence of the weights used in scoring. Over the past two decades, Data Envelopment Analysis (DEA) has emerged as an important tool in the field of efficiency measurement. DEA is used to compare similar “Decision Making Units” (DMUs) such as potential suppliers in which one or more inputs secure one or more outputs. The DMUs use the same inputs and secure the same outputs but generally at varying levels. DEA provides the ability to perform objective, comparative efficiency analyses that go beyond purely financial measures of performance. For example, one bank has used DEA to substantially improve its branch productivity and profits while maintaining its service quality. It identified over $6 million of annual expense savings not identifiable with traditional analysis. Up to now, DEA has been used to evaluate and compare DMUs in a wide variety of contexts including educational departments in public schools and universities, health care units, prisons, agricultural production, and courts. Many business enterprises are beginning to explore the use of DEA. Several software companies are beginning to develop DEA solutions. Yet a fundamental study of DEA for the softgoods industry is missing and, in particular, when qualitative as well as quantitative measures are involved. Fuzzy mathematics has proven to be useful for handling both quantitative and qualitative linguistic factors in business decision making. Members of the team have been involved in developing prototype tools involving fuzzy modeling for delivery date negotiation and supply chain design for the U.S. softgoods and furniture industries. Once potential partnerships have been identified partnership formation and contract negotiation must take place. Two key issues in this context are how to function so as to increase sales to the ultimate consumer and how to rationally distribute the increased profits, which result among the entities in the supply chain. A potentially fruitful approach to addressing these issues is to view the entities in the supply chain as "players" in a "cooperative game" in which each player has its own perhaps conflicting goals, but there is potential gain for all players through cooperation. In recent years there has been increasing interest in the theory and application of cooperative games. However, little work has been done on cooperative games involving qualitative as well as quantitative data and there have been few if any applications to the softgoods supply chain. Even in the presence of partnerships, individual companies or groups of companies will typically need to acquire materials and/or distribute product to entities outside the partnership. With the rapid development of e-commerce, on-line auctions are becoming a legitimate means for reaching buyers and sellers in today's competitive world marketplace. The nature of on-line auctions is different from that of the traditional marketplace in which companies in the softgoods industry have operated. With the increased globalization of the industry, research into the structure and operation of on-line auctions and their application in the softgoods is needed. Previous work by members of this project team on a prototype software package called the "Due-Date Negotiator" was a first step in developing tools to bring customers and a manufacturer together in a contract for guaranteed delivery date at the best price. Specific objectives of the project include: NTC Project: S01-NS01 (formerly I01-S01) 3 National Textile Center Annual Report: November 2002 1. Investigate existing DEA formulations and expand to best fit softgoods supply chain scenarios. 2. Integrate fuzzy mathematics into DEA to reflect both qualitative and quantitative criteria. 3. Conduct research on fuzzy cooperative game theory and fuzzy auctions for partnership formation and contract negotiation. 4. Identify a specific segment of the softgoods supply chain for an internet-based prototype software system to demonstrate the effectiveness of DEA and cooperative games. II. ACCOMPLISHMENTS TO DATE We have conducted literature surveys on DEA, cooperative games, and auctions. Some of these are summarized in the references at the end of the report. Reference lists can be found at the project web site. For performance assessment of soft goods supply chain firms and potential trading partners, we have developed a number of approaches to solve fuzzy DEA models. To facilitate illustration and explanation, these approaches are implemented in a prototype software package. We have applied game theoretic concepts to the specification and analysis of optimal ordering strategies in several distribution system scenarios. This work is also implemented in prototye software. We have done preliminary work on interval computations for fuzzy relational equations for use in the modeling of cooperative games. We also examined the formulation of auctions using fuzzy sets and fuzzy logic. 1. Fuzzy Data Envelopment Analysis (Fuzzy DEA) Productivity and efficiency analysis plays a significant role for firms or organizations in assessing their performance or that of potential trading partners. A well-known technique for the performance measurement is Data Envelopment Analysis (DEA). It evaluates the performance of business units (DMUs) performing similar functions (i.e., similar resources, or inputs, are consumed, and similar outputs are produced). DEA is a special application of linear programming based on frontier methodology as shown in Figure 1 for the simple case of one input and one output. DEA compares the inputs and outputs of a group of decision-making units and assesses their relative efficiency. A given DMU is inefficient if at least one other DMU can produce the same or more output by using less input. Figure 1. Efficient frontier of DEA NTC Project: S01-NS01 (formerly I01-S01) 4 National Textile Center Annual Report: November 2002 DEA is becoming increasingly popular as a decision making tool owing to its ability to convert multiple inputs and multiple outputs into a single productive efficiency measure, to measure performance based on peer-group comparisons, to identify the most efficient performer(s), and to pinpoint opportunities for improvement. DEA has been shown to be applicable in a wide range of settings, including banking, logistics, public administration, manufacturing, and retailing. In the softgoods industry, DMUs can be manufacturing systems, production processes, distribution centers, or retailers. While the traditional DEA requires precise data for its analysis, the evaluation environment often involves vagueness and uncertainty. As system complexity increases, measuring precise data measurement becomes a difficult task. Furthermore decision-makers often think and operate on the basis of vague linguistic data (e.g., quality is "good", on time performance is "poor"). In a softgoods supply chain, many evaluations must be based on vague and uncertain data and measures. Furthermore, the vagueness and uncertainty is often amplified as information is passed along the chain. In order to provide powerful tools for assessing the performance of a set of DMUs in the softgoods supply chain, we are integrating fuzzy modeling and possibility theory with traditional DEA analysis. Simply introducing fuzzy sets into the traditional DEA models in order to represent vague or imprecise data leads to fuzzy linear programs which are not well-defined due to the ambiguity which occurs in the ranking of fuzzy sets. To deal with this ambiguity, we have developed three new approaches, an alpha-level based approach, a possibility approach and a credibility approach. For the case in which the membership functions of fuzzy data are trapezoidal, these approaches transform fuzzy DEA models into unambiguous linear programming models. The alpha-level approach solves the fuzzy DEA models by a parametric programming approach. At each alpha level (representing degree of data uncertainty), the fuzzy inputs and fuzzy outputs correspond to crisp-valued intervals. An interval-valued linear programming model is created by using these input and output intervals. By considering decision maker’s preference, four different methods, i.e., the best-best method, the worst-worst method, the worst-best method, and the best-worst method, can be generated. With the possibility approach, the uncertainty in fuzzy objectives and fuzzy constraints is handled through the use of possibility measures in possibility theory. Following the possibility approach, fuzzy DEA models can be transformed into well-defined possibility DEA models. The problem of ranking fuzzy sets required by the fuzzy constraints can be handled in a consistent way. Particularly, the possibility approach from both optimistic and pessimistic viewpoints is developed. The credibility approach transforms fuzzy DEA models into well-defined credibility programming models, in which fuzzy variables are replaced by “expected credits” expressed in terms of credibility measures that are based on the possibility and necessity measures. By using the expected credits of fuzzy variables to deal with the uncertainty in fuzzy objectives and fuzzy constraints this approach avoids the problem of ranking fuzzy sets required by the fuzzy constraints. This work is documented in references 5-9 at the end of this report. To communicate our results, a software package utilizing “Fuzzy DEA” has been developed. This software uses fuzzy sets to quantify imprecise and vague data, and analyze the data by the DEA approach. The software provides insights into how well the individual DMUs are performing their activities, as well as how their efficiency can be enhanced. The interface is written in Microsoft Visual Basic and linked with a Microsoft Access database. The Fuzzy DEA engine is written in C++ and dynamically linked to the interface. The software includes several key features helping users to implement the analysis. These features include data displays for data input, graphical tools for setting membership functions of fuzzy inputs and fuzzy outputs, alternative methods for solving fuzzy DEA linear program, and efficiency score NTC Project: S01-NS01 (formerly I01-S01) 5 National Textile Center Annual Report: November 2002 table for data displays. Figures 2 and 3 illustrate the interfaces for input and output (i.e., performance) data entry. Figure 2. DEA Data Interface Figure 3. Performance Measure Specification The fuzziness of inputs and performance measures can be modeled by entering all parameters directly or by simply scrolling to set parameters of the membership functions based on a visual of the function. Membership function types available in this package at this point are triangular and trapezoidal. Figure 4 illustrates the screen that is presented to the users for keying in the input data directly. Figure 5 illustrates setting input membership function data graphically. Figure 4. Manual Membership Function Entry Figure 5. Graphical Membership Function Entry NTC Project: S01-NS01 (formerly I01-S01) 6 National Textile Center Annual Report: November 2002 Another feature of the prototype software is that it allows the users to select from seven alternative methods from among the three solution approaches (i.e., the alpha-level approach, the possibility approach, and the credibility approach) to analyze the performance of DMUs. The alpha-level and possibility alternatives capture the user's outlook (optimistic or pessimistic) relative to the business environment. Figure 6 shows the form for choosing different methods. Efficiency scores are reported in a tabular form, indicating the most efficient DMU(s). Figure 7 illustrates the output of the relative efficiencies of a group of five potential fabric suppliers as determined by the so-called Best-Best method. All of the inputs, outputs and results are stored in the database permitting later manipulation and analysis. Figure 6. Alternative approach form Figure 7. Results from credibility approach Currently, we are developing an internet-based version of the package to allow online access. 2. Cooperative Games "Game theory" refers to the analysis of situations involving conflicting interests (as in business or military strategy) in terms of gains and losses among opposing players. In a cooperative game, groups of players are allowed to form teams or coalitions. Members of a team may cooperate with each other to the mutual benefit of the team. A team may in turn act as a single player in the game to achieve a bigger piece of pie. Contracts are formed within a team to determine players' actions and returns. Some contracts focus on how to increase the total return of this team. Others provide a means to rationally distribute the pie among the players. A softgoods supply chain involves the activity and interaction of many entities. In this situation, each entity is a player in a game. Cooperative game theory is a potentially useful tool for achieving efficient NTC Project: S01-NS01 (formerly I01-S01) 7 National Textile Center Annual Report: November 2002 and effective collaboration in the supply chain. It can be used in selecting partners, structuring contracts, and sharing profit/cost. Cooperative game theory can also be used to optimize the performance of a supply chain, i.e., increase the total profit of the supply chain. In this project, we have conducted a thorough study of the theory of cooperative games for potential application in the softgoods supply chain. We have also explored game theoretic approaches to the determination of optimal ordering strategies of retailers in a distribution system, where the retailers compete for both supplier capacity and for customers, as is common in softgoods scenarios. Specifically, we have analyzed two, two-retailer supply chains with different cost and revenue structures. For the first supply chain, we have been successful in developing an approach to determine the equilibrium ordering strategies of the retailers for the case under which neither is the dominant player. We can also determine the optimal strategies of both the "leader" and the "follower" for the situation in which one retailer (e.g., a Wal-Mart) is dominant. For the second supply chain, we have studied both decentralized and centralized decision making settings. Applying the concept of "channel coordination", we have shown how to set the wholesale price so that the retailers in optimizing their own profit will act so as to optimize the profit of the whole supply chain. As with the DEA models, to communicate our results, we are developing a demonstration software package implementing the “game theoretic approach.” The software provides insights into how well the retailers are performing their activities, as well as how their performance can be enhanced. The user interface is written in Microsoft Visual Basic while the engine is written in Matlab and dynamically linked to the interface. The demo package performs the analysis for each of the two supply chain structures described above. The cost and revenue parameters are entered directly through the interface. For example, the upper section of Figure 8 illustrates the screen that is presented to the users for setting parameters for the second supply chain structure. One feature of the prototype software is that it allows the users to select from among four alternative distributions (Normal, Uniform, Gamma and Beta) for modeling customer demand. These alternatives capture the user's outlook relative to the business environment. The lower section of Figure 8 illustrates the output of the channel coordination approach. It shows the equilibrium stocking policy, the wholesale prices that maximize the performance of the whole supply chain, and the profits of each entity at equilibrium. All of the inputs, outputs and results are stored in a database, permitting later manipulation and analysis. Currently, we are enhancing the demo to include more functionality such as graphical displays. NTC Project: S01-NS01 (formerly I01-S01) 8 National Textile Center Annual Report: November 2002 Figure 8: The Input/Output Interface In many supply chains with competing retailers, the price charged by one retailer affects his/her own demand and the demand at competing retailers. An increase in the price of one retailer may result in the reduction in his/her demand and increases in the demands of competing retailers. In determining the pricing strategy of each retailer, there is a trade-off between unit profit and demand volume. We are currently applying game theory to study the pricing strategies of two competing retailers under both deterministic and stochastic customer demand scenarios. Current results are documented in a working paper cited (reference 3) at the end of the report. As with DEA, when vagueness is taken into account data is represented by interval-valued fuzzy numbers. Preliminary work on interval computations for fuzzy relational equations and applications in cooperative game theory is documented in the dissertation proposal and three papers (references 13-16).