An outranking-based fuzzy logic model for collaborative group preferences

Some ideas coming from Multi Criteria Decision Aid are here extended to group decision. We present a logical model in order to reflect the degree of truth of the following predicate “group G considers that option x is at least as good as y.” The proposal considers the strength of the majority using its number and the intensity of its preference, and it also acknowledges the importance of the minorities of a certain numerical significance that manifest an intense disagreement with the predicate of the outranking. The effects of the “majority dictatorship” are restricted. Since it considers simultaneously the strength of the majority, the importance of unhappy minorities, and the intensity of the preference/opposition, this model exhibits desirable qualities of the classic methods by Condorcet and Borda. This model can be used to solve problems regarding selection, ranking, classification, and sorting. Various examples are given, which show the quality of the solutions that were obtained.     

Secure collaborative supply chain planning and inverse optimization – The JELS model

It is a well-acknowledged fact that collaboration between different members of a supply chain yields a significant potential to increase overall supply chain performance. Sharing private information has been identified as prerequisite for collaboration and, at the same time, as one of its major obstacles. One potential avenue for overcoming this obstacle is Secure Multi-Party Computation (SMC). SMC is a cryptographic technique that enables the computation of any (well-defined) mathematical function by a number of parties without any party having to disclose its input to another party. In this paper, we show how SMC can be successfully employed to enable joint decision-making and benefit sharing in a simple supply chain setting. We develop secure protocols for implementing the well-known “Joint Economic Lot Size (JELS) Model” with benefit sharing in such a way that none of the parties involved has to disclose any private (cost and capacity) data. Thereupon, we show that although computation of the model’s outputs can be performed securely, the approach still faces practical limitations. These limitations are caused by the potential of “inverse optimization”, i.e., a party can infer another party’s private data from the output of a collaborative planning scheme even if the computation is performed in a secure fashion. We provide a detailed analysis of “inverse optimization” potentials and introduce the notion of “stochastic security”, a novel approach to assess the additional information a party may learn from joint computation and benefit sharing. Based on our definition of “stochastic security” we propose a stochastic benefit sharing rule, develop a secure protocol for this benefit sharing rule, and assess under which conditions stochastic benefit sharing can guarantee secure collaboration.     

Does collaborative and experiential work influence the solution of real-context estimation problems? A study with prospective teachers

Although it is a challenge for primary school teachers, real-context estimation problems can be used as an introduction to mathematical modeling. With this aim, we designed a two-phase activity: in the first phase, 224 prospective teachers developed individual action plans to solve a sequence of real-context estimation problems in the classroom; in the second phase, they completed the solution of the same problems working in groups in the real location where the four problems were contextualized. A comparative study showed that, in the second phase, prospective teachers were able to adapt their solutions to contextual features detected in situ that had not been anticipated in the action plans developed during the first phase. Two-phase modeling activities, which permit a comparison of different perspectives on problems, facilitate the experience of collaborative work. These activities could be incorporated into prospective teachers’ initial training as a useful resource for improving their problem-solving expertise.     

Cost allocation in the establishment of a collaborative transportation agreement—an application in the furniture industry

Transportation is an important part of the Canadian furniture industry supply chain. Even though there are often several manufacturers shipping in the same market region, coordination between two or more manufacturers is rare. Recently, important potential cost savings and delivery time reduction have been identified through transportation collaboration. In this paper we propose and test on a case study involving four furniture companies, a logistics scenario that allows transportation collaboration. Moreover, we address the key issue of cost savings sharing, especially when heterogeneous requirements by each collaborating company impact the cost-savings. To do so, we propose a new cost allocation method that is validated through a case study. Sensibility analysis and details about the actual outcome of the case study complete the discussion.     

Teachers’ mathematical problem-solving knowledge: In what way is it constructed during teachers’ collaborative work?

This research aims to analyze the type of mathematics problem-solving knowledge for teaching used when working collaboratively in a Lesson Study (LS) process and examine how dialogic interactions contribute to knowledge construction. Five meetings during one LS cycle of a group of eight Swiss primary teachers were video recorded, transcribed and coded with the help of qualitative data analysis software. This analysis is conducted by crossing theoretical frameworks from two different fields in education, namely mathematics education and dialogic analysis. The mixed-method uses quantitative analysis with Markov chains and cross-tables, as well as qualitative analysis at micro-, meso- and macro-levels. This research suggests that participants collectively use their mathematics and their problem-solving content knowledge to focus on pedagogical problem-solving knowledge, that they navigate between different knowledge levels and that the roles of teachers and facilitators are differentiated but are also coequal.     

Modeling the synergy level in a vertical collaborative supply chain through the IMP interaction model and DEA framework

This work develops a mathematical programming model that characterizes the main variables present in the interaction dynamics of each agent in a collaborative vertical logistical system, such as a supply chain, and measures the synergy level of such system. The model is based on the interaction model developed by the IMP (Industrial Marketing and Purchasing) group and also on the DEA (Data Envelopment Analysis) framework. The basics of these two approaches allow modeling of the characteristics of an agent as well as the collaborative relationships with other agents within the chain. The model was validated using information of supply chain of leather and its products, classified by DANE (Departamento Nacional de Estadistica—Colombia) as the sector CIIU323.