Number Of Item Types Research Articles

Fair and efficient allocation with few agent types, few item types, or small value levels

In fair division of indivisible goods, allocations that satisfy fairness and efficiency simultaneously are highly desired but may not exist or, even if they do exist, are computationally hard to find. Conditions under which such allocations, or allocations satisfying specific levels of fairness and efficiency simultaneously, can be efficiently found have thus been explored. Following this line of research, this study is concerned with the problem in a high-multiplicity setting where instances come with certain parameters, including agent types, item types, and value levels. Particularly, we address two computational problems. First, we wish to compute fair and Pareto-optimal allocations, w.r.t. any of the common fairness criteria: proportionality, maximin share, and max-min fairness. Second, we seek to find a max-min fair allocation that is efficient in the sense of maximizing utilitarian social welfare. We show that the first problem is tractable for most of the fairness criteria when the number of item types is fixed, or when at least two of the three parameters are fixed. For the second problem, we model it as a bi-criteria optimization problem that is solved approximately by determining an approximate Pareto set of bounded size. Our results are obtained based on dynamic programming and linear programming approaches. Our techniques strengthen known methods and can be potentially applied to other notions of fairness and efficiency.

Top-k Recommended Items: Applying Clustering Technique for Recommendation

This research proposes the Top-k Items Recommendation System which uses clustering techniques based on memory-based collaborative filtering technique. Currently, data sparsity and quantity of system are problems in memory-based collaborative filtering technique. We offer recommend or show some items set for user’s preference. In this research, we propose methods for recommended items set to user preference on data sparsity, movie lens datasets (1M) consisting of 671 users and 163,949 product items were used by determining the preference level between 1 and 5 and user satisfaction levels of all 98,903 items being build and test the models. Methods was divided into three parts included 1) Simple Agent Module 2) Neighbor Filtering and 3) Prediction and Recommend. Simple clustering was used to create a system to provide suggestions for sparsity data. Datasets obtained from clustering represented the sample agent of dataset to being create the recommendation system. Datasets were divided into two categories, 1) Traditional Data (TD) and 2) Statistic Data (SD), and each dataset clustered by k-means clustering. The experimental results demonstrated that the number of item types in the system were recommended in the TD and Euclidean (DIS). DIS was used to find the nearest value in TD for the item list recommendation to active users in the system with the a lot of number choice of recommendation system.

Unbounded knapsack problem with controllable rates: the case of a random demand for items

This paper focuses on a dynamic, continuous-time control generalization of the unbounded knapsack problem. This generalization implies that putting items in a knapsack takes time and has a due date. Specifically, the problem is characterized by a limited production horizon and a number of item types. Given an unbounded number of copies of each type of item, the items can be put into a knapsack at a controllable production rate subject to the available capacity. The demand for items is not known until the end of the production horizon. The objective is to collect items of each type in order to minimize shortage and surplus costs with respect to the demand. We prove that this continuous-time problem can be reduced to a number of discrete-time problems. As a result, solvable cases are found and a polynomial-time algorithm is suggested to approximate the optimal solution with any desired precision.

A simple heuristic for maximizing service of carousel storage

We consider a system that stores cases of items. Items are removed from storage in groups. A group consists of a certain number of items of each type. The (integer maximization) problem is to determine how many cases of each type should be stored in order to maximize the number of groups of items that can be retrieved without re-loading. We give a simple heuristic that yields a feasible solution whose error can be bounded. Our method takes only linear time. Scope and purpose Performance of an automated storage and retrieval system such as a carousel depends greatly upon the way it is loaded. Commonly a carousel will be loaded with cases of items that will be retrieved in groups. A group is a certain number of items of each type. For example, a group might constitute the parts needed to manufacture one instance of a product. Typically the carousel operator wants to retrieve as many groups as possible without running out of items of any type. We present a simple heuristic that prescribes how many cases of each item type should be loaded. The number of groups supplied by our solution is close to optimal. The solution is given by explicit equations, and can be computed in time linear in the number of item types.

The cutting stock problem in a hardboard industry: A case study

This paper deals with the problem of cutting rectangular plates into smaller ones in a Brazilian hardboard industry. The problem is to determine the best patterns to be cut by an automated machine composed of a set of circular saws, devices to move and hold the plates, and loading and unloading stations. This machine involves unusual constraints such as bounds on the number of item types and the difference between the largest and the smallest length of the items in the cutting pattern, as well as usual constraints such as availability of longitudinal and transversal saws, orthogonal and two-staged guillotine cuttings without trimming, among others. A particular two-phase column generation procedure is described for the cutting stock formulation of the hardboard industry. Each phase of the procedure is modeled as an integer program and solved by two alternative methods: The first is based on dynamic programming and the second is a simple extension of the implicit enumeration procedure proposed in Gilmore and Gomory [1]. The application of the methodology is illustrated solving several random examples in a microcomputer as well as an actual problem derived of the hardboard industry under consideration.

Assessing teachers' pedagogical content knowledge: Item development issues

The work of Lee Shulman and his colleagues in the Teacher Assessment Program, supported by the Carnegie Corporation, has led to new conceptions of teaching and teacher assessment (Shulman, 1986, 1987a, 1987b). A key feature of these new conceptions is the proposition that pedagogical content knowledge is an important category of the knowledge base for teaching (Shulman, 1987a). This article describes some issues related to the development of test items to assess pedagogical content knowledge for an elementary teacher licensure test, the Connecticut Elementary Education Certification Examination. Following a brief description of the exam, pedagogical content knowledge is defined. Next is a discussion of three issues that arose when attempting to develop a teacher licensure test that includes assessment of pedagogical content knowledge. Finally, a number of item types that seem to be useful for assessing pedagogical content knowledge are described briefly.