Cost allocation and convex data envelopment

This paper considers allocation rules. First, we demonstrate that costs allocated by the Aumann–Shapley and the Friedman–Moulin cost allocation rules are easy to determine in practice using convex envelopment of registered cost data and parametric programming. Second, from the linear programming problems involved it becomes clear that the allocation rules, technically speaking, allocate the non-zero value of the dual variable for a convexity constraint on to the output vector. Hence, the allocation rules can also be used to allocate inefficiencies in non-parametric efficiency measurement models such as Data Envelopment Analysis (DEA). The convexity constraint of the BCC model introduces a non-zero slack in the objective function of the multiplier problem and we show that the cost allocation rules discussed in this paper can be used as candidates to allocate this slack value on to the input (or output) variables and hence enable a full allocation of the inefficiency on to the input (or output) variables as in the CCR model.     

Shelf-space allocation of national and private brands

We propose a game-theoretic model in which one national-brand manufacturer, acting as a leader, maximizes her own profit and one retailer, selling the national brand and her private label and acting as a follower, maximizes her category profit. We characterize the resulting Stackelberg equilibrium in terms of the amount of shelf space allocated to these brands as well as their prices. The results suggest that the allocation of the shelf space depends on the quality of the private label. In our framework, quality is measured by the baseline sales (or brand equity), the degree of brand substitution and the price positioning.     

Multirate multicast service provisioning I: an algorithm for optimal price splitting along multicast trees

In this two-part paper we present a general framework for addressing the optimal rare control problem in multirate multicast where the objective is the maximization of a social welfare function expressed by the sum of the users’ utility functions. Specifically, we propose a market-based mechanism that satisfies the informational constraints imposed by the decentralization of information in multirate multicast service provisioning, and achieves an optimal solution to the corresponding centralized optimization problem. In Part I we discover properties of an optimal solution to the centralized problem. Based on these properties, we develop a distributed algorithm that determines how link prices are split among users whose connections along a multicast tree share the same link.     

R-D optimized tree-structured compression algorithms with discrete directional wavelet transform

A new image coding method based on discrete directional wavelet transform (S-WT) and quad-tree decomposition is proposed here. The S-WT is a kind of transform proposed in [V. Velisavljevic, B. Beferull-Lozano, M. Vetterli, P.L. Dragotti, Directionlets: anisotropic multidirectional representation with separable filtering, IEEE Trans. Image Process. 15(7) (2006)], which is based on lattice theory, and with the difference with the standard wavelet transform is that the former allows more transform directions. Because the directional property in a small region is more regular than in a big block generally, in order to sufficiently make use of the multidirectionality and directional vanishing moment (DVM) of S-WT, the input image is divided into many small regions by means of the popular quad-tree segmentation, and the splitting criterion is on the rate-distortion sense. After the optimal quad-tree is obtained, by means of the embedded property of SPECK, a resource bit allocation algorithm is fast implemented utilizing the model proposed in [M. Rajpoot, Model based optimal bit allocation, in: IEEE Data Compression Conference, 2004, Proceedings, DCC 2004.19]. Experiment results indicate that our algorithms perform better compared to some state-of-the-art image coders.     

On the manpower allocation within matrix organization: A fuzzy linear programming approach

In this study, we provide a framework of fuzzy linear programming model for the function management division dealing with manpower allocation problem within matrix organization. The proposed model reveals how the function management division seeks a minimized cost and satisfies with the requirement of subordinate functional departments as far as possible under limited manpower and project budget. Numerical example illustrates that an adjustable parameter in the proposed model can be employed by the function management division to generate many different alternatives and grasp the degree of satisfaction of each subordinate functional department.     

A joint optimisation model for inventory replenishment,product assortment,shelf space and display area allocation decisions

In this paper, we propose an optimisation model to determine the product assortment, inventory replenishment, display area and shelf space allocation decisions that jointly maximize the retailer’s profit under shelf space and backroom storage constraints. The variety of products to be displayed in the retail store, their display locations within the store, their ordering quantities, and the allocated shelf space in each display area are considered as decision variables to be determined by the proposed integrated model. In the model formulation, we include the inventory investment costs, which are proportional to the average inventory, and storage and display costs as components of the inventory costs and make a clear distinction between showroom and backroom inventories. We also consider the effect of the display area location on the item demand. The developed model is a mixed integer non-linear program that we solved using LINGO software. Numerical examples are used to illustrate the developed model.     

SRPT applied to bandwidth-sharing networks

We consider bandwidth-sharing networks, and show how the SRPT (Shortest Remaining Processing Time) discipline can be used in order to improve the delay performance of the system. Our main idea is not to use SRPT globally between the traffic classes, which has been shown to induce instability, but rather deploy SRPT only locally within each traffic class. We show that with this approach, the performance of any stable bandwidth allocation policy can be improved. Importantly, our result is valid for any network topology and any flow size distribution. A numerical study is included to illustrate the results.     

A capital allocation based on a solvency exchange option

In this paper we propose a new capital allocation method based on an idea of [Sherris, M., 2006. Solvency, capital allocation and fair rate of return in insurance. J. Risk Insurance 73 (1), 71-96]. The proposed method explicitly accommodates the notion of limited liability of the shareholders. We show how the allocated capital can be decomposed, so that each stakeholder can have a clearer understanding of their contribution. We also challenge the no undercut principle, one of the widely accepted allocation axioms, and assert that this axiom is merely a property that certain allocation methods may or may not meet.     

DOES A RENEWABLE NATURAL RESOURCE USUALLY HAVE MANY NEAR‐OPTIMAL ALLOCATION PATHS?

ABSTRACT. Utilizing a deterministic single‐species computational renewable natural resource model, it is found that there exist many dynamic allocation paths near‐optimal to the efficient path, where the latter maximizes conventionally‐defined social welfare. Some alternative paths involve substantial trading of surplus over time among market participants and hold different implications for income distribution. Universality of findings cannot be asserted, but the results are intuitively plausible and suggest that multiple near‐optimal allocation paths may exist in related models as well. Existence of many near‐optimal paths holds significant implications for theory and policy.     

Basin-wide cooperative water resources allocation

The Cooperative Water Allocation Model (CWAM) is designed within a general mathematical programming framework for modeling equitable and efficient water allocation among competing users at the basin level and applied to a large-scale water allocation problem in the South Saskatchewan River Basin located in southern Alberta, Canada. This comprehensive model consists of two main steps: initial water rights allocation and subsequent water and net benefits reallocation. Two mathematical programming approaches, called the priority-based maximal multiperiod network flow (PMMNF) method and the lexicographic minimax water shortage ratios (LMWSR) technique, are developed for use in the first step. Cooperative game theoretic approaches are utilized to investigate how the net benefits can be fairly reallocated to achieve optimal economic reallocation of water resources in the second step. The application of this methodology to the South Saskatchewan River Basin shows that CWAM can be utilized as a tool for promoting the understanding and cooperation of water users to achieve maximum welfare in a river basin and minimize the potential damage caused by water shortages, through water rights allocation, and water and net benefit transfers among water users under a regulated water market or administrative allocation mechanism.