scholarly journals Unitary Owen Points in Cooperative Lot-Sizing Models with Backlogging

Mathematics ◽  
2021 ◽  
Vol 9 (8) ◽  
pp. 869
Author(s):  
Luis A. Guardiola ◽  
Ana Meca ◽  
Justo Puerto
Keyword(s):  
Cost Sharing ◽  
Lot Sizing ◽  
Operating Cost ◽  
Sufficient Conditions ◽  
Planning Horizon ◽  
New Family ◽  
Production Inventory ◽  
Necessary And Sufficient ◽  
Stable Allocations ◽  
Inventory Games

This paper analyzes cost sharing in uncapacitated lot-sizing models with backlogging and heterogeneous costs. It is assumed that several firms participate in a consortium aiming at satisfying their demand over the planning horizon with minimal operating cost. Each individual firm has its own ordering channel and holding technology, but cooperation with other firms consists in sharing that information. Therefore, the firms that cooperate can use the best ordering channels and holding technology among members of the consortium. This mode of cooperation is stable. in that allocations of the overall operating cost exist, so that no group of agents benefit from leaving the consortium. Our contribution in the current paper is to present a new family of cost sharing allocations with good properties for enforcing cooperation: the unitary Owen points. Necessary and sufficient conditions are provided for the unitary Owen points to belong to the core of the cooperative game. In addition, we provide empirical evidence, through simulation, showing that, in randomly-generated situations, the above condition is fulfilled in 99% of the cases. Additionally, a relationship between lot-sizing games and a certain family of production-inventory games, through Owen’s points of the latter, is described. This interesting relationship enables easily constructing a variety of coalitionally stable allocations for cooperative lot-sizing models.

Study on the Bounded Inventory Model with Returning Items and Disposals

2010 ◽  
Vol 102-104 ◽  
pp. 920-925
Author(s):  
Neng Min Wang ◽  
Zheng Wen He ◽  
Lin Yan Sun
Keyword(s):  
Lot Sizing ◽  
Dynamic Programming Algorithm ◽  
Planning Horizon ◽  
Cost Functions ◽  
Programming Algorithm ◽  
Inventory Level ◽  
Lot Sizing Problem ◽  
Production Inventory ◽  
Dynamic Lot Sizing ◽  
Inventory Holding

This paper addresses a dynamic lot sizing problem with mixed returning items and disposals and bounded inventory. The returning items mean that returns are in good enough condition to re-enter the inventory supply stream. The producing, the holding, backlogging and disposals cost functions are concave cost functions. Furthermore, backlogging level and inventory level at each period is limited. The goal is to minimize the total cost of production, inventory holding/backlogging and disposal. A dynamic programming algorithm with complexity O(T3) is developed to solve this model, where T is the length of the planning horizon.

scholarly journals Generating Function Approach to the Derivation of Higher-Order Iterative Methods for Solving Nonlinear Equations

2018 ◽  
Vol 173 ◽  
pp. 03024
Author(s):  
Tugal Zhanlav ◽  
Ochbadrakh Chuluunbaatar ◽  
Vandandoo Ulziibayar
Keyword(s):  
Iterative Methods ◽  
Generating Function ◽  
Generating Functions ◽  
Order Of Convergence ◽  
Sufficient Conditions ◽  
Optimal Order ◽  
Eighth Order ◽  
New Family ◽  
Special Cases ◽  
Necessary And Sufficient

In this paper we propose a generating function method for constructing new two and three-point iterations withp(p= 4, 8) order of convergence. This approach allows us to derive a new family of optimal order iterative methods that include well known methods as special cases. Necessary and sufficient conditions forp-th (p= 4, 8) order convergence of the proposed iterations are given in terms of parameters τnand αn. We also propose some generating functions for τnand αn. We develop a unified representation of all optimal eighth-order methods. The order of convergence of the proposed methods is confirmed by numerical experiments.

scholarly journals Characterizations of the symmetrized polydisc via another family of domains

2021 ◽  
pp. 2150036
Author(s):  
Sourav Pal ◽  
Samriddho Roy
Keyword(s):  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Linear Transformations ◽  
New Family ◽  
Spectral Interpolation ◽  
Polynomially Convex ◽  
Symmetrized Polydisc ◽  
Necessary And Sufficient

We find new characterizations for the points in the symmetrized polydisc [Formula: see text], a family of domains associated with the spectral interpolation, defined by [Formula: see text] We introduce a new family of domains which we call the extended symmetrized polydisc [Formula: see text], and define in the following way: [Formula: see text] [Formula: see text] We show that [Formula: see text] for [Formula: see text] and that [Formula: see text] for [Formula: see text]. We first obtain a variety of characterizations for the points in [Formula: see text] and we apply these necessary and sufficient conditions to produce an analogous set of characterizations for the points in [Formula: see text]. Also, we obtain similar characterizations for the points in [Formula: see text], where [Formula: see text]. A set of [Formula: see text] fractional linear transformations plays central role in the entire program. We also show that for [Formula: see text], [Formula: see text] is nonconvex but polynomially convex and is starlike about the origin but not circled.

Titik Setimbang Nash pada Permainan Linear Kuadratik Non-kooperatif dengan Asumsi Keseluruhan Pemain dapat Menstabilkan Sistem

2017 ◽  
Vol 1 (2) ◽  
pp. 211-224
Author(s):  
Ezhari Asfa’ani
Keyword(s):  
Quadratic Differential ◽  
Information Structure ◽  
Nash Equilibria ◽  
Sufficient Conditions ◽  
Planning Horizon ◽  
Open Loop ◽  
Linear Quadratic ◽  
Linear Quadratic Differential Games ◽  
Necessary And Sufficient ◽  
Infinite Planning Horizon

We discuss about Nash equilibria for the linear quadratic differential game for an infinite planning horizon. We consider an open-loop information structure. In the standard literature this problem is solved under the assumption and provide both necessary and sufficient conditions for existence of Nash equilibria for this game under the assumption that the system as a whole is stabilizable.      Keywords: linear quadratic differential games, open-loop information structure

scholarly journals Some new harmonic mappings convex in one direction and their convolution

Filomat ◽  
2019 ◽  
Vol 33 (19) ◽  
pp. 6131-6139
Author(s):  
Chinu Singla ◽  
Sushma Gupta ◽  
Sukhjit Singh
Keyword(s):  
Unit Disc ◽  
Sufficient Conditions ◽  
Harmonic Mappings ◽  
Open Unit ◽  
Open Unit Disc ◽  
Hadamard Products ◽  
New Family ◽  
Convex In One Direction ◽  
A New Technique ◽  
Necessary And Sufficient

In the present article, we construct a new family of locally univalent and sense preserving harmonic mappings by considering a suitable transformation of normalized univalent analytic functions defined in the open unit disc D. We present necessary and sufficient conditions for the functions of this new family to be univalent. Apart from studying properties of this new family, results about the convolutions or Hadamard products of functions from this family with some suitable analytic or harmonic mappings are proved by introducing a new technique which can also be used to simplify the proofs of earlier known results on convolutions of harmonic mappings. The technique presented also enables us to generalize existing such results.

A new family of positive recurrent semimartingale reflecting Brownian motions in an orthant

2020 ◽  
Vol 28 (3) ◽  
pp. 177-181
Author(s):  
Abdelhak Yaacoubi
Keyword(s):  
Queueing Networks ◽  
Diffusion Processes ◽  
Three Dimensional ◽  
Sufficient Conditions ◽  
Brownian Motions ◽  
Nonnegative Orthant ◽  
New Family ◽  
Standard Problem ◽  
Positive Recurrent ◽  
Necessary And Sufficient

AbstractSemimartingale reflecting Brownian motions (SRBMs) are diffusion processes, which arise as approximations for open d-station queueing networks of various kinds. The data for such a process are a drift vector θ, a nonsingular {d\times d} covariance matrix Δ, and a {d\times d} reflection matrix R. The state space is the d-dimensional nonnegative orthant, in the interior of which the processes evolve according to a Brownian motions, and that reflect against the boundary in a specified manner. A standard problem is to determine under what conditions the process is positive recurrent. Necessary and sufficient conditions are formulated for some classes of reflection matrices and in two- and three-dimensional cases, but not more. In this work, we identify a new family of reflection matrices R for which the process is positive recurrent if and only if the drift {\theta\in\mathring{\Gamma}}, where {\mathring{\Gamma}} is the interior of the convex wedge generated by the opposite column vectors of R.

scholarly journals Feedback saddle point equilibria for soft-constrained zero-sum linear quadratic descriptor differential game

2013 ◽  
Vol 23 (4) ◽  
pp. 473-493
Author(s):  
Muhammad Wakhid Musthofa ◽  
Jacob C. Engwerda ◽  
Ari Suparwanto ◽  
Keyword(s):  
Saddle Point ◽  
Sufficient Conditions ◽  
Planning Horizon ◽  
Descriptor Systems ◽  
Linear Quadratic ◽  
Linear Quadratic Differential Games ◽  
Zero Sum ◽  
Necessary And Sufficient ◽  
Saddle Point Equilibrium ◽  
Infinite Planning Horizon

Abstract In this paper the feedback saddle point equilibria of soft-constrained zero-sum linear quadratic differential games for descriptor systems that have index one will be studied for a finite and infinite planning horizon. Both necessary and sufficient conditions for the existence of a feedback saddle point equilibrium are considered

The extinction time of a general birth and death process with catastrophes

1986 ◽  
Vol 23 (04) ◽  
pp. 851-858 ◽  
Author(s):  
P. J. Brockwell
Keyword(s):  
Laplace Transform ◽  
Size Distribution ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Death Process ◽  
Extinction Time ◽  
Birth And Death Process ◽  
Different Types ◽  
The Laplace Transform ◽  
Necessary And Sufficient

The Laplace transform of the extinction time is determined for a general birth and death process with arbitrary catastrophe rate and catastrophe size distribution. It is assumed only that the birth rates satisfyλ0= 0,λj> 0 for eachj> 0, and. Necessary and sufficient conditions for certain extinction of the population are derived. The results are applied to the linear birth and death process (λj=jλ, µj=jμ) with catastrophes of several different types.

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