Optimal production lot sizing with backlogging, random defective rate, and rework derived without derivatives

2009 ◽  
Vol 223 (8) ◽  
pp. 1081-1084 ◽  
Author(s):  
K N F Leung
Keyword(s):  
Lot Sizing ◽  
Sufficient Conditions ◽  
Algebraic Method ◽  
Solution Procedure ◽  
Natural Manner ◽  
First Order ◽  
Economic Production ◽  
Perfect Squares ◽  
Unity Decomposition ◽  
Second Order Sufficient Conditions

Several researchers have recently derived formulae for economic production quantities (EPQs) with some variants without reference to the use of derivatives, neither for first-order necessary conditions nor for second-order sufficient conditions. In addition, this algebraic derivation immediately produces an individual formula for evaluating the minimum expected annual cost. The purpose of this note is twofold. First, this study extends earlier results to the EPQ formula, taking the imperfect rework process into account. Second, the algebraic complete-squares and perfect-squares methods can readily derive optimal expressions from an objective function in a more simple, direct, and natural manner than the algebraic method of unity decomposition adopted earlier. A numerical example has been solved to illustrate the solution procedure, and some remarks are made to conclude the note.

scholarly journals Conceptual Analysis and Empirical Observations of Animal Minds

Philosophia ◽  
2021 ◽  
Author(s):  
Ricardo Parellada
Keyword(s):  
Conceptual Analysis ◽  
Animal Cognition ◽  
Sufficient Conditions ◽  
Second Order ◽  
Alarm Calls ◽  
Vervet Monkeys ◽  
Animal Minds ◽  
First Order

AbstractThe relation between conceptual analysis and empirical observations when ascribing or denying concepts and beliefs to non-human animals is not straightforward. In order to reflect on this relation, I focus on two theoretical proposals (Davidson’s and Allen’s) and one empirical case (vervet monkeys’ alarm calls), the three of which are permanently discussed and considered in the literature on animal cognition. First, I review briefly Davidson’s arguments for denying thought to non-linguistic animals. Second, I review Allen’s criteria for ascribing concepts to creatures capable of correcting their discriminatory powers by taking into account their previous errors. Allen affirms that this is an empirical proposal which offers good reasons, but not necessary or sufficient conditions, for concept attribution. Against Allen, I argue that his important proposal is not an empirical, but a conceptual one. Third, I resort to vervet monkeys to show that Allen’s criteria, and not Davidson’s, are very relevant for ascribing first-order and denying second-order beliefs to this species and thus make sense of the idea of animal cognition.

Resolution systems and their applications I

1980 ◽  
Vol 3 (2) ◽  
pp. 235-268
Author(s):  
Ewa Orłowska
Keyword(s):  
Theorem Proving ◽  
Sufficient Conditions ◽  
Predicate Calculus ◽  
Resolution Method ◽  
First Order ◽  
Deductive Systems ◽  
Resolution System ◽  
Resolution Principle ◽  
Necessary And Sufficient ◽  
Classical Predicate

The central method employed today for theorem-proving is the resolution method introduced by J. A. Robinson in 1965 for the classical predicate calculus. Since then many improvements of the resolution method have been made. On the other hand, treatment of automated theorem-proving techniques for non-classical logics has been started, in connection with applications of these logics in computer science. In this paper a generalization of a notion of the resolution principle is introduced and discussed. A certain class of first order logics is considered and deductive systems of these logics with a resolution principle as an inference rule are investigated. The necessary and sufficient conditions for the so-called resolution completeness of such systems are given. A generalized Herbrand property for a logic is defined and its connections with the resolution-completeness are presented. A class of binary resolution systems is investigated and a kind of a normal form for derivations in such systems is given. On the ground of the methods developed the resolution system for the classical predicate calculus is described and the resolution systems for some non-classical logics are outlined. A method of program synthesis based on the resolution system for the classical predicate calculus is presented. A notion of a resolution-interpretability of a logic L in another logic L ′ is introduced. The method of resolution-interpretability consists in establishing a relation between formulas of the logic L and some sets of formulas of the logic L ′ with the intention of using the resolution system for L ′ to prove theorems of L. It is shown how the method of resolution-interpretability can be used to prove decidability of sets of unsatisfiable formulas of a given logic.

scholarly journals Oscillatory Behaviour of a First-Order Neutral Differential Equation in relation to an Old Open Problem

2020 ◽  
Vol 2020 ◽  
pp. 1-11
Author(s):  
K. C. Panda ◽  
R. N. Rath ◽  
S. K. Rath
Keyword(s):  
Differential Equation ◽  
Delay Differential Equation ◽  
Sufficient Conditions ◽  
Continuous Functions ◽  
Oscillatory Behaviour ◽  
Neutral Delay ◽  
First Order ◽  
Neutral Delay Differential Equation ◽  
Delay Differential ◽  
Oscillation And Nonoscillation

In this paper, we obtain sufficient conditions for oscillation and nonoscillation of the solutions of the neutral delay differential equation yt−∑j=1kpjtyrjt′+qtGygt−utHyht=ft, where pj and rj for each j and q,u,G,H,g,h, and f are all continuous functions and q≥0,u≥0,ht<t,gt<t, and rjt<t for each j. Further, each rjt, gt, and ht⟶∞ as t⟶∞. This paper improves and generalizes some known results.

System Properties of One-Dimensional Distributed Systems

1977 ◽  
Vol 99 (2) ◽  
pp. 85-90 ◽  
Author(s):  
L. S. Bonderson
Keyword(s):  
Distributed Systems ◽  
Sufficient Conditions ◽  
State Variables ◽  
One Dimensional ◽  
First Order ◽  
Lumped Element ◽  
Order Form ◽  
Power Product ◽  
System Properties ◽  
Necessary And Sufficient

The system properties of passivity, losslessness, and reciprocity are defined and their necessary and sufficient conditions are derived for a class of linear one-dimensional multipower distributed systems. The utilization of power product pairs as state variables and the representation of the dynamics in first-order form allows results completely analogous to those for lumped-element systems.

scholarly journals The effect of consolidated periods in heterogeneous lot-sizing games

Top ◽  
2021 ◽  
Author(s):  
Luis A. Guardiola ◽  
Ana Meca ◽  
Justo Puerto
Keyword(s):  
Time Horizon ◽  
Lot Sizing ◽  
Sufficient Conditions ◽  
Minimum Cost ◽  
Cost Allocations ◽  
Lot Sizing Problem ◽  
Stable Family ◽  
Finite Time Horizon ◽  
The Stability ◽  
Operation Cost

AbstractWe consider a cooperative game defined by an economic lot-sizing problem with heterogeneous costs over a finite time horizon, in which each firm faces demand for a single product in each period and coalitions can pool orders. The model of cooperation works as follows: ordering channels and holding and backlogging technologies are shared among the members of the coalitions. This implies that each firm uses the best ordering channel and holding technology provided by the participants in the consortium. That is, they produce, hold inventory, pay backlogged demand and make orders at the minimum cost of the coalition members. Thus, firms aim at satisfying their demand over the planing horizon with minimal operation cost. Our contribution is to show that there exist fair allocations of the overall operation cost among the firms so that no group of agents profit from leaving the consortium. Then we propose a parametric family of cost allocations and provide sufficient conditions for this to be a stable family against coalitional defections of firms. Finally, we focus on those periods of the time horizon that are consolidated and we analyze their effect on the stability of cost allocations.

scholarly journals El autoconocimiento de las creencias: una objeción al método de la transparencia

2019 ◽  
pp. 429
Author(s):  
Javier Vidal
Keyword(s):  
Practical Reasoning ◽  
Sufficient Conditions ◽  
Second Order ◽  
Mental Life ◽  
The Unconscious ◽  
First Order ◽  
Rational Deliberation ◽  
Self Knowledge

According to the method of transparency, genuine self-knowledge is the outcome of an inference from world to mind. A. Byrne (2018) has developed a theory in which the method of transparency consists in following an epistemic rule in order to form self-verifying second-order beliefs. In this paper, I argue that Byrne’s theory does not establish sufficient conditions for having self-knowledge of first-order beliefs. Examining a case of self-deception, I strive to show that following such a rule might not result in self-knowledge when one is involved in rational deliberation. In the case under consideration, one precisely comes to believe that one believes that p without coming to believe that p. The justification for one’s not forming the belief that p with its distinctive causal pattern in mental life and behaviour, is that one already had the unconscious belief that not-p, a belief that is not sensitive to the principles governing theoretical and practical reasoning.

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