Squiggly Economics

2020 ◽  
pp. 87-122
Author(s):  
Robert G. Chambers
Keyword(s):  
Optimization Problems ◽  
Cost Minimization ◽  
Profit Maximization ◽  
Relevant Information ◽  
Revenue Maximization ◽  
Conjugate Duality ◽  
Economic Optimization ◽  
Duality Results ◽  
Dual Representations

Three generic economic optimization problems (expenditure (cost) minimization, revenue maximization, and profit maximization) are studied using the mathematical tools developed in Chapters 2 and 3. Conjugate duality results are developed for each. The resulting dual representations (E(q;y), R(p,x), and π‎(p,q)) are shown to characterize all of the economically relevant information in, respectively, V(y), Y(x), and Gr(≽(y)). The implications of different restrictions on ≽(y) for the dual representations are examined.

scholarly journals Duality Theorems for (ρ,ψ,d)-Quasiinvex Multiobjective Optimization Problems with Interval-Valued Components

Mathematics ◽  
2021 ◽  
Vol 9 (8) ◽  
pp. 894
Author(s):  
Savin Treanţă
Keyword(s):  
Multiobjective Optimization ◽  
Optimization Problems ◽  
Integral Functional ◽  
Multiple Integral ◽  
Control Problems ◽  
Duality Theorems ◽  
New Class ◽  
Duality Results ◽  
Multiobjective Optimization Problems ◽  
Interval Valued

The present paper deals with a duality study associated with a new class of multiobjective optimization problems that include the interval-valued components of the ratio vector. More precisely, by using the new notion of (ρ,ψ,d)-quasiinvexity associated with an interval-valued multiple-integral functional, we formulate and prove weak, strong, and converse duality results for the considered class of variational control problems.

scholarly journals Study on Profitable Shared Parking Management Based on Day-to-Day Evolution Model

2021 ◽  
Vol 33 (1) ◽  
pp. 17-33
Author(s):  
Duo Xu ◽  
Huijun Sun
Keyword(s):  
Urban Area ◽  
Optimal Allocation ◽  
Cost Minimization ◽  
Profit Maximization ◽  
Evolution Model ◽  
Residential Areas ◽  
Short Supply ◽  
Parking Lots ◽  
Morning Commute ◽  
Quantity Control

Parking problems are getting increasingly serious in the urban area. However, the parking spots in the urban area are underutilized rather than really scarce. There is a large number of private spots in the residential areas that have the potential of being shared. Due to its private nature, shared parking is usually operated by a profitable mode. To study the utilization of shared parking and its impact on the morning commute, this paper proposes an evolution model. The supply side is a profit-chasing manager who decides on the selling prices and the business scale, while the demand side refers to travellers who respond to costs and choose the trip mode. By analysing the behaviour (strategy) of both sides, the study covers: 1 - the attraction and competition between parking lots and trip modes, 2 - the utilization and user composition of the parking lots. By inducing two numerical examples, the conclusions are that 1 - managers can achieve maximum profit and optimal allocation through price adjustment and quantity control; 2 - publicity (system cost minimization) and profitability (profit maximization) are consistent under certain threshold conditions; 3 - competition exists between parking lots as well as trip modes; some parking lots are even in short supply; profitable management does not create a market monopoly.

Constrained Economic Optimization of Shell-and-Tube Heat Exchangers Using a Self-Adaptive Multipopulation Elitist-Jaya Algorithm

2018 ◽  
Vol 10 (4) ◽  
Author(s):  
R. Venkata Rao ◽  
Ankit Saroj
Keyword(s):  
Optimization Problems ◽  
Search Algorithm ◽  
Harmony Search ◽  
Benchmark Problems ◽  
Jaya Algorithm ◽  
Economic Optimization ◽  
Setup Cost ◽  
Tube Heat Exchanger ◽  
Shell And Tube ◽  
Self Adaptive

This paper explores the use of a self-adaptive multipopulation elitist (SAMPE) Jaya algorithm for the economic optimization of shell-and-tube heat exchanger (STHE) design. Three different optimization problems of STHE are considered in this work. The same problems were earlier attempted by other researchers using genetic algorithm (GA), particle swarm optimization (PSO) algorithm, biogeography-based optimization (BBO), imperialist competitive algorithm (ICA), artificial bee colony (ABC), cuckoo-search algorithm (CSA), intelligence-tuned harmony search (ITHS), and cohort intelligence (CI) algorithm. The Jaya algorithm is a newly developed algorithm and it does not have any algorithmic-specific parameters to be tuned except the common control parameters of number of iterations and population size. The search mechanism of the Jaya algorithm is upgraded in this paper by using the multipopulation search scheme with the elitism. The SAMPE-Jaya algorithm is proposed in this paper to optimize the setup cost and operational cost of STHEs simultaneously. The performance of the proposed SAPME-Jaya algorithm is tested on four well-known constrained, ten unconstrained standard benchmark problems, and three STHE design optimization problems. The results of computational experiments proved the superiority of the proposed method over the latest reported methods used for the optimization of the same problems.

scholarly journals Interval-Valued Optimization Problems Involvingα,ρ-Right Upper-Dini-Derivative Functions

2014 ◽  
Vol 2014 ◽  
pp. 1-5 ◽  
Author(s):  
Vasile Preda
Keyword(s):  
Optimization Problems ◽  
Directional Derivative ◽  
Efficient Solutions ◽  
Sufficient Optimality Conditions ◽  
Dini Derivative ◽  
Duality Results ◽  
Multiobjective Problem ◽  
Necessary And Sufficient ◽  
Generalized Convexities ◽  
Interval Valued

We consider an interval-valued multiobjective problem. Some necessary and sufficient optimality conditions for weak efficient solutions are established under new generalized convexities with the tool-right upper-Dini-derivative, which is an extension of directional derivative. Also some duality results are proved for Wolfe and Mond-Weir duals.

Inventory Replenishment for Profit Maximization over a Finite Horizon under One-time Cost Changes

2018 ◽  
Vol 19 (3_suppl) ◽  
pp. S235-S248
Author(s):  
F. J. Arcelus ◽  
T. P. M. Pakkala ◽  
G. Srinivasan
Keyword(s):  
Cost Minimization ◽  
Profit Maximization ◽  
Planning Horizon ◽  
Finite Horizon ◽  
Maximization Problem ◽  
Decision Variable ◽  
Time Cost ◽  
For Profit ◽  
Optimal Policies ◽  
The Cost

This article considers the optimal inventory ordering, purchasing and holding policies of the profit-maximization problem, as against the well-known cost-minimization case, over a finite horizon of length H, under two special conditions. First, there is change in at least one of the inventory costs, that is, in the cost of ordering and/or purchasing/holding, at some point, Tc < H, during the planning horizon. Second, it is not necessary to satisfy the demand, at a rate of R units per year, for the entire horizon. Rather, the objective is to meet the demand for a period of length H1 ≤ H. In fact, if the retailer does not have the obligation to meet the entire demand, this article shows the conditions wherein it may be more profitable to meet only a portion or may be even none of the demand. Further, such a determination can be made up front, with H1 as a decision variable and the optimal policies of the cost-minimization models, by fulfilling the entire demand, will result in lower profits. Numerical examples are included to identify the demand fulfilment and the profit differences between the cost-minimization and profit-maximization optimal policies, under the different one-time cost changes.

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