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Simultaneous Optimization via Approximate Majorization for Concave Profits or Convex Costs

Ashish Goel, Adam Meyerson
2005 Algorithmica  
For multi-criteria problems and problems with poorly characterized objective, it is often desirable to simultaneously approximate the optimum solution for a large class of objective functions.  ...  Maximizing all symmetric concave functions, and 2. Minimizing all symmetric convex functions.  ...  Acknowledgement Ashish Goel would like to thank David Tse for introducing him to the concept of majorization.  ... 
doi:10.1007/s00453-005-1177-7 fatcat:cpvvmi22p5al3llvxhqykrzlsa

Coordinating Inventory Control and Pricing Strategies for Perishable Products

Xin Chen, Zhan Pang, Limeng Pan
2014 Operations Research  
holding and backlogging or lost-sales penalty cost and disposal cost.  ...  Employing the concept of L -concavity, we show some monotonicity properties of the optimal policies.  ...  Acknowledgments We thank the anonymous associate editor and two referees, Paul Zipkin and Yi Yang for their valuable comments on this paper.  ... 
doi:10.1287/opre.2014.1261 fatcat:hcsopuwhxzdzzmuj4jut2nqgky

Combined Pricing and Inventory Control Under Uncertainty

Awi Federgruen, Aliza Heching
1999 Operations Research  
Finally, we report on an extensive numerical study that characterizes various qualitative properties of the optimal strategies and corresponding optimal profit values.  ...  We characterize the structure of an optimal combined pricing and inventory strategy for all of the above types of models.  ...  Also, choosing G t ( ⅐ , ⅐ ) as the one-step expected cost function, results in an upper bound approximation for the entire problem.  ... 
doi:10.1287/opre.47.3.454 fatcat:a4foml3oqvhrhoelrnvtkjnsj4

Service Competition with General Queueing Facilities

Gad Allon, Awi Federgruen
2008 Operations Research  
We show that across the above broad spectrum of queueing models, the capacity cost function belongs to a specific four parameter class of function, either exactly or as a close approximation.  ...  A firm's waiting time standard may either be defined in terms of the expected value or a given, for instance 95%, percentile of the steady state waiting time distribution.  ...  Acknowledgement We thank Ward Whitt and Assaf Zeevi for many helpful comments regarding an earlier version of the paper.  ... 
doi:10.1287/opre.1080.0545 fatcat:nheamzzxgjcsffrtvxri7uivgi

Service Competition with General Queueing Facilities

Gad Allon, Awi Federgruen
2006 Social Science Research Network  
We show that across the above broad spectrum of queueing models, the capacity cost function belongs to a specific four parameter class of function, either exactly or as a close approximation.  ...  A firm's waiting time standard may either be defined in terms of the expected value or a given, for instance 95%, percentile of the steady state waiting time distribution.  ...  Acknowledgement We thank Ward Whitt and Assaf Zeevi for many helpful comments regarding an earlier version of the paper.  ... 
doi:10.2139/ssrn.907355 fatcat:aufclgy4obhdzhdxcox3mgwhdq

Channel capacity optimization for an integrated wi-fi and free-space optic communication system (WiFiFO)

Qiwei Wang, Thinh Nguyen, Alan X. Wang
2014 Proceedings of the 17th ACM international conference on Modeling, analysis and simulation of wireless and mobile systems - MSWiM '14  
We show that the power allocation problem for WiFiFO can be approximated well as a convex optimization problem. To that end, an algorithm based on gradient decent method is developed.  ...  Specifically, we consider the problem of power allocation for multiple FSO and WiFi transmitters in order to achieve maximum system capacity for given budget power.  ...  Convexity: Because φ(p Ot , p RF t ) is a sum of concave functions, it is concave. So the approximate problem is a convex problem with linear constraints. Algorithm.  ... 
doi:10.1145/2641798.2641823 dblp:conf/mswim/WangNW14 fatcat:h6hwj3lm2zhhtewlpvdmepevgu

Competition under time-varying demands and dynamic lot sizing costs

Awi Federgruen, Joern Meissner
2009 Naval Research Logistics  
Fixed as well as variable procurement costs are incurred for each procurement order, along with inventory carrying costs.  ...  Based on each period's system of demand equations, these prices determine a time series of demands for each firm, which needs to service them with an optimal corresponding dynamic lot sizing plan.  ...  While the revenue term in (38) is concave in p i , the cost term is (piecewise linear) concave, as well, adding a convex term to the profit function.  ... 
doi:10.1002/nav.20321 fatcat:f7myzdppajcyjknbcku7zeo75m

Integrating Dynamic Pricing and Replenishment Decisions Under Supply Capacity Uncertainty

Qi Feng
2010 Management science  
Whether or not the supply capacity is limited has a major implication on the value of dynamic pricing.  ...  Under unlimited supply, dynamic pricing is more valuable when procurement cost is high or when demand is more sensitive to price.  ...  The author is also indebted to Alain Bensoussan, Suresh Sethi, George Shanthikumar, and Paul Zipkin for helpful discussions.  ... 
doi:10.1287/mnsc.1100.1238 fatcat:sqeadohepjagvf5bs26yhbjwam

Incorporating Transportation Mode Decisions into Production-Shipping Planning: Considering Shipping Consolidation

Qian Huang, Shunichi Ohmori, Kazuho Yoshimoto
2020 Operations and Supply Chain Management An International Journal  
We present mathematical formulations of tramp, liner and mixed modes and apply a piecewise approximation technique with mixed-linear integer programming to linearly approximate the concave minimization  ...  This study develops a global production-shipping planning model that incorporates a decision on transportation mode after considering the cost function of different transportation modes from the shipper's  ...  An exhaustive search of all extreme points would provide an optimal flow, since a concave function achieves its minimum at an extreme point of the convex feasible region.  ... 
doi:10.31387/oscm0440286 fatcat:drgslvmrhjdllovlg6qwvlpfje

Multilocation Combined Pricing and Inventory Control

Awi Federgruen, Aliza Heching
2002 Manufacturing & Service Operations Management  
The approximate model thus provides analytically computable approximations for systemwide profits and other performance measures.  ...  Allocations arrive after a second "allocation leadtime.' ' We develop an approximate model that is tractable and in which an optimal policy of simple structure exists.  ...  Its optimal solution provides analytically computable approximations for systemwide profits and other performance measures.  ... 
doi:10.1287/msom.4.4.275.5730 fatcat:w25rj77pijbzfelhrhp2s6c3zm

A piecewise linearization framework for retail shelf space management models

Jens Irion, Jye-Chyi Lu, Faiz Al-Khayyal, Yu-Chung Tsao
2012 European Journal of Operational Research  
Managing shelf space is critical for retailers to attract customers and to optimize profit.  ...  We propose a piecewise linearization technique for approximating the complicated nonlinear model that relaxes the nonconvex optimization problem into a linear Mixed Integer Program (MIP).  ...  To complete the overestimating linearization of (13), the bilinear terms z i g i are linearized via an equivalent linearly constrained reformulation using the convex and concave envelope technique of Appendix  ... 
doi:10.1016/j.ejor.2012.04.021 fatcat:r3ip7pw3s5cnjpwuosmsg6uzce

Distributed utility maximization for network coding based multicasting: a shortest path approach

Yunnan Wu, Sun-Yuan Kung
2006 IEEE Journal on Selected Areas in Communications  
Second, assuming the netutility function is strictly concave, our proposed method enables a near-optimal primal variable to be uniquely recovered from a near-optimal dual variable.  ...  For ill-conditioned problems that arise, for instance, when the cost functions are linear, we propose to use the proximal method, which solves a sequence of wellconditioned problems obtained from the original  ...  Since U is strictly concave and each p vw is strictly convex, r * = r(ε * ) and g * = g(ε * ). In practice, very often one can only hope for an approximate optimal dual solution.  ... 
doi:10.1109/jsac.2006.879356 fatcat:i55sz4ckqfbarpbiy2rvivylwy

BANK INTEREST MARGINS AND BUSINESS START-UP COLLATERAL: TESTING FOR CONVEXITY

Andrew Burke, Aoife Hanley
2006 Scottish Journal of Political Economy  
The paper investigates the relationship between bank interest rate margins and collateral for loans issued to new ventures. The analysis finds a convex U-shaped relationship.  ...  The results indicate that while provision of collateral initially reduces bank exposure to risk (through security, more optimal levels of capital and lower moral hazard among entrepreneurs) that beyond  ...  However, the scope of these papers does not enable them to test to see if this concave venture performance function transforms into a convex cost of loan or equity capital relationship.  ... 
doi:10.1111/j.1467-9485.2006.00382.x fatcat:pbtqa7uye5cjvjyz3i4sn7laxa

Transfer pricing in vertically integrated industries

Thomas A. Gresik, Petter Osmundsen
2007 International Tax and Public Finance  
The transactional profit-based rules adopted by the United States Treasury in 1994 and by the OECD in 1995 perform poorly in this regard.  ...  With private and heterogeneous cost information, the Cost-Plus method generates an "incentive comparability" effect that tax officials can exploit.  ...  The assumptions of decreasing and concave marginal operating profit and convex marginal costs are economically intuitive and satisfied by many demand and cost curves.  ... 
doi:10.1007/s10797-007-9019-y fatcat:mntw5j32hjgzpfgclcaz36orse

Competition Under Generalized Attraction Models: Applications to Quality Competition Under Yield Uncertainty

Awi Federgruen, Nan Yang
2009 Management science  
These choices have implications for their per-unit cost rates.  ...  Here an industry has N suppliers of a given product, who compete for the business of one or more buyers.  ...  The concavity condition (G) is satisfied, for example, when all G i -functions are concave themselves and the H · -function is convex.  ... 
doi:10.1287/mnsc.1090.1073 fatcat:tbwx7yljprhd7mytrxdzifssby
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