# Elsevier

# European Journal of Operational Research

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**Editor:**

**Current editor:**Jesus Artalejo

**Current editor:**Jean-Charles. Billaut

**Current editor:**Robert Dyson

**Current editor:**Lorenzo Peccati

**For corrections or technical questions regarding this series, please contact (Shamier, Wendy)**

**Series handle:**repec:eee:ejores

**ISSN:**0377-2217

**Citations RSS feed:**at CitEc

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### October 1994, Volume 78, Issue 1

**130-140 A bounding scheme for deriving the minimal cycle time of a single-transporter N-stage process with time-window constraints***by*Armstrong, Ronald & Lei, Lei & Gu, Shanhong

### September 1994, Volume 77, Issue 3

**357-374 Practical applications of OR in an underdeveloped nation***by*Aggarwal, Sumer C.**375-391 Multiobjective modelling for regional agricultural planning: Case study in Tunisia***by*Siskos, Y. & Despotis, D. K. & Ghediri, M.**392-403 Capacity expansion with alternative technology choices***by*Rajagopalan, S.**404-414 On the complexity of preemptive openshop scheduling problems***by*Sriskandarajah, C. & Wagneur, E.**415-428 Scheduling a two-stage hybrid flowshop with separable setup and removal times***by*Gupta, Jatinder N. D. & Tunc, Enar A.**429-439 Job shop leadtime requirements under conditions of controlled delivery performance***by*Enns, S. T.**440-465 Discriminant characteristics of US banks acquired with or without federal assistance***by*Zanakis, Stelios H. & Walter, Gary A.**466-474 Integrated container loading software for pulp and paper industry***by*Fraser, Hamish J. & George, John A.**475-485 Optimizing the assignment of aircrews to aircraft in an airlift operation***by*Kress, M. & Golany, B.**486-495 Direct and inverse solution of the Lanchester square law with general reinforcement schedules***by*Helmbold, Robert L.**496-515 An ME-based approximation for multi-server queues with preemptive priority***by*Kouvatsos, Demetres & Tabet-Aouel, Nasredine

### September 1994, Volume 77, Issue 2

**195-207 Polyhedral structure and properties of a model for layout design***by*Leung, Janny**208-223 A state-space search approach for parallel processor scheduling problems with arbitrary precedence relations***by*Chang, Pei Chann & Jiang, Yen Shean**224-240 Optimal sequential file search***by*Monahan, George E.**241-252 The two-group discriminant problem with equal group mean vectors: An experimental evaluation of six linear/nonlinear programming formulations***by*Hosseini, Jamshid C. & Armacost, Robert L.**253-271 Constrained regression median for measuring possible salary discrimination***by*Sueyoshi, Toshiyuki**272-286 Incorporating preference information into multi-objective scheduling***by*Daniels, Richard L.**287-302 The stochastic single machine scheduling problem with earliness and tardiness costs***by*Soroush, H. M. & Fredendall, L. D.**303-313 Stochastic optimization of the cost of automatic assembly systems***by*Tandiono, Elly & Gemmill, Douglas D.**314-324 Convex programs with an additional constraint on the product of several convex functions***by*Kuno, Takahito & Yajima, Yasutoshi & Yamamoto, Yoshitsugu & Konno, Hiroshi**325-343 A joint chance-constrained programming model with row dependence***by*Watanabe, Tsunemi & Ellis, Hugh**344-356 Topological design of a centralized communication network with unreliable links and node outage costs***by*Dutta, Amitava & Kawatra, Rakesh

### August 1994, Volume 77, Issue 1

**1-26 Containing groundwater contamination: Planning models using stochastic programming with recourse***by*Wagner, Janet M. & Shamir, Uri & Marks, David H.**27-39 A linguistic approach to stochastic comparison of queuing systems***by*Lin, Feng**40-59 Using case based reasoning for basis development in intelligent decision systems***by*McGovern, Jim & Samson, Danny & Wirth, Andrew**60-69 An algorithm for the committee construction problem***by*Ceylan, Demet & Saatcioglu, Omer & Sepil, Canan**70-81 Constrained gaming approaches to decisionmaking under uncertainty***by*Ryan, Michael J.**82-95 An investigation on the conditions of pruning an induced decision tree***by*Kim, Hyunsoo & Koehler, Gary J.**96-110 Interior dual proximal point algorithm for linear programs***by*Setiono, Rudy**111-125 On using approximations of the Benders master problem***by*Holmberg, Kaj**126-140 Strengthening Gilmore's bound for the quadratic assignment problem***by*White, D. J.**141-153 An algorithm for the planar three-index assignment problem***by*Magos, D. & Miliotis, P.**154-168 Procedures for solving a 1-dimensional cutting problem***by*Corominas, Albert & Bautista, Joaquin**169-178 Solving a cutting problem based on existing patterns***by*Elomri, A. & Morel, P. & Pun, L. & Doumeingts, G.**179-188 The hybrid spanning tree problem***by*Chen, Y. L.

### August 1994, Volume 76, Issue 3

**385-386 Editorial***by*Aikens, C. H.**387-392 Application of facility location modeling constructs to vendor selection problems***by*Current, John & Weber, Charles**393-409 Reason based solutions and the complexity of distribution network design problems***by*Robinson, E. Powell & Swink, Morgan**410-427 Uncapacitated facility location: General solution procedure and computational experience***by*Gao, Li-Lian & Robinson, E. Powell**428-439 Multiple reservoir system operational planning using multi-criterion decision analysis***by*Ko, Seok-Ku & Fontane, Darrell G. & Margeta, Jure**440-454 An approach to using the analytic hierarchy process for solving multiple criteria decision making problems***by*Bryson, Noel & Mobolurin, Ayodele**455-465 Estimating aspiration levels from discrete choices - computational techniques and experiences***by*Vetschera, Rudolf**466-485 A multiple criteria linguistic decision model (MCLDM) for human decision making***by*Liu, Chih-Ming & Wang, Mao-Jiun & Pang, Yock-Seng**486-500 TOPSIS for MODM***by*Lai, Young-Jou & Liu, Ting-Yun & Hwang, Ching-Lai**501-510 Targeting problems in manufacturing queueing networks - An iterative scheme and convergence***by*Bitran, G. R. & Sarkar, D.**511-528 CMIT, capacitated multi-level implosion tool***by*Escudero, L. F.**529-551 Performance sensitivity analysis of open Markovian queueing networks***by*Cao, Xi-Ren**552-562 An approximation method for the M/G/1 retrial queue with general retrial times***by*Yang, T. & Posner, M. J. M. & Templeton, J. G. C. & Li, H.**563-572 Analytic derivation of tail probabilities for queue lengths and waiting times in ATM multiserver queues***by*Bruneel, Herwig & Steyaert, Bart & Desmet, Emmanuel & Petit, Guido H.

### July 1994, Volume 76, Issue 2

**245-246 Editorial***by*Wagner, Udo & Wright, Gordon P.**247-258 Semiparametric estimation of heterogeneous count data models***by*Brannas, Kurt & Rosenqvist, Gunnar**259-272 An examination of consumer heterogeneity in a stochastic model of consumer purchase dynamics with explanatory variables***by*Pedrick, James H. & Zufryden, Fred S.**273-282 Intertemporal aggregation of heterogeneous consumers***by*Givon, Moshe & Horsky, Dan**283-289 Regularity, recency and rates***by*Wheat, Rita D. & Morrison, Donald G.**290-297 Cyclical patterns in brand switching behavior: An issue of pattern recognition***by*Givon, Moshe & Muller, Eitan**298-308 Analyzing household brand switching: A stochastic model***by*Jain, Dipak C. & Niu, Shun-Chen**309-320 Implications and relative fit of several first-order Markov models of consumer variety seeking***by*Feinberg, Fred M. & Kahn, Barbara E. & McAlister, Leigh**321-330 Bootstrap method for measuring accuracy of probabilistic-choice models***by*Soofi, Ehsan S. & Gensch, Dennis H.**331-343 Latent class models to infer market structure: A comparative analysis***by*Jain, Dipak C. & Rao, Ram C.**344-358 A nonhierarchical brand switching model for inferring market structure***by*Zahorik, Anthony J.**359-374 Understanding price effects for new nondurables: How price responsiveness varies across depth-of-repeat classes and types of consumers***by*Helsen, Kristiaan & Schmittlein, David**375-384 A replication study of two brand-loyalty measures***by*Uncles, M. D. & Hammond, K. A. & Ehrenberg, A. S. C. & Davis, R. E.

### July 1994, Volume 76, Issue 1

**1-14 Scheduling with resource management in manufacturing systems***by*Blazewicz, Jacek & Finke, Gerd**15-27 Water quality management with imprecise information***by*Julien, Benoit**28-48 A subgradient-based optimization for reservoirs system management***by*Sylla, Cheikna**49-59 Design of components for schedulability***by*Kusiak, Andrew & He, Weihua**60-71 Preemptive scheduling with release dates, delivery times and sequence independent setup times***by*Zdrzalka, Stanislaw**72-82 A dynamic programming method for single machine scheduling***by*Ibaraki, Toshihide & Nakamura, Yuichi**83-97 A three-person game theory model arising in stochastic inventory control theory***by*Wang, Qinan & Parlar, Mahmut**98-110 A tabu search algorithm for computing an operational timetable***by*Costa, Daniel**111-127 A heuristic solution to the warehouse location-routing problem***by*Hansen, P. H. & Hegedahl, B. & Hjortkjaer, S. & Obel, B.**128-142 The spacefilling curve with optimal partitioning heuristic for the vehicle routing problem***by*Bowerman, Robert L. & Calamai, Paul H. & Brent Hall, G.**143-154 Use of a fuzzy theory technique for grouping of trips in the vehicle routing and scheduling problem***by*Kagaya, Seiichi & Kikuchi, Shinya & Donnelly, Robert A.**155-164 A fuzzy approach to the vessel dispatching problem***by*Vukadinovic, Katarina & Teodorovic, Dusan**165-175 A dynamic allocation rule for the funding of projects and its long-run properties***by*Stadje, W.**176-191 A 0-1 goal programming model for scheduling multiple maintenance projects at a copper mine***by*Chen, Vincent Y. X.**192-205 Heuristics for scheduling resource-constrained projects in MPM networks***by*Zhan, Ji**206-217 Determining priorities for projects with uncertain benefits: an application to data management***by*Ballou, Donald P. & Tayi, Giri Kumar**218-228 On a paper by Christofides et al. for solving the multiple-resource constrained, single project scheduling problem***by*Demeulemeester, Erik & Herroelen, Willy & Simpson, Wendell P. & Baroum, Sami & Patterson, James H. & Yang, Kum-Khiong**229-239 A clustering heuristic to detect staircase structures in large scale linear programming models***by*Jayakumar, Maliyakal D. & Ramasesh, Ranga V.

### June 1994, Volume 75, Issue 3

**475-476 Emerging trends in risk management***by*Brehmer, Berndt & Eriksson, Erik Anders & Wulff, Petter**477-487 Models, modelling and modellers: an application to risk analysis***by*Wahlstrom, Bjorn**488-498 Overview of problems of risk management of accidents with dangerous chemicals in Europe***by*Haastrup, Palle**499-507 Safe transport of dangerous goods: road, rail or sea? A screening of technical and administrative factors***by*Andersson, Sven-Eric**508-520 A real-time routing model for hazardous materials***by*Beroggi, Giampiero E. G.**521-539 A probabilistic method for analyzing the reliability effect of time and organizational factors***by*Reer, Bernhard**540-552 Psychological aspects of traffic safety***by*Brehmer, Berndt**553-566 Costs of occupational accidents and diseases in Norway***by*Rognstad, Kirsten**567-581 Developing and validating a decision support system for locating emergency medical vehicles in Louisville, Kentucky***by*Repede, John F. & Bernardo, John J.**582-588 The relocation of ambulance stations: A successful case study***by*McAleer, W. E. & Naqvi, I. A.**589-599 Barter contracts in intertemporal energy exchange***by*Ruusunen, Jukka**600-616 Diffusion models in forecasting: A comparison with the Box-Jenkins approach***by*Gottardi, Giorgio & Scarso, Enrico**617-633 An empirical comparison of utility assessment programs***by*Kimbrough, Steven O. & Weber, Martin**634-646 An optimal state-age dependent replacement for a network system***by*Feng, W. & Adachi, K. & Kowada, M.**647-658 The constant fallacy: A persistent logical flaw in applications of Lanchester's equations***by*Helmbold, Robert L.

### June 1994, Volume 75, Issue 2

**243-263 Batching decisions: structure and models***by*Kuik, Roelof & Salomon, Marc & van Wassenhove, Luk N.**264-274 Flexibility and product variety in lot-sizing models***by*de Groote, Xavier**275-286 On practical resource allocation for production planning and scheduling with period overlapping setups***by*Dillenberger, Christof & Escudero, Laureano F. & Wollensak, Artur & Zhang, Wu**287-295 Lot sizing for a product subject to obsolescence or perishability***by*Jain, Karuna & Silver, Edward A.**296-311 A heuristic for dynamic multi-item multi-level capacitated lotsizing for general product structures***by*Tempelmeier, Horst & Helber, Stefan**312-331 Using geometric techniques to improve dynamic programming algorithms for the economic lot-sizing problem and extensions***by*van Hoesel, Stan & Wagelmans, Albert & Moerman, Bram**332-341 A new heuristic approach for the multi-item dynamic lot sizing problem***by*Kirca, Omer & Kokten, Melih**342-353 A linear description of the discrete lot-sizing and scheduling problem***by*van Hoesel, Stan & Kolen, Antoon**354-364 Feasibility of scheduling lot sizes of two frequencies on one machine***by*Glass, Celia A.**365-377 A job-splitting heuristic for lot-size scheduling in multi-stage, multi-product production processes***by*El-Najdawi, M. K.**378-394 Lot streaming in three-stage production processes***by*Glass, C. A. & Gupta, J. N. D. & Potts, C. N.**395-404 The discrete lot-sizing and scheduling problem with sequence-dependent setup costs***by*Fleischmann, Bernhard**405-412 Multi-level production-inventory control: Material requirements planning or reorder point policies?***by*Axsater, Sven & Rosling, Kaj**413-426 Integration of lotsizing and scheduling decisions in a job-shop***by*Dauzere-Peres, Stephane & Lasserre, Jean-Bernard**427-440 An effective algorithm for the capacitated single item lot size problem***by*Chung, Chia-Shin & Flynn, James & Lin, Chien-Hua Mike**441-461 Cyclic scheduling to minimize inventory in a batch flow line***by*Dobson, Gregory & Arai Yano, Candace**462-466 A simple lower bound to the dynamic assembly problem***by*Atkins, Derek R.**467-468 Comments on "Balancing capacity and lot sizes" by J. Olhager and B. Rapp (European Journal of Operational Research 19, 337-344)***by*Rosling, Kaj**469-473 Different approaches to a flow shop problem***by*Olhager, Jan & Rapp, Birger

### May 1994, Volume 75, Issue 1

**1-12 A review of optimisation models of Kanban-based production systems***by*Price, Wilson & Gravel, Marc & Nsakanda, Aaron Luntala**13-40 Alternative optimization strategies for large-scale production-allocation problems***by*Lootsma, F. A.**41-61 Solving the staircase cost facility location problem with decomposition and piecewise linearization***by*Holmberg, Kaj**62-73 An heuristic algorithm for the production line layout problem***by*Gutierrez, J. M. & Mata, V.**74-88 An analytical framework for comparing material requirements planning to reorder point systems***by*Bregman, Robert L.**89-99 Evaluating the impact of lead time uncertainty in material requirements planning systems***by*Ho, Chrwan-jyh & Lau, Hon-Shiang**100-111 Simulated annealing procedures for forming machine cells in group technology***by*Chen, W. -H. & Srivastava, B.**112-135 A decomposition approach for a resource constrained scheduling problem***by*Serafini, P. & Speranza, M. G.**136-150 On incorporating business risk into continuous review inventory models***by*Singhal, Vinod R. & Raturi, Amitabh S. & Bryant, John**151-170 Solving a class of network models for dynamic flow control***by*Carey, Malachy & Srinivasan, Ashok**171-185 Traffic allocation for manufacturing systems***by*Tang, Christopher S. & van Vliet, Mario**186-199 Production allocation with dual provisioning***by*Ahmadi, Reza H. & Tang, Christopher S.**200-216 Expected waiting times in single-device trip-based material handling systems***by*Bozer, Yavuz A. & Cho, Myeon-Sig & Srinivasan, Mandyam M.**217-232 A branch-and-bound approach for spare unit allocation in a series system***by*Sung, C. S. & Lee, H. K.**233-234 Comment on "The facility layout problem"***by*Bharitkar, Sunil & Tsuchiya, Kazuhiro & Takefuji, Yoshiyasu**235-237 A note on the article "An improved version of Wang's algorithm for two-dimensional cutting problems" written by J.F. Oliveira and J.S. Ferreira, Volume 44, 1990, pp. 256-266***by*Holthaus, Oliver**238-241 A remark on "Integer linear programming formulation for a Vehicle Routing Problem" by N.R. Achutan and L. Caccetta, or how to use the Clark & Wright savings to write such integer linear programming formulations***by*Naddef, Denis

### May 1994, Volume 74, Issue 3

**379-390 Fuzzy sets theory applications in traffic and transportation***by*Teodorovic, Dusan**391-406 Unified interactive multiple objective programming***by*Gardiner, Lorraine R. & Steuer, Ralph E.**407-419 Avoiding rank reversal in AHP decision-support models***by*Schenkerman, Stan**420-425 Reply to Schenkerman's avoiding rank reversal in AHP decision support models***by*Vargas, Luis G.**426-447 Highlights and critical points in the theory and application of the Analytic Hierarchy Process***by*Saaty, Thomas L.**448-465 Throughput analysis in manufacturing networks***by*Bitran, G. R. & Sarkar, D.**466-478 Stochastic frontier production analysis: Measuring performance of public telecommunications in 24 OECD countries***by*Sueyoshi, Toshiyuki**479-494 Mathematical programming models for ownership and control of European and American groups of companies***by*Kornbluth, J. S. H. & Salkin, G. R.**495-508 The log bucking problem: A comparison of dynamic programming versus branch and bound***by*Bobrowski, Paul M.**509-518 Overlapping machine groups in semiconductor wafer fabrication***by*Johri, Pravin K.**519-527 A decision modes for shift scheduling of nurses***by*Siferd, Sue Perrott & Benton, W. C.**528-539 Stochastic allocation of a resource among partially interchangeable activities***by*Martel, Alain & Ouellet, Jean**540-551 Working set generation methods for labor tour scheduling***by*Bechtold, Stephen E. & Brusco, Michael J.**552-571 The dynamics of make or buy decisions***by*Balakrishnan, Srinivasan**572-581 On the role of discrete bid levels in oral auctions***by*Rothkopf, Michael H. & Harstad, Ronald M.

### April 1994, Volume 74, Issue 2

**197-581 Editorial***by*Martikainen, Teppo & Virtanen, Ilkka & Yli-Olli, Paavo**198-229 World wide security market regularities***by*Ziemba, William T.**230-242 Distributional analysis to model atypical behavior***by*Baestaens, Dirk-Emma**243-256 An interest rate risk management model for commercial banks***by*Bessler, Wolfgang & Geoffrey Booth, G.**257-272 Threshold margins, growth, and inflation: Creating real economic value***by*Doyle, Barry & Blakely, Daniel L. & Murray, L. William**273-283 Nonlinear dependence in Finnish stock returns***by*Booth, G. Geoffrey & Martikainen, Teppo & Sarkar, Salil K. & Virtanen, Ilkka & Yli-Olli, Paavo**284-293 A diagnostic model for improving the efficiency of an existing portfolio***by*Bradfield, David J.**294-309 A market utility approach to investment valuation***by*Kasanen, Eero & Trigeorgis, Lenos**310-324 The theory of geometric stable distributions and its use in modeling financial data***by*Kozubowski, Tomasz J. & Rachev, Svetlozar T.**325-343 The diversification of currency loans: A comparison between safety-first and mean-variance criteria***by*Seppala, Juha**344-349 The economic explanation of the strategy of a self financing firm during the recession period***by*Verheyen, Piet A.**350-358 Evaluating probabilistic forecasts of stock prices in a developing stock market***by*Onkal, Dilek & Muradoglu, Gulnur**359-377 The economic value of stock and call options on the Swedish financial market***by*Ostermark, Ralf & Aaltonen, Jaana

### April 1994, Volume 74, Issue 1

**1-17 Equity measurement in facility location analysis: A review and framework***by*Marsh, Michael T. & Schilling, David A.**18-49 Multiproduct integrated production--distribution systems***by*Pyke, David F. & Cohen, Morris A.**50-60 Valuing fixed price supply contracts***by*Kamrad, Bardia & Ritchken, Peter**61-69 Measuring dynamic efficiency under risk aversion***by*Sengupta, Jati K.**70-77 An insight into dynamic channel assignment in cellular mobile communications systems***by*Johri, Pravin K.**78-85 A stochastic dominance analysis of ranked voting systems with scoring***by*Stein, William E. & Mizzi, Philip J. & Pfaffenberger, Roger C.**86-94 A multi-echelon queueing model with dynamic priority scheduling***by*Gupta, Amit & Webster, Scott**95-110 A decomposition approximation for finite-buffered flow lines of exponential queues***by*Springer, Mark C.**111-119 Scheduling jobs to minimize total cost***by*Chen, Y. L.**120-127 Scheduling jobs with release times on a machine with finite storage***by*Nawijn, W. M. & Kern, W. & Baas, S.**128-134 A note on worst-case analysis of approximation algorithms for a scheduling problem***by*Nowicki, Eugeniusz & Smutnicki, Czeslaw**135-142 A search strategy for the one-size assortment problem***by*Yanasse, Horacio Hideki**143-151 Value considerations in three-dimensional packing -- A heuristic procedure using the fractional knapsack problem***by*Mohanty, Bidhu B. & Mathur, Kamlesh & Ivancic, Nancy J.**152-160 Decomposition method application to a large scale linear programming WIP projection model***by*Kim, Jong Soo & Leachman, Robert C.**161-169 A computational analysis of the Auction algorithm***by*Schwartz, B. L.**170-178 An approximate algorithm for nonlinear integer programming***by*Vassilev, Vassil & Genova, Krassimira**179-187 Stability in multiobjective possibilistic linear programs***by*Fuller, Robert & Fedrizzi, Mario**188-195 An ordered independence system and its applications to scheduling problems***by*Lin, Yixun

### March 1994, Volume 73, Issue 3

**407-422 Review of delay-time OR modelling of engineering aspects of maintenance***by*Baker, R. D. & Christer, A. H.**423-429 A generalized oil exploration problem***by*Benkherouf, Lakdere**430-442 An information-economics approach to quality control attribute sampling***by*Ronen, Boaz**443-449 Weighted matching with vertex weights: An application to scheduling training sessions in NASA space shuttle cockpit simulators***by*Bell, Colin E.**450-457 The case for research in decision support systems***by*Syam, Sid S. & Courtney, James F.**458-464 Determination of reorder points for spare parts in a two-echelon inventory system: The case of non identical maintenance facilities***by*Shtub, Avraham & Simon, Moti**465-471 Ordering policies for the cyclical replenishment problem given leadtime-dependent discounts***by*Matta, Khalil F.**472-479 Maximal wearing-out of a deteriorating system: An optimal stopping approach***by*Stadje, W.**480-486 An adaptive statistical method for the discriminant problem***by*Markowski, Carol A.**487-494 Efficiency improvement in data envelopment analysis***by*Kao, Chiang**495-501 Solution procedures for cutting lumber into furniture parts***by*Carnieri, Celso & Mendoza, Guillermo A. & Gavinho, Luciano G.**502-509 On tabu search for the location of interacting hub facilities***by*Skorin-Kapov, Darko & Skorin-Kapov, Jadranka**510-516 Weights improvement in column aggregation***by*Storoy, Sverre**517-523 Strong linear programming relaxations for the orienteering problem***by*Leifer, Adrienne C. & Rosenwein, Moshe B.**524-531 Controlled dual perturbations for central path trajectories in geometric programming***by*Zhu, J. & Kortanek, K. O. & Huang, S.**532-538 An algorithm for decomposing the parametric space in multiobjective dynamic programming problems***by*Abo-Sinna, Mahmoud A. & Hussein, Mohammad L.**539-546 Obtaining clique, cover and coefficient reduction inequalities as Chvatal-Gomory inequalities and Gomory fractional cuts***by*Dietrich, B. L. & Escudero, L. F.**547-554 Derivation of duality in mathematical programming and optimization theory***by*Johri, Pravin K.**555-561 A multi-KP modeling for the maximum-clique problem***by*Della Croce, Federico & Tadei, Roberto**562-568 The three-dimensional bottleneck assignment problem with capacity constraints***by*Geetha, S. & Vartak, M. N.**569-576 Complexity of a class of nonlinear combinatorial problems related to their linear counterparts***by*Sethi, Suresh P. & Kubiak, Wieslaw**577-582 Pseudo-invexity and symmetric duality in nonlinear fractional programming***by*Nanda, S. & Das, L. N.