Efficient model for interval goal programming with arbitrary penalty function

Penalty function is a key factor in interval goal programming (IGP), especially for decision makers weighing resources vis-à-vis goals. Many approaches (Chang et al. J Oper Res Soc 57:469–473, 2006; Chang and Lin Eur J Oper Res 199, 9–20, 2009; Jones et al. Omega 23, 41–48, 1995; Romero Eur J Oper Res 153, 675–686, 2004; Vitoriano and Romero J Oper Res Soc 50, 1280–1283, 1999)have been proposed for treating several types of penalty functions in the past several decades. The recent approach of Chang and Lin (Eur J Oper Res 199, 9–20, 2009) considers the S-shaped penalty function. Although there are many approaches cited in literature, all are complicated and inefficient. The current paper proposes a novel and concise uniform model to treat any arbitrary penalty function in IGP. The efficiency and usefulness of the proposed model are demonstrated in several numeric examples.     

Mixed binary interval goal programming

This paper focuses on the mixed binary preferences decision problem associated with the use of penalty functions in goal programming. In this sense, a new formulation approach for interval goal programming is derived, which is more efficient than the model of Jones and Tamiz. In addition, to enhance the usefulness of the proposed model, binary variables subject to the environmental constraints are added. This leads to the model of binary interval goal programming. Finally, examples to illustrate these models are given.     

Binary fuzzy goal programming approach to single model straight and U-shaped assembly line balancing

Assembly line balancing generally requires a set of acceptable solutions to the several conflicting objectives. In this study, a binary fuzzy goal programming approach is applied to assembly line balancing. Models for balancing straight and U-shaped assembly lines with fuzzy goals (the number of workstations and cycle time goals) are proposed. The binary fuzzy goal programming models are solved using the methodology introduced by Chang [Chang, C.T., 2007. Binary fuzzy goal programming. European Journal of Operational Research 180 (1), 29–37]. An illustrative example is presented to demonstrate the validity of the proposed models and to compare the performance of straight and U-shaped line configurations.     

Revised multi-choice goal programming

Chang [C.-T. Chang, Multi-choice goal programming, Omega, The Inter. J. Manage. Sci. 35 (2007) 389–396] has recently proposed a new method namely multi-choice goal programming (MCGP) for multi-objective decision problems. The multi-choice goal programming allows the decision maker to set multi-choice aspiration levels for each goal to avoid underestimation of the decision. However, to express the multi-choice aspiration levels, multiplicative terms of binary variables are involved in their model. This leads to difficult implementation and it is not easily understood by industrial participants. In this paper, we propose an alternative method to formulate the multi-choice aspiration levels with two contributions: (1) the alternative approach does not involve multiplicative terms of binary variables, this leads to more efficient use of MCGP and is easily understood by industrial participants, and (2) the alternative approach represents a linear form of MCGP which can easily be solved by common linear programming packages, not requiring the use of integer programming packages. In addition, a new concept of constrained MCGP is introduced for constructing the relationships between goals in this paper. Finally, to demonstrate the usefulness of the proposed method, an illustrate example is included.     

Reply to the note on article “The evidential reasoning approach for multiple attribute decision analysis using interval belief degrees”

In a very recent note by Gao and Ni [B. Gao, M.F. Ni, A note on article “The evidential reasoning approach for multiple attribute decision analysis using interval belief degrees”, European Journal of Operational Research, in press, doi:10.1016/j.ejor.2007.10.0381], they argued that Yen’s combination rule [J. Yen, Generalizing the Dempster–Shafer theory to fuzzy sets, IEEE Transactions on Systems, Man and Cybernetics 20 (1990) 559–570], which normalizes the combination of multiple pieces of evidence at the end of the combination process, was incorrect. If this were the case, the nonlinear programming models we proposed in [Y.M. Wang, J.B. Yang, D.L. Xu, K.S. Chin, The evidential reasoning approach for multiple attribute decision analysis using interval belief degrees, European Journal of Operational Research 175 (2006) 35–66] would also be incorrect. In this reply to Gao and Ni, we re-examine their numerical illustrations and reconsider their analysis of Yen’s combination rule. We conclude that Yen’s combination rule is correct and our nonlinear programming models are valid.     

A note on article “A tolerance approach to the fuzzy goal programming problems with unbalanced triangular membership function”

Kim and Whang use a tolerance approach for solving fuzzy goal programming problems with unbalanced membership functions [J.S. Kim, K. Whang, A tolerance approach to the fuzzy goal programming problems with unbalanced triangular membership function, European Journal of Operational Research 107 (1998) 614–624]. In this note it is shown that some results in that article are incorrect. The necessary corrections are proposed.     

Random effects Weibull regression model for occupational lifetime

With great interest we read the recent publication of Sohn et al. [Sohn, S.Y., Chang, I.S., Moon, T.H., 2007. Random effects Weibull regression model for occupational lifetime. European Journal of Operational Research 179, 124–131] on a Weibull regression model with random effects for modelling occupational lifetime. We congratulate Sohn and colleagues on their comprehensive and clearly written paper. Nevertheless, we would like to comment on two points, the first regarding the moments of the underlying Weibull distribution, the second regarding the relations of Sohn’s model to the class of frailty models.     

A note on article “The evidential reasoning approach for multiple attribute decision analysis using interval belief degrees”

Wang et al. use an evidential reasoning approach for solving multiple attribute decision analysis (MADA) problems under interval belief degrees [Y.M. Wang, J.B. Yang, D.L. Xu, K.S. Chin, The evidential reasoning approach for multiple attribute decision analysis using interval belief degrees, European Journal of Operational Research 175 (2006) 35–66]. In this note it is shown some nonlinear optimization models in that paper are incorrect. The necessary corrections are proposed.     

Linear Bi-level Programming Problems — A Review

Journal of the Operational Research Society - Multi-level programming is characterized as mathematical programming to solve decentralized planning problems. The decision variables are partitioned...     

“Optimistic” weighted Shapley rules in minimum cost spanning tree problems

We introduce optimistic weighted Shapley rules in minimum cost spanning tree problems. We define them as the weighted Shapley values of the optimistic game v⁺ introduced in Bergantiños and Vidal-Puga [Bergantiños, G., Vidal-Puga, J.J., forthcoming. The optimistic TU game in minimum cost spanning tree problems. International Journal of Game Theory. Available from: <http://webs.uvigo.es/gbergant/papers/cstShapley.pdf>]. We prove that they are obligation rules [Tijs, S., Branzei, R., Moretti, S., Norde, H., 2006. Obligation rules for minimum cost spanning tree situations and their monotonicity properties. European Journal of Operational Research 175, 121–134].     

Partitioning sequencing situations and games

The interaction between sequencing situations and cooperative games starting from the paper of Curiel et al. [Curiel, I., Pederzoli, G., Tijs S., 1989. Sequencing games. European Journal of Operational Research 40, 344–351], has become an established line of research within the theory of operation research games.     

Reply to comments by Soleimani-damaneh and Mostafaee (2006) and Zhang (2006)

In Fukuyama [Fukuyama, H., 2000. Returns to scale and scale elasticity in data envelopment analysis. European Journal of Operational Research 125, 93–112], I investigated some mathematical structure on scale elasticity and returns to scale. Soleimani-damaneh and Mostafaee [Soleimani-damaneh, M., Mostafaee, A., in press. A comment on “Returns to scale and scale elasticity in data envelopment analysis”. European Journal of Operational Research. doi:10.1016/j.ejor.2006.11.042] and Zhang [Zhang, B., in press. A Note on Fukuyama (2000). European Journal of Operational Research. doi:10.1016/j.ejor.2006.11.040] claim that some results, which are related to homogeneity, are incorrect. This note replies to their comments by demonstrating that Fukuyama (2000) results are still valid.     

Multi-Item Single-Machine Scheduling with Material Supply Constraints

Journal of the Operational Research Society - This article presents an extension of a dynamic programming algorithm for scheduling production of multiple items on a single machine with time-varying...     

A note on the paper “Fractional programming with convex quadratic forms and functions” by H.P. Benson

In this technical note, we give a short proof based on some standard results in convex analysis of some important characterization results listed in Theorems 3 and 4 of Benson [Benson, H.P., 2006. Fractional programming with convex quadratic forms and functions. European Journal of Operational Research]. Actually our result is slightly more general since we do not specify the nonempty convex set X. For clarity we use the same notation for the different equivalent optimization problems as done in Benson (2006).     

Approximately Optimal Recovery of a Multicohort Fishery from Depleted Stocks and Excess Vessel Capacity

Journal of the Operational Research Society - The effect of current harvesting on future fish stocks is best captured with a multicohort model. In principle, numerical dynamic programming can be...     

A note on “A mixed integer programming model for advanced planning and scheduling (APS)”

In a recent paper, Chen and Ji [Chen, K., Ji, P., 2007. A mixed integer programming model for advanced planning and scheduling (APS). European Journal of Operational Research 181, 515–522] develop a mixed integer programming model for advanced planning and scheduling problem that considers capacity constraints and precedence relations between the operations. The orders require processing of several operations on eligible machines. The model presented in the above paper works for the case where each operation can be processed on only one machine. However, machine eligibility means that only a subset of machines are capable of processing a job and this subset may include more than one machine. We provide a general model for advanced planning and scheduling problems with machine eligibility. Our model can be used for problems where there are alternative machines that an operation can be assigned to.     

Comment on “Complete solution to a conjecture on Randić index”

In this paper we will show that the proof of Theorem 2.1 from “Complete solution to a conjecture on Randi? index”, by Xueliang Li, Bolian Liu and Jianxi Liu, European Journal of Operational Research 200, Issue 1, (2010), 9–13, is not correct. They tried to prove the conjecture given by M. Aouchiche, P. Hansen in “On a conjecture about the Randi? index” (Discrete Mathematics, 307 (2), 2007, 262–265), but they failed in it. The mathematical model given by them is a problem of quadratic programming which they tried to solve by wrong use of linear programming. This error invalidates all further work.     

A generalization of sensitivity of the inventory model with partial backorders

In this paper, we use the elementary techniques of differential calculus to investigate the sensitivity analysis of Montgomery et al.’s [Montgomery, D.C., Bazaraa, M.S., Keswani, A.K., 1973. Inventory models with a mixture of backorders and lost sales. Naval Research Logistics Quarterly 20, 225–263] inventory model with a mixture of backorders and lost sales and generalize Chu and Chung’s [Chu, P., Chung, K.J., 2004. The sensitivity of the inventory model with partial backorders. European Journal of Operational Research 152, 289–295] sensitivity analysis. We provide three numerical examples to demonstrate our findings, and remark the interpretation of the global minimum of the average annual cost at which the complete backordering occurs.     

Comment on “A new clustering approach using data envelopment analysis”

In a recent paper Po, Guh and Yang [Po, R.-W., Guh, Y.-Y., Yang, M.-S., 2009. A new clustering approach using data envelopment analysis. European Journal of Operational Research 199, 276–284] propose a new algorithm for forming clusters from the results of a DEA analysis. In this comment it is explained that the algorithm only generates information that is readily available from the usual DEA results.     

A note on Liu–Iwamura’s dependent-chance programming

Sometimes a complex stochastic decision system undertakes multiple tasks called events, and the decision-maker wishes to maximize the chance functions which are defined as the probabilities of satisfying these events. Originally introduced by Liu and Iwamura [B. Liu, K. Iwamura, Modelling stochastic decision systems using dependent-chance programming, European Journal of Operational Research 101 (1997) 193–203], dependent-chance programming is aimed at maximizing some chance functions of events in an uncertain environment. In this work, we show that the original dependent chance-programming framework needs to be extended in order to capture an exact reliability measure for a given plan.