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### Page 1165 of Mathematical Reviews Vol. , Issue 92b [page]

1992 Mathematical Reviews
In this note the handling of utilizable residual lengths is investi- gated for the one-dimensional cutting stock problem.  ...  Alternative methods for constructing a 0-1 integer programming formulation from a deduction problem in propositional calculus are compared.  ...

### SIMPL: A System for Integrating Optimization Techniques [chapter]

Ionuţ Aron, John N. Hooker, Tallys H. Yunes
2004 Lecture Notes in Computer Science
In recent years, the Constraint Programming (CP) and Operations Research (OR) communities have explored the advantages of combining CP and OR techniques to formulate and solve combinatorial optimization  ...  problems.  ...  The relaxation stage drops the integrality constraints and solves the resulting problem with a linear or perhaps nonlinear programming solver.  ...

### Minimizing waste (off-cuts) using cutting stock model: The case of one dimensional cutting stock problem in wood working industry

Gbemileke A. Ogunranti, Ayodeji E. Oluleye
2016 Journal of Industrial Engineering and Management
Purpose: The main objective of this study is to develop a model for solving the one dimensional cutting stock problem in the wood working industry, and develop a program for its implementation.Design/methodology  ...  Also, to evaluate the efficiency of the application, Case I problem was solved using two top commercial 1D-cutting stock software.  ...  We also thank the anonymous referees for their helpful comments and all those who made suggestions as to making the application simple to use in practice.  ...

### Modelling and solving environments for mathematical programming (MP): a status review and new directions

B Dominguez-Ballesteros, G Mitra, C Lucas, N-S Koutsoukis
2002 Journal of the Operational Research Society
A heuristic procedure can be used for this purpose and solve the cutting stock problem. . Determine the new cutting pattern by solving the knap- sack problem.  ...  out favourably in the resulting cutting stock optimisation problem.  ...

### Logic, Optimization, and Constraint Programming

John N. Hooker
2002 INFORMS journal on computing
It traces the history of logic-based methods in optimization and the development of constraint programming in artificial intelligence.  ...  (Optimization, Constraint programming, Logic-based methods, Artificial Intelligence)  ...  Constraint logic programming (CLP) addresses this problem. Its key idea is to regard the unification step of logic programming as a special case of constraint solving.  ...

### Dynamic lot size MIPs for multiple products and ELSPs with shortages, capacity and changeover limits [article]

Wolfgang Garn
2020 arXiv   pre-print
Especially, logical constraints are a key ingredient in succeeding in this endeavour. They were used to formulate the setup/changeover of items in the production line.  ...  This work presents mixed integer programs (MIPs) that solve the Economic Lot Sizing Problem (ELSP) and other Dynamic Lot-Sizing (DLS) models with multiple items.  ...  The GLPK (Gnu Linear Programming Kit) performance was analysed in Pryor and Chinneck (2011) . The CBC (Coin-or branch and cut) uses LP relaxations, heuristics and cut generations.  ...

### A matching approach for replenishing rectangular stock sizes

F J Vasko, J A McNamara, R N Parkes, F E Wolf, L R Woodyatt
2000 Journal of the Operational Research Society
We are aware of only one paper that uses a matching approach in order to solve a cutting stock problem.  ...  Fritsch and Vornberger® solved a special type of two-dimensional cutting stock problem by solving a series of weighted nonbipartite matching problems.  ...

### Arrays, bounded quantification and iteration in logic and constraint logic programming

Krzysztof R. Apt
1996 Science of Computer Programming
To convince the reader about their merits we present several examples of logic and constraint logic programs which use iteration and arrays instead of explicit recursion and lists.  ...  These programs are substantially simpler than their counterparts written in the conventional way.  ...  Problem 11. Solve Problem 6 by means of constraints.  ...

### Logic based Benders' decomposition for orthogonal stock cutting problems

Maxence Delorme, Manuel Iori, Silvano Martello
2017 Computers & Operations Research
The master problem is solved through a new ILP model based on the arc flow formulation, while constraint programming is used to solve the slave problem.  ...  Benders' decomposition in which the master problem is a MILP model and the slave is solved through branch-and-bound.  ...  We thank him and his coauthors for providing a working copy of their computer code developed for [18] . We thank an anonymous referee for helpful comments.  ...

### Recent developments and future directions in mathematical programming

E. L. Johnson, G. L. Nemhauser
1992 IBM Systems Journal
programming using strong linear programming formulations, and a renewed interest in decomposition.  ...  L inear programming grew out of work begun during the 1930s: in transportation problems by Kantorovich, game theory by Morgenstern and Von Neumann, and input-output models by  ...  A major reason for using column generation, as done for cutting stock problems and clustering problems, is that easier integer programs (knapsack problems in the case of the cutting stock problem) can  ...

### Page 625 of The Journal of the Operational Research Society Vol. 50, Issue 6 [page]

1999 The Journal of the Operational Research Society
Solving a cutting-stock problem in constraint logic programming. In: Kowalski RA and Bowen KA (eds). Logic Programming. MIT Press: Cambridge, MA, pp 42-58. van Hentenrych P (1989).  ...  Constraint Satisfaction in Logic Programming. MIT Press: Cambridge, MA. Wallace M (1996). Practical applications of constraint program- ming. Constraints 1: 139-168.  ...

### Page 257 of The Journal of the Operational Research Society Vol. 51, Issue 3 [page]

2000 The Journal of the Operational Research Society
The system was tested setting the threshold value high enough so that the constraint-based logic was not invoked vs a threshold of 300, 200, and 100.  ...  Cutting stock by iterated matching, operations research proceedings. In: Design U, Batham A and Drexl A (eds). Selected Papers of the Interna- tional Conference on OR94.  ...

### Hybrid fuzzy-stochastic approach for multi-product, multi-period, and multi-resource master production scheduling problem: case of a polyethylene pipe and fitting manufacturer

2018 Scientia Iranica. International Journal of Science and Technology
A hybrid approach is also proposed to solve the extended model. The application of the proposed method is examined in a practical problem of a polyethylene pipe and fitting Co. in Iran.  ...  This problem requires investigating a wide range of parameters, regarding demand, manufacturing resource usage and costs. Uncertainty is an intrinsic characteristic of these parameters.  ...  The problem is solved with a mixed integer programing model.  ...

### Combinatorial optimization: Current successes and directions for the future

Karla L. Hoffman
2000 Journal of Computational and Applied Mathematics
Our ability to solve large, important combinatorial optimization problems has improved dramatically in the past decade.  ...  We note that each section of this paper will include only a limited number of survey references. These survey papers contain the references to the much larger body of work in each area.  ...  stock problem, are employed.  ...

### Advances in mathematical programming models for enterprise-wide optimization

Ignacio E. Grossmann
2012 Computers and Chemical Engineering
We provide an overview of EWO in terms of a mathematical programming framework.  ...  We then address some of the major issues involved in the modeling and solution of these problems.  ...  A linear programming problem that includes as special constraints disjunctions (Balas, 1979) is denoted as a disjunctive programming problem.  ...
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