Theory of constraints and linear programming: a comparison

Luebbe, Richard L.; Finch, Byron J.

doi:10.1080/00207549208942967

Cited by 125 publications

(84 citation statements)

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“…As discussed in the previous section, it is believed that the optimal solution of most real-world optimization problems is found on the edge of a feasible area of the search space of the problem [49]. This belief is not limited to computer science, but it is also found in operational research (linear programming, LP) [12] and management sciences (theory of constraints, TOC) [30,46] articles. The reason behind this belief is that, in real-world optimization problems, constraints usually represent limitations of availability of resources.…”

Section: Bottlenecksmentioning

confidence: 97%

Evolutionary Computation for Real-World Problems

Bonyadi

Michalewicz

2015

Studies in Computational Intelligence

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In this paper we discuss three topics that are present in the area of realworld optimization, but are often neglected in academic research in evolutionary computation community. First, problems that are a combination of several interacting sub-problems (so-called multi-component problems) are common in many real-world applications and they deserve better attention of research community. Second, research on optimisation algorithms that focus the search on the edges of feasible regions of the search space is important as high quality solutions usually are the boundary points between feasible and infeasible parts of the search space in many real-world problems. Third, finding bottlenecks and best possible investment in real-world processes are important topics that are also of interest in real-world optimization. In this chapter we discuss application opportunities for evolutionary computation methods in these three areas.

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Section: Bottlenecksmentioning

confidence: 97%

Evolutionary Computation for Real-World Problems

Bonyadi

Michalewicz

2015

Studies in Computational Intelligence

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“…They conclude that TOC and LP present the same performance and are superior to traditional accounting Fredendall and Lea (1997) Revise the TOC product mix heuristic to identify conditions where the original TOC heuristic fails Hsu and Chung (1998) Indicate the use of an explicit algorithm when a plant has multiple resource constraints, but do not compare its effectiveness with the TOC-h of Lea (1997) Mabin andGibson (1998) Reveal how the TOC and LP spreadsheet approaches can complement each other and may be integrated in a simple way Finch and Luebbe (2000) Criticise the comparison of TOC with LP performed by Balakrishnan and Cheng (2000); they affirm that they have different natures Balakrishnan and Cheng (2000) Contrary to the conclusions of Luebbe and Finch (1992), they show that using LP is preferable to the $ return/constraint unit method Onwubolu and Mutingi (2001a,b) Apply a genetic algorithm for the product mix decision Onwubolu (2001) Employs a Tabu-search-based algorithm to product mix problems Boyd and Cox (2002) Demonstrate that TOC outperforms three accounting systems when making some decisions, including product mix problems Mabin and Davies (2003) Study the product mix problem according to a variety of TOC approaches that complement traditional treatments such as LP Aryanezhad and Komijan (2004) Present and compare TOC-h and LP, and recommend an algorithm to determine the product mix Bhattacharya and Vasant (2007), Bhattacharya et al (2008) Describe an alternative to the LP solution for a TOC product mix using a fuzzy linear programming approach in order to maximise the degree of satisfaction of the decision maker Linhares (2009) Reinforces the fragility of the TOC heuristic, pointing out some facts that go against the TOC literature, including showing some particular cases where the application of TOC to define the production mix fails even for small problems and with a single bottleneck Wang, Sun, and Yang (2009) Propose an immune algorithm as a means to solve product mix problems Ray, Sarkar, and Sanyal (2010) Demonstrate the combined use of TOC and the analytic hierarchy process (AHP) in the product mix definition Sobreiro and Nagano (2012) Evaluate some constructive heuristics and propose a new and better (according to their findings) constructive heuristic based on the Theory of Constraints and the Knapsack Problem…”

Section: Authorsmentioning

confidence: 97%

“…The proposed heuristic is applied to solve a range of 100 problems, 12 of them based on problems proposed by Goldratt (1990), Luebbe and Finch (1992), Patterson (1992), Lee and Plenert (1993), Fredendall and Lea (1997) and Aryanezhad and Komijan (2004). The remaining 88 problems are randomly generated problems, including scenarios that blend manufacturing environments with two to eight products and with four to eight resources.…”

Section: Numerical Examplesmentioning

confidence: 99%

“…Research summary Luebbe and Finch (1992) Compare TOC and Linear Programming (LP) using examples, and clarify the relationships between TOC's five-step focusing process and LP Patterson (1992) Suggests the effectiveness of the TOC method for the product mix decision when compared with labour-based management accounting Plenert (1993) By means of an example, compares the LP method and the TOC philosophy, pointing out the differences between them Lee and Plenert (1993) Demonstrate the process used by TOC to determine the product mix that maximises the throughput as a very simple series of steps and that the LP can be used to calculate the optimal solution Maday (1994), Posnack (1994) Claim that TOC heuristic's solution would be optimal even without an integer solution Finch and Luebbe (1995) Identify weaknesses in the TOC methodology when there are multiple constraints Zegordi et al (1995), Mishra et al (2005), Chaharsooghi and Jafari (2007) Apply Simulated Annealing to product mix problems Lee and Plenert (1996) Compare three product mix approaches: traditional accounting, TOC and LP. They conclude that TOC and LP present the same performance and are superior to traditional accounting Fredendall and Lea (1997) Revise the TOC product mix heuristic to identify conditions where the original TOC heuristic fails Hsu and Chung (1998) Indicate the use of an explicit algorithm when a plant has multiple resource constraints, but do not compare its effectiveness with the TOC-h of Lea (1997) Mabin andGibson (1998) Reveal how the TOC and LP spreadsheet approaches can complement each other and may be integrated in a simple way Finch and Luebbe (2000) Criticise the comparison of TOC with LP performed by Balakrishnan and Cheng (2000); they affirm that they have different natures Balakrishnan and Cheng (2000) Contrary to the conclusions of Luebbe and Finch (1992), they show that using LP is preferable to the $ return/constraint unit method Onwubolu and Mutingi (2001a,b) Apply a genetic algorithm for the product mix decision Onwubolu (2001) Employs a Tabu-search-based algorithm to product mix problems Boyd and Cox (2002) Demonstrate that TOC outperforms three accounting systems when making some decisions, including product mix problems Mabin and Davies (2003) Study the product mix problem according to a variety of TOC approaches that complement traditional treatments such as LP …”

Section: Authorsmentioning

confidence: 99%

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When less is better: Insights from the product mix dilemma from the Theory of Constraints perspective

Souza

Sobreiro

Nagano

et al. 2013

International Journal of Production Research

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Perhaps due to its origins in a production scheduling software called Optimised Production Technology (OPT), plus the idea of focusing on system constraints, many believe that the Theory of Constraints (TOC) has a vocation for optimal solutions. Those who assess TOC according to this perspective indicate that it guarantees an optimal solution only in certain circumstances. In opposition to this view and founded on a numeric example of a production mix problem, this paper shows, by means of TOC assumptions, why the TOC should not be compared to methods intended to seek optimal or the best solutions, but rather sufficiently good solutions, possible in non-deterministic environments. Moreover, we extend the range of relevant literature on product mix decision by introducing a heuristic based on the uniquely identified work that aims at achieving feasible solutions according to the TOC point of view. The heuristic proposed is tested on 100 production mix problems and the results are compared with the responses obtained with the use of Integer Linear Programming. The results show that the heuristic gives good results on average, but performance falls sharply in some situations.

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“…The unit selling price of i product X 11 The selling quantities of drawn textured yarn X 12 The future processing quantities of drawn textured yarn X 21 The selling quantities of greige fabric X 22 The selling quantities of finished fabric…”

Section: Objective Functionmentioning

confidence: 99%

Green Production Planning and Control for the Textile Industry by Using Mathematical Programming and Industry 4.0 Techniques

Tsai

2018

Energies

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Abstract:The textile industry is one of the world's major sources of industrial pollution, and related environmental issues are becoming an ever greater concern. This paper considers the environmental issues of carbon emissions, energy recycling, and waste reuse, and uses a mathematical programming model with Activity-Based Costing (ABC) and the Theory of Constraints (TOC) to achieve profit maximization. This paper discusses the combination of mathematical programming and Industry 4.0 techniques to achieve the purpose of green production planning and control for the textile industry in the new era. The mathematical programming model is used to determine the optimal product mix under various production constraints, while Industry 4.0 techniques are used to control the production progress to achieve the planning targets. With the help of an Industry 4.0 real-time sensor and detection system, it can achieve the purposes of recycling waste, reducing carbon emission, saving energy and cost, and finally achieving a maximization of profit. The main contributions of this research are using mathematical programming approach to formulate the decision model with ABC cost data and TOC constraints for the textile companies and clarifying the relation between mathematical programming models and Industry 4.0 techniques. Managers in the textile companies can apply this decision model to achieve the optimal product-mix under various constraints and to evaluate the effect on profit of carbon emissions, energy recycling, waste reuse, and material quantity discount.

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Theory of constraints and linear programming: a comparison

Cited by 125 publications

References 0 publications

Evolutionary Computation for Real-World Problems

Evolutionary Computation for Real-World Problems

When less is better: Insights from the product mix dilemma from the Theory of Constraints perspective

Green Production Planning and Control for the Textile Industry by Using Mathematical Programming and Industry 4.0 Techniques

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