Benders Decomposition Algorithm for Robust Aggregate Production Planning Considering Pricing Decisions in Competitive Environment: A Case Study

This paper studies a real-world manufacturing problem, which is modeled as a bi-objective integer programming problem. The variables and constraints involved are usually numerous and dramatically vary according to the manufacturing data. It is very challenging to directly solve such large-scale problems using heuristic algorithms or commercial solvers. Considering that the decision space of such problems is usually sparse and has a block-like structure, we propose to use decomposition methods to accelerate the optimization process. However, the existing decomposition methods require that the problem has strict block structures, which is not suitable for our problem. To deal with problems with such block-like structures, we propose a game theory based decomposition algorithm. This new method can overcome the large-scale issue and guarantee convergence to some extent, as it can narrow down the search space and accelerate the convergence. Extensive experimental results on real-world industrial manufacturing planning problems show that our method is more effective than the world fastest commercial solver Gurobi. The results also indicate that our method is less sensitive to the problem scale comparing with Gurobi.

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“…with γ as the real vector. 1 To get the optimal controller, we have ∂H u 2 ∂u 2 = 0, which leads to:…”

Section: Theoretical Discussionmentioning

confidence: 99%

“…A new method based on symmetry-breaking constraints have been utilized for both reformulation and reduction of model in solving large-scale LP and IP [9,10]. Otherwise, there also exists some related research from the field of game [1,4]. They have combined different games with various decomposition algorithms.…”

Section: Introductionmentioning

confidence: 99%

Accelerate the optimization of large-scale manufacturing planning using game theory

Zhen

Wang

et al. 2021

Complex Intell. Syst.

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“…A way to dissolve such an issue is by using particular quadratic programming (e.g. Holt et al [8]), and numerous models have spawned henceforth [9][10][11][12][13][14][15][16], among which subjective criteria are rare in the majority and rather transformed into quantitative ones [17]. Aydin and Tirkolaee [18] conducted a systematic review of the literature on APP over the last 50 years.…”

Section: Literature Reviewmentioning

confidence: 99%

Solving Aggregate Production Planning Problems: An Extended TOPSIS Approach

Kao

Chiang

et al. 2022

Applied Sciences

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Aggregate production planning (APP) was developed for solving the problem of determining production, inventory, and workforce levels to meet fluctuating demand requirements over a planning horizon. In this work, multiple objectives were considered to determine the most effective means of satisfying forecasted demand by adjusting production rates, hiring and layoffs, inventory levels, overtime work, back orders, and other controllable variables. An extended technique for order preference via the similarity ideal solution (TOPSIS) approach was developed. It was formulated to solve this complicated, multi-objective APP decision problem. Compromise (ideal solution) control minimized the measure of distance, providing which of the closest solutions has the shortest distance from a positive ideal solution (PIS) and the longest distance from a negative ideal solution (NIS). The proposed method can transform multiple objectives into two objectives. The bi-objective problem can then be solved by balancing satisfaction using a max–min operator for resolving the conflict between the new criteria based on PIS and NIS. Finally, an application example demonstrated the proposed model’s applicability to practical APP decision problems.

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“…According to previous research, the potential demand depends on price as stated in Equation (1) [7,30,31]:…”

Section: Development Of Demand Functionmentioning

confidence: 99%

A Bi-objective Robust Optimization Model for an Integrated Production-distribution Problem of Perishable Goods with Demand Improvement Strategies: A Case Study

Aazami

Saidi‐Mehrabad

Seyedhosseini

2021

IJE

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This paper develops a bi-objective optimization model for the integrated production-distribution planning of perishable goods under uncertainty. The first objective seeks to maximize the profit in a specific supply chain with three levels: plants, distribution centers, and in the last level, customers. Since transportation is one of the major pollution sources in a distribution problem, the second objective is to minimize their emission. In the considered problem, the decisions of production, location, inventory, and transportation are made in an integrated structure. In developing the demand function, the effect of the product freshness and the price is formulated. Besides, to encourage customers, three strategies, including perished product return, discount, and credit policies, are proposed. Also, robust optimization is utilized to cope with the operational uncertainty of some cost parameters. To prove the applicability of this research and the feasibility of the environmental aspect, a case study is conducted. Finally, the numerical computations on the case study provide a trade-off between the environmental and economic goals and indicate a 37.5 percent increase in the profit using the developed model.

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Benders Decomposition Algorithm for Robust Aggregate Production Planning Considering Pricing Decisions in Competitive Environment: A Case Study

Cited by 5 publications

References 73 publications

Accelerate the optimization of large-scale manufacturing planning using game theory

Accelerate the optimization of large-scale manufacturing planning using game theory

Solving Aggregate Production Planning Problems: An Extended TOPSIS Approach

A Bi-objective Robust Optimization Model for an Integrated Production-distribution Problem of Perishable Goods with Demand Improvement Strategies: A Case Study

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