Aggregate Production Planning Problem Research Articles

A bi-level decision-making system to optimize a robust-resilient-sustainable aggregate production planning problem

This study introduces a sustainable-robust aggregate production planning (APP) problem taking into account workforce productivity, outsourcing option and supplier resilience. In this regard, a bi-level decision-making system is designed using multi-attribute decision-making (MADM) and multi-objective decision-making (MODM) models, respectively. In the MADM section, a hybrid method called BWM-WASPAS-Neutrosophic based on best-worst method (BWM) and weighted aggregated sum-product assessment (WASPAS) under type-2 neutrosophic number (T2NN) is utilized to investigate resilient supplier selection. To design the MODM section, a multi-objective mixed-integer linear programming (MILP) model is suggested which is then treated with the help of weighted goal programming (WGP) method. The multi-objective model honors sustainable development goals as it aims not only to minimize total cost and maximize weighted purchasing from suppliers, but also to minimize negative environmental impacts simultaneously. Robust optimization (RO) technique is then implemented to the MODM model to address the demand uncertainty. In order to validate the suggested methodology, a real case study from the literature is examined. The obtained results reveal the efficiency of our decision-making system in finding the optimal policy in less than 1 s where sensitivity analyses also contribute to practical managerial implications. Finally, it is revealed that the total weighted purchase from suppliers has the highest sensitivity to the conservatism levels, which determine the extent to which our uncertain demand parameter can deviate from its nominal value.

Integrated Possibilistic Linear Programming with Beta-Skewness Degree for a Fuzzy Multi-Objective Aggregate Production Planning Problem Under Uncertain Environments

This study proposes an improved Fuzzy Programming (FP) approach to optimise multi-objective Aggregate Production Planning (APP) problem under uncertain environments. The proposed approach integrates the concept of Possibilistic Linear Programming (PLP) with Beta-Skewness Degree that decision-makers can manipulate the best level of data fuzziness as well as maintain such fuzziness in the optimisation process (by not turning it to deterministic data too early). The effectiveness of the proposed approach is demonstrated through a case study by minimising the highest overall deviation from the ideal solution of total costs under imprecise operating costs, customer demand, labour level, and machine capacity. Our comparative result clearly shows that the obtained solution outperforms the solutions from traditional defuzzification methods. The proposed approach also helps decision-makers not only to know and optimise the most likely situation, but also realise the outcomes in the optimistic and the pessimistic business situations so that decision makers can prepare and take necessary actions for future uncertainty.

Integrating a Weighted Additive Multiple Objective Linear Model with Possibilistic Linear Programming for Fuzzy Aggregate Production Planning Problems

This study uses an integrated optimization method by applying a weighted additive multiple objective linear model with Possibilistic Linear Programming (PLP) to fuzzy Aggregate Production Planning (APP) problems under an uncertain environment. The uncertainty conditions include uncertainties of operating times and costs, customer demand, labor level, as well as machine capacity. The aim of this study is to minimize total costs of the plan that consist of the production cost and costs of changes in labor level. The proposed hybrid approach minimizes the most possible value of the imprecise total costs, maximizes the possibility of obtaining lower total costs, and minimizes the risk of obtaining higher total costs from PLP as multiple objectives for the fuzzy multiple objective linear model optimization. The outcome of the proposed approach shows that the solution is closer to the ideal solution obtained from Linear Programming than a typical solution obtained from PLP. There is also a higher overall satisfaction value.

A Pareto-based approach to optimise aggregate production planning problem considering reliable supplier selection

This work presents a multi objective model for a multi-product, multi-site aggregate production planning (APP) problem in a supply chain. The objectives are: 1) minimising the total cost of supply chain including inventory costs, manufacturing costs, work force costs, hiring, and firing costs; 2) maximising the reliability of the supply chain's production plan with regard to the selection of reliable facilities which have probabilistic lead times. Based on the complexity of the proposed model, two Pareto-based multi-objective metaheuristic algorithms including multi-objective imperialist competitive algorithm (MOICA) and non-dominated sorting genetic algorithm (NSGA-II) were applied to solve the proposed model. In order to evaluate the results, several numerical examples were generated, by which the algorithms were analysed statistically and graphically.

A Pareto-based approach to optimise aggregate production planning problem considering reliable supplier selection

This work presents a multi objective model for a multi-product, multi-site aggregate production planning (APP) problem in a supply chain. The objectives are: 1) minimising the total cost of supply chain including inventory costs, manufacturing costs, work force costs, hiring, and firing costs; 2) maximising the reliability of the supply chain's production plan with regard to the selection of reliable facilities which have probabilistic lead times. Based on the complexity of the proposed model, two Pareto-based multi-objective metaheuristic algorithms including multi-objective imperialist competitive algorithm (MOICA) and non-dominated sorting genetic algorithm (NSGA-II) were applied to solve the proposed model. In order to evaluate the results, several numerical examples were generated, by which the algorithms were analysed statistically and graphically.

A bi-objective aggregate production planning problem with learning effect and machine deterioration: Modeling and solution

The learning effects of the workers and machine deterioration in an aggregate production planning (APP) problem have not been taken into account in the literature yet. These factors affect the performance of any real-world production system and require attention. In this paper, a bi-objective optimization model is developed for an APP problem with labor learning effect and machine deterioration. The first objective of this model maximizes the profit by improving learning and reducing the failure cost of the system. The second objective function minimizes the costs associated with repairs and deterioration, which depend on the failure rate of the machines in the production periods. The aim of this article is to obtain appropriate levels of production rates in regular and overtimes, inventory and shortage levels, workers' hiring and firing levels, and the quantities of the products that are subcontracted. To demonstrate the validity of the proposed mathematical formulation, the multi-objective model is converted into a single-objective model using the fuzzy goal programming method, based on which computational experiments are performed on a set of random small-sized instances solved by the LINGO software. As the problem is shown NP-hard, a subpopulation genetic algorithm (SPGA) is proposed to solve large-size problems. In addition, two other meta-heuristics called weighted sum multi-objective genetic algorithm (WMOGA) and non-dominated sorting genetic algorithm II (NSGA-II) are utilized to solve a set of benchmark problems, in order to validate the results obtained and to assess the performance of the SPGA. For tuning the parameters, the Taguchi method is proposed in order to obtain high-quality solutions. Finally, the performances of the proposed algorithms are statistically compared together. The computational results show that SPGA compared to the other algorithms has a better performance in terms of some multi-objective optimization criteria.

Optimal Control Approaches to the Aggregate Production Planning Problem

In the area of production planning and control, the aggregate production planning (APP) problem represents a great challenge for decision makers in production-inventory systems. Tradeoff between inventory-capacity is known as the APP problem. To address it, static and dynamic models have been proposed, which in general have several shortcomings. It is the premise of this paper that the main drawback of these proposals is, that they do not take into account the dynamic nature of the APP. For this reason, we propose the use of an Optimal Control (OC) formulation via the approach of energy-based and Hamiltonian-present value. The main contribution of this paper is the mathematical model which integrates a second order dynamical system coupled with a first order system, incorporating production rate, inventory level, and capacity as well with the associated cost by work force in the same formulation. Also, a novel result in relation with the Hamiltonian-present value in the OC formulation is that it reduces the inventory level compared with the pure energy based approach for APP. A set of simulations are provided which verifies the theoretical contribution of this work.

A Fuzzy Goal Programming model for solving aggregate production-planning problems under uncertainty: A case study in a Brazilian sugar mill

This paper proposes a Fuzzy Goal Programming model (FGP) for a real aggregate production-planning problem. To do so, an application was made in a Brazilian Sugar and Ethanol Milling Company. The FGP Model depicts the comprehensive production process of sugar, ethanol, molasses and derivatives, and considers the uncertainties involved in ethanol and sugar production. Decision-makings, related to the agricultural and logistics phases, were considered on a weekly-basis planning horizon to include the whole harvesting season and the periods between harvests. The research has provided interesting results about decisions in the agricultural stages of cutting, loading and transportation to sugarcane suppliers and, especially, in milling decisions, whose choice of production process includes storage and logistics distribution.

Solving Fuzzy Multiproduct Aggregate Production Planning Problems Based on Extension Principle

Aggregate production planning (APP) plays a critical role in supply chain management (SCM). This paper investigates multiproduct, multiperiod APP problems with several distinct types of fuzzy uncertainties. In contrast to the existing studies, the modelling in this work conserves the fuzziness such that the obtained APP is more effective. Based on Zadeh’s extension principle, the results obtained are fuzzy solutions described by membership functions, in contrast to results from previous studies. A pair of two-level parametric mathematical programs is formulated to calculate the lower and upper bounds of the optimum fuzzy performance measure. The membership function of the fuzzy total cost is constructed by enumerating various possibility levels. A case studied in previous research is investigated to demonstrate the validity of the proposed model and solution procedure. Because the optimal objective value and associated decision variables are expressed using fuzzy numbers rather than crisp values, the proposed approach is able to represent APP systems more accurately, and therefore, the results obtained can provide decision makers with more effective and informative APPs and more chance to achieve the optimal disaggregate plan.

Solving an Aggregate Production Planning Problem by Fuzzy Based Genetic Algorithm (FBGA) Approach

This paper work demonstrated an interactive Fuzzy Based Genetic Algorithm (FBGA) approach for solving a two products & two periods aggregate production planning (APP) with some vulnerable managerial constraints like imprecise demands, variable manufacturing costs etc. This proposed approach used the strategy of simultaneously minimizing the most possible value, the most pessimistic value & also most optimistic value of the imprecise total costs in lieu of some strong resource constraints. Another important purpose of this study is to derive & observe the variations along with the scope of the imprecise total cost, maximizing the possibility of obtaining lower total costs and also minimizing the risk of obtaining higher total costs. Here the authors employed different unique genetic algorithm parameters scrupulously for solving nondeterministic polynomials problems like APP problems. For reinforcing & accelerating the decision making for the decision maker a case study was considered in a Ready Made garment company in Bangladesh. Consequently, the proposed FBGA approach yields an efficient APP compromise solution and could be efficient for large scale problems.

Solving an aggregate production planning problem by using multi-objective genetic algorithm (MOGA) approach

: Received 5 September 2012 Received in revised format 25 September 2012 Accepted September 27 2012 Available online 27 September 2012 In hierarchical production planning system, Aggregate Production Planning (APP) falls between the broad decisions of long-range planning and the highly specific and detailed short-range planning decisions. This study develops an interactive Multi-Objective Genetic Algorithm (MOGA) approach for solving the multi-product, multi-period aggregate production planning (APP) with forecasted demand, related operating costs, and capacity. The proposed approach attempts to minimize total costs with reference to inventory levels, labor levels, overtime, subcontracting and backordering levels, and labor, machine and warehouse capacity. Here several genetic algorithm parameters are considered for solving NP-hard problem (APP problem) and their relative comparisons are focused to choose the most auspicious combination for solving multiple objective problems. An industrial case demonstrates the feasibility of applying the proposed approach to real APP decision problems. Consequently, the proposed MOGA approach yields an efficient APP compromise solution for large-scale problems.

A membership function approach for aggregate production planning problems in fuzzy environments

This paper proposes a novel approach for the aggregate production planning (APP) problem with fuzzy parameters. Different from the results of previous studies, in this paper the membership function of the fuzzy minimal total cost is constructed based on Zadeh's extension principle and fuzzy solutions are provided. A pair of mathematical programs parameterised by possibility level α is formulated to calculate the lower and upper bounds of the fuzzy total cost at α. By enumerating different values of α, the membership function of the fuzzy total cost is constructed. To illustrate the validity of the proposed approach, the example studied by Lai and Hwang (1992) using Chanas's approach is investigated. Since the objective value is expressed by a membership function rather than by a crisp value, the proposed approach can represent APP systems more accurately, thus obtained solutions which contain more information can offer more chance to achieve the feasible disaggregate plan, and it is beneficial to the decision-maker in practical applications. The proposed approach can also be applied to APP problems with other characteristics.

A tabu search approach to fuzzy goal programs and an application to aggregate production planning

In this article, a multiple-objective tabu-search-based solution method is developed to solve fuzzy goal programs. The application of the method is shown on a fuzzy aggregate production-planning problem. Extensive computational work is carried out to present the performance of the algorithm and the effect of its parameters on the solution quality.

Global Production Planning Under Exchange-Rate Uncertainty

Motivated by an aggregate production-planning problem in an actual global manufacturing network, we examine the impact of exchange-rate uncertainty on the choice of optimal production policies when the allocation decision can be deferred until the realization of exchange rates. This leads to the formulation of the problem as a two-stage recourse program whose optimal policy structure features two forms of flexibility denoted as operational hedging: (1) production hedging, where the firm deliberately produces less than the total demand; and (2) allocation hedging, where due to unfavorable exchange rates, some markets are not served despite having unused production. Our characterization of the optimal policy structure leads to an economic valuation of production and allocation hedging. We show that the prevalence of production hedging is moderated by the degree of correlation between exchange rates. A comprehensive examination under the following four generalized settings provides the depth, scope, and relevancy that our proposed operational hedges play to facilitate aggregate planning: (1) multiple periods, (2) demand uncertainty, (3) price setting or monopolistic pricing, and (4) price setting under demand uncertainty. We show that production and allocation hedging are robust for these generalizations and should be integrated into the overall aggregate planning strategy of a global manufacturing firm.

HYBRID GENETIC — ANT COLONY ALGORITHMS FOR SOLVING AGGREGATE PRODUCTION PLAN

It is necessary for the management of any industry to workout an intermediate range plan also known as aggregate production plan, consistently with the long range policies and resources allocated by long range decisions. It is a procedure of translating the expected demand and production capacity of the available facilities into future manufacturing plans for a family of products. It includes decisions on production quantity, work force and inventory to workout a low cost product and timely delivery. Ant colony optimization algorithm finds its extensive application in solving job shop scheduling, assignment problems, transportation problems, etc. Genetic algorithms are proposed to solve the problem, already by the authors. In this paper, an attempt is made to solve an aggregate production-planning problem for obtaining an effective solution using ant colony algorithm. Also a hybrid algorithm that combines genetic algorithm and ant colony algorithm is proposed and its effectiveness over the models developed using genetic algorithms and ant colony algorithm is also analyzed.

Optimization of continuous-time production planning using hybrid genetic algorithms-simulated annealing

Evolutionary algorithms are stochastic search methods that mimic the principles of natural biological evolution to produce better and better approximations to a solution and have been used widely for optimization problems. A general problem of continuous-time aggregate production planning for a given total number of changes in production rate over the total planning horizon is considered. It is very important to identify and solve the problem of continuous-time production planning horizon with varying production rates over the interval of the planning period horizon. Some of the researchers have proposed global search methods for the continuous-time aggregate production-planning problem. So far, less work is reported to solve the problem of continuous-time production planning using local search methods like genetic algorithms (GA) and simulated annealing (SA). So in this work, we propose a modified single objective evolutionary program approach, namely GA, SA, and hybrid genetic algorithms-simulated annealing (GA-SA) for continuous-time production plan problems. The results are compared with each other and it was found that the hybrid algorithm performs better.

A robust optimization model for stochastic aggregate production planning

The aggregate production planning (APP) problem considers the medium-term production loading plans subject to certain restrictions such as production capacity and workforce level. It is not uncommon for management to often encounter uncertainty and noisy data, in which the variables or parameters are stochastic. In this paper, a robust optimization model is developed to solve the aggregate production planning problems in an environment of uncertainty in which the production cost, labour cost, inventory cost, and hiring and layoff cost are minimized. By adjusting penalty parameters, decision-makers can determine an optimal medium-term production strategy including production loading plan and workforce level while considering different economic growth scenarios. Numerical results demonstrate the robustness and effectiveness of the proposed model. The proposed model is realistic for dealing with uncertain economic conditions. The analysis of the tradeoff between solution robustness and model robustness is also presented.

Aggregate production planning for a continuous reconfigurable manufacturing process

Most of the research on aggregate production planning has been focused on discrete parts manufacturing models. In environments where intermediate inventory cannot be stored, and multiple products are produced simultaneously using complex configurations of production machines, these models may produce erroneous results. In this paper, we present a configuration-based formulation for one such manufacturing environment, where production may involve dissimilar machines performing similar operations at different rates and equipment can be connected together to form different production lines. The production process is continuous and no in-process inventory can be kept. We present and compare several heuristics to generate input data to solve the aggregate production-planning problems using the configuration-based formulation. Computational experiments show that large-scale real-world problems we encountered can be solved in reasonable time using our heuristics and commercial optimization software like CPLEX.

Fuzzy modelling and simulation for aggregate production planning

The market demands and financial constraints in medium- to long-term production planning are often subject to uncertainties. As an extension of the author's previous paper, this paper focuses on a formulation and simulation analysis for multi-product aggregate production-planning problems with fuzzy demands and fuzzy capacities. The fuzzy production–inventory balance equation is formulated as a soft equation and can be interpreted as the possibility level of meeting the market demands, which is more meaningful and accepted by the practitioner than the previous one. With this interpretation, a fuzzy multi-product aggregate production-planning model is transformed into a parametric programming model. A simulation of a practical instance is conducted to illustrate the model and demonstrate the performance and effect of various parameters on the optimal aggregate production plan. The proposed formulation and simulation analysis can help the decision-maker make a reasonable and preferred aggregate plan to guarantee feasibility of the downstream family disaggregation plans.

Fuzzy formulation for multi-product aggregate production planning

Considering that the demand requirements are fuzzy demand in each period during the planning horizon, this paper focuses on a novel approach to modelling multi-product aggregate production planning (APP) problems with fuzzy demands and fuzzy capacities. The objective of the problem considered is to minimize the total costs of quadratic production costs and linear inventory holding costs. By means of formulation of fuzzy demand, fuzzy addition and fuzzy equation, the productioninventory balance equation in single stage and dynamic balance equation are formulated as soft equations in terms of a degree of truth, and interpreted as the levels of satisfaction with production and inventory plan in meeting market demands. As a result, the multi-product aggregate production planning problem with fuzzy demands and fuzzy capacities can be modelled into a fuzzy quadratic programming with fuzzy objective and fuzzy constraints. The fuzzy solution approach to the model is also proposed in this paper. It can offer the decision-maker (DM) more choices to construct an aggregate production plan so as to ensure the feasibility of family disaggregation plan, especially in fuzzy environment.