Product Mix Problem Research Articles

Determining the optimal product mix in multiple constraints manufacturing environment: an application in the textile industry

Theory of constraints (TOC) is an approach to production planning and control by focusing on the constraints of an organization to increase throughput by effectively managing constraints. TOC approach has been applied in many sectors, and efficient results have been taken. One of the application areas of TOC is product mix decisions. Product mix decisions are important for multi-product manufacturing systems because they affect the performance measures of the companies. This study aims to present how TOC is applied to determine the optimum product mix in a multiple- constraint environment in the textile industry. To achieve this, we first select three basic products of a textile company and examine the production processes of these products from TOC perspective. Next, we perform a bottleneck process and identify three bottlenecks for the problem. Then, based on our bottleneck process results, we generate three scenarios. Upon assessing these scenarios, we determine the most appropriate product mix by implementing the TOC approach. Finally, we employ a goal programming approach to solve the product mix problem and compare its results with those obtained by the TOC.

Solution of Large-Scale Linear Programming Problem by Using Computer Technique

Linear programming (LP) is an important part of applied mathematics. This method has found its applications to important areas of product mix, blending, and diet problems. Steel, chemical, food processing industries and Oil refineries industry are also using LP with considerable success. But in practical LP can be very large. In this paper, our intent is to formulate an LP model of some large-scale real-life-oriented problems and to apply computer techniques for solving these problems. Starting with the graphical procedure which provides an ample amount of understanding into some fundamental concepts, the simple procedure of solving LP problems is developed. Finally, a special class of LP problem, namely Transportation is taken up and solved. We also solved the simplex system by using FORTRAN programming.

“Case Study: Application for optimizing the product mix problem of linear programming in the Apparel Industry”

The industry has made effective management decision-making techniques possible through surveys and the efficient use of sources and assets. Linear programming can be used for the optimization problem of product mix. We have to understand the concept behind the optimization problem of product mix is important to get success in the industry for meeting customer needs. The manufacturing profit depends on the proper distribution of product material and usage of available production time material and labor resources. The findings of the study show that the profit of the company and the demand for the product.

Cuckoo Search Optimization for Solving Product Mix Problem

The success of industrial companies is characterized by the efficient use of its resources. Most of decisions regarding to the efficient use of resources such as man, machine and material are subject to constraints. This paper considers a class of resource allocation problem named Product Mix Problem (PMP). The PMP is considered as an important production planning decision in the field of industrial engineering and management. The objective of this paper is to find the optimal quantities of different products that are required different amount of resources to maximize the return profit of a company where resources are limited. A Cuckoo Search Optimization (CSO) is proposed in this paper to as a methodology to search optimal solution. MATLAB Software is used to perform the proposed CSO method. Then, a comparative study between the CSO solution and existing solution in the literature is given. The simulations outcomes show the superiority of CSO over other methods.

Shifting bottleneck-driven TOCh for solving product mix problems

Product mix optimisation is one of the most important strategic decisions determining the product type and the corresponding quantity to maximise the system throughput. This paper proposes a new heuristic named shifting bottleneck-driven TOC heuristic (STOCh) for solving product mix problems with multiple bottleneck resources. STOCh is comprised of master product schedule (MPS) generation and its local adjustment. The major improvement is that STOCh dynamically identifies and utilises shifting bottlenecks, rather than fixed bottlenecks commonly used in the existing literature, to avoid being caught in a local optimum. Besides, local adjustment strategy can refine neighbourhood space and limit the search in a high-quality solution space to gain better solutions. Numerical studies show that STOCh outperforms three most famous TOC heuristics in the existing literature, i.e. RTOCh, TOC_AK and TOC_SN. The average relative deviation of the solutions by STOCh from the optimal solutions by CPLEX is only around 3%. Further results show that STOCh performs particularly well when facing multiple bottleneck scenarios, especially when the capacity of bottleneck resource is very scarce. A case study based on real data from a SME in China demonstrates the effectiveness of the proposed STOCh.

Group decision-making and grey programming approaches to optimal product mix in manufacturing supply chains

Group decision-making is a significant task that involves trade-offs, risks and the interplay of various factors. Optimization models developed from group decision-making are often built on uncertainties and negotiated parameters and may not yield factual solutions. Manufacturing decision-making environment is subject to several uncertainties, and grey theory is an effective tool to improve the exactitude of decision-making in such situations. An application of grey programming in manufacturing decision-making environment has been implemented in this research. Grey programming models can potentially avoid the loss of data while formulating optimization models from group decisions. A grey programming model for optimizing profits has been constructed and solved for an indeterminate product mix problem of a case electronics manufacturing industry. For the case, the optimization models were constructed and solved for the ideal model, critical model and the most typical model. And the results favor the decision on the introduction of a new product variant in the smartphone segment. In the most favorable and unfavorable conditions, it is seen that the introduction of new variant in the smartphone section is meritorious when compared to the tablet or laptop segments. The solution to the case endorses flexibility of grey programming in uncertain decision-making environments. As the decisions from the group can be signified in intervals using grey numbers, managers are recommended to comprise the benefits of grey programming models into their optimization problems for increasing flexibility and reliability of solutions.

Solving product mix problem in multiple constraints environment using goal programming

The theory of constraints is an approach to production planning and control that emphasizes on the constraints to increase throughput by effectively managing constraint resources. One application in theory of constraints is product mix decision. Product mix influences the performance measures in multi-product manufacturing system. This paper presents an alternative approach by using of goal programming to determine the product mix of the manufacturing system. The objective of paper is to provide a methodology in order to make product mix decision. Key point of the proposed methodology is considering decision maker idea to determine the weights of objective functions that are throughput and bottleneck exploitation. Therefore the weights of the objective functions are determined by the information get from decision maker. Through an example, inefficiency of theory of constraints in multiple bottleneck problems has been showed. Comparison of theory of constraints, linear programming and other methods to product mix problem has also discussed to show the advantages of the proposed method.

Sustainability Concept in Decision-Making: Carbon Tax Consideration for Joint Product Mix Decision

Carbon emissions are receiving greater scrutiny in many countries due to international forces to reduce anthropogenic global climate change. Carbon taxation is one of the most common carbon emission regulation policies, and companies must incorporate it into their production and pricing decisions. Activity-based costing (ABC) and the theory of constraints (TOC) have been applied to solve product mix problems; however, a challenging aspect of the product mix problem involves evaluating joint manufactured products, while reducing carbon emissions and environmental pollution to fulfill social responsibility. The aim of this paper is to apply ABC and TOC to analyze green product mix decision-making for joint products using a mathematical programming model and the joint production data of pharmaceutical industry companies for the processing of active pharmaceutical ingredients (APIs) in drugs for medical use. This paper illustrates that the time-driven ABC model leads to optimal joint product mix decisions and performs sensitivity analysis to study how the optimal solution will change with the carbon tax. Our findings provide insight into ‘sustainability decisions’ and are beneficial in terms of environmental management in a competitive pharmaceutical industry.

The product-mix problem for multiple production lines in sequenced stages: a case study in the steel industry

The product-mix problem is common and widely applicable in many industries. This paper formulates the product-mix problem for multiple production lines in sequenced stages where the output of the upstream stage is the input for other downstream operations. The objective is to maximize the upstream production (throughput per time) by which throughput of the whole system including the downstream operations will be maximized to satisfy production constraints: productivity, capacity, and sales requirements. The problem is formulated using an integer linear programming (ILP) model and demonstrated in a steel plant in Saudi Arabia. The 480-MT steel plant has six production lines, namely push-pickling line, cold-reversing mill, batch-annealing facility, temper mill, continuous galvanizing line, and color-coating line. The plant intended to leverage its annual production capacity. Hence, a recent expansion was done on the batch annealing facility. After the expansion, the plant had several production interruptions and stoppages in the downstream facilities. The model provided the maximum throughput for all production stages and avoids production interruptions.

Evaluating productive performance: A new approach based on the product-mix problem consistent with Data Envelopment Analysis

We propose a new approach to estimate technical coefficients from a set of Decision Making Units (DMUs) under the assumption that their production plans are set by process engineers through Linear Programming (LP) techniques. The idea behind this approach is that most manufacturing and agricultural firms routinely resort to LP-based modeling in their decision making processes in order to plan output production and, therefore, this particularity should be taken into account when estimating their technical efficiency. A usual model of LP for these sectors is the so-called product-mix problem, which we relate to a standard Data Envelopment Analysis (DEA) model in terms of the Directional Distance Function. In this paper, we finally show how to estimate the technical coefficients of a sample of Andalusian farms in Spain and how this information can be seen as a complement to the usual by-products associated with estimating technical efficiency by DEA.

Robust efficiency measures for linear knapsack problem variants

Numerous combinatorial optimization applications, such as the mobile retailer product mix problem, utilize the multidemand, multidimensional knapsack problem variant in which there are multiple knapsack constraints requiring a weighted summation of the variables to be less than or equal to a nonnegative value and multiple demand constraints requiring a weighted summation of the variables to be greater than or equal to a nonnegative value. The purpose of this paper is to demonstrate that core variables and efficiency measures, concepts used in the most efficient solvers to-date for binary knapsack problems and some of its variants, can be extended to the multidemand, multidimensional knapsack problem variant. Specifically, new efficiency measure calculations are provided and their properties are mathematically proven and experimentally demonstrated. The contribution of such measures to knapsack problem research is that these measures are applicable to all knapsack problem variants with a single linear objective function and linear constraints of any quantity. The applicability of these new measures is demonstrated through the development of three heuristic procedures: a Fixed-Core heuristic, a Genetic Algorithm, and a Kernel Search heuristic. The results from these tests are compared with the results from a commercial solver and an existing heuristic. The findings from these tests demonstrate that the Fixed-Core and Kernel Search heuristics developed for this paper are the most efficient solvers to-date for hard multidemand, multidimensional knapsack problems.

Incessant Allocation Method for Solving Transportation Problems

Industries require planning in transporting their products from production centres to the users end with minimal transporting cost to maximize profit. This process is known as Transportation Problem which is used to analyze and minimize transportation cost. This problem is well discussed in operation research for its wide application in various fields, such as scheduling, personnel assignment, product mix problems and many others, so that this problem is really not confined to transportation or distribution only. In the solution procedure of a transportation problem, finding an initial basic feasible solution is the prerequisite to obtain the optimal solution. Again, development is a continuous and endless process to find the best among the bests. The growing complexity of management calls for development of sound methods and techniques for solution of the problems. Considering these factors, this research aims to propose an algorithm “Incessant Allocation Method” to obtain an initial basic feasible solution for the transportation problems. Several numbers of numerical problems are also solved to justify the method. Obtained results show that the proposed algorithm is effective in solving transportation problems.

Throughput accounting and performance of a manufacturing company under stochastic demand and scrap rates

Theory of constraints (TOC) has emerged as an effective management philosophy suggesting practical solutions to various complex problems including product mix problem. Scholars have shown the superiority of various optimization (and artificial intelligence) approaches over the TOC-based heuristic to a “static” product mix problem, but have failed to see TOC as a whole, i.e. to take into consideration the impact of resource inter-dependencies, feedback loops, and importantly, statistical fluctuations ever present in any dynamic business environment. We proposed a system dynamics (SD) based simulation model to investigate product-mix problem under stochastic demand and scrap rates. We analyzed various scenarios by employing the drum-buffer-rope approach and constraint focused systematic scrap rate reduction approach, and importantly, evaluating performance using throughput accounting based global measures such as throughput and inventory. We conclude this paper by suggesting that future research efforts should be directed to develop an enabling hybrid expert simulation system to learn fundamental and powerful concepts underlying the theory of constraints.

Product mix optimization for a semiconductor fab: Modeling approaches and decomposition techniques

To optimize the product mix of a semiconductor fab, the production capabilities and capacities are matched with the demand in the most profitable way. In this paper we address a linear programming model of the product mix problem considering product dependent demand limits (e.g. obligations and demand forecast) and profits while respecting the capacity bounds of the production facility. Since the capacity consumption is highly dependent on choosing from different production alternatives we are implicitly solving a static capacity planning problem for each product mix. This kind of planning approach is supported by the fluid flow concept and complete resource pooling in high traffic. We propose a general model that considers a wide range of objectives, and we introduce a heuristic that is based on the decomposition of the static capacity planning problem. A computational study reports on the quality of the decomposition approaches, and examples from practice demonstrate the versatility of the model.

Interior analysis of the green product mix solution

When modeling optimal product mix under emission restrictions produces a solution with unacceptable level of profit, analyst is moved to investigate the cause(s). Interior analysis (IA) is proposed for this purpose. With IA, analyst can investigate the impact of accommodating emission controls in step-by-step one-at-a-time manner and in doing so track how profit and other important features of product mix degrade and to which emission control enforcements its diminution may be attributed. In this way, analyst can assist manager in identifying implementation strategies. Although IA is presented within context of a linear programming formulation of the green product mix problem, its methodology may be applied to other modeling frameworks. Quantity dependent penalty rates and transformations of emissions to forms with or without economic value are included in the modeling and illustrations of IA.

The TOC-Based Algorithm for Solving Multiple Constraint Resources: A Re-examination

In a previous paper in this journal named The TOC-Based Algorithm for Solving Multiple Constraint Resources, Ray considered an integrated heuristic approach named AHP/TOC comprising the analytic hierarchy process (AHP) and theory of constraints (TOC) in a multiple constraints resource product mix problem. This paper gives three typical examples and points out that the proposed approach would not generate the optimal solution. Furthermore, the reasons are analyzed in terms of the ranking approach of product priority using AHP and the adjustment approach of product mix after a new bottleneck has been identified. We clarify the cases under which the AHP/TOC method can and cannot output the optimal solution. Finally, some possible improvements are given.

An integrated model for product mix problem and scheduling considering overlapped operations

Article history: Received February 14, 2014 Accepted May 29, 2014 Available online May 31 2014 Product mix problem is one of the most important decisions made in production systems. Several algorithms have been developed to determine the product mix. Most of the previous works assume that all resources can perform, simultaneously and independently, which may lead to infeasibility of the schedule. In this paper, product mix problem and scheduling are considered, simultaneously. A new mixed-integer programming (MIP) model is proposed to formulate this problem. The proposed model differentiates between process batch size and transfer batch size. Therefore, it is possible to have overlapped operations. The numerical example is used to demonstrate the implementation of the proposed model. In addition, the proposed model is examined using some instances previously cited in the literature. The preliminary computational results show that the proposed model can generate higher performance than conventional product mix model. © 2014 Growing Science Ltd. All rights reserved.

A multi-criteria decision-making approach to solve the product mix problem with interval parameters based on the theory of constraints

The product mix problem is one of the most important problems in production systems. Several algorithms to determine the product mix under the theory of constraints have been developed. Most of the previous works focused on one bottleneck (dominant bottleneck) and considered the product mix problem with exact data. In this paper, all bottlenecks are used in order to determine the aggregated priority of each product, and a multi-criteria decision-making approach is proposed for product mix problem with interval parameters. The proposed approach involves bottlenecks identification, determination of the production priority and the weights vector of bottlenecks, application of interval TOPSIS to calculate the aggregated priority of each product, and use of reducing and increasing process to improve the production plan. At the end, a numerical example is presented to illustrate the procedure of the proposed approach. The results obtained from the computational study have shown that the proposed algorithm is an effective approach to solve the product mix problem.

Intelligent Decision Making Using Evolutionary System for Optimizing Product-Mix Model

The development and deployment of managerial decision support system represents an emerging trend in the business and organizational field in which the increased application of Decision Support Systems (DSS) can be compiling by Intelligent Systems (IS). Decision Support Systems (DSS) are a specific class of computerized information system that supports business and organizational decision-making activities. A properly designed DSS is an interactive software-based system intended to help decision makers compile useful information from raw data, documents, personal knowledge, and/or business models to identify and solve problems and make decisions. Competitive business pressures and a desire to leverage existing information technology investments have led many firms to explore the benefits of evolutionary system data management solutions such as Particle Swarm Optimization (PSO) and Genetic Algorithm (GA). This study proposes a new model for product mix problem based on evolutionary system for optimizing constraint values as well as objective function. The formulations of the objective function for the minimization problem. This technology is designed to help businesses to finding multi objective functions.

Extension of an algorithm for product mix problems with fuzzy conditions

In the real world of production, there are some uncertain parameters such as capacity, profit, and processing time. On the other hand, the fuzzy sets theory is applied as a suitable tool for managing production where dynamicity of the production environment prevents from determining target function, constraints and other parameters of the model. In this paper, a genetic algorithm embedded in fuzzy revised theory of constraints is presented for product mix problems. Results of implementing the proposed algorithm show efficiency and flexibility of this algorithm.