linear programming

The objective of this manuscript is to introduce an innovative methodology for addressing multiple attribute group decision-making (MAGDM) problems utilizing interval-valued intuitionistic fuzzy sets (IVIFS). The proposed approach solves the problem using a mathematical programming methodology. In the present investigation, a group decision-making problem characterized by IVIF multiple attributes is conceptualized as a linear programming model and resolved expeditiously. The models that are being proposed have been reformulated into two analogous linear programming (LP) models through the application of a variable transformation and the concept of aggregation operators. The obtained LP models are solvable by common approaches. The principal benefit of the suggested methodology is its facilitation of decision-makers (DM) in identifying an alternative that exhibits optimal performance, and the decision-making process does not rely on DM knowledge. Application of the proposed method is represented in a decision-making problem, and the results are compared with similar methods, proving the compatibility of the proposed method with previous ones. The solid and understandable logic with computational easiness are the main advantages of the proposed method.

Measuring the efficiency of real businesses is not a simple task, because a real business may involve several processes and sub-processes, forming a very complicated dynamic network of interactions. In this paper, a customized dynamic network data envelopment analysis (NDEA) model is proposed to measure the efficiency of the sub-processes in a real business. The proposed dynamic NDEA model is fully designed and customized for IMI which is a leading institute in providing consulting management, publication, and educational services. First, we have identified the network of the Industrial Management Institute (IMI) which includes educational, consulting, and publication sub-processes. Then, the most important sub-processes and the associated dynamic interactions are determined. Afterward, a dynamic NDEA model is proposed to measure the efficiency of sub-processes. The main theoretical properties of the proposed dynamic NDEA model are also discussed through theorems. Assessing the performance of IMI's sub-processes is not a trivial task due to the complexity of sub-processes in IMI. The proposed dynamic NDEA model is applied using real operational data of the IMI gathered through a sixty-month planning horizon. An attempt has been accomplished to form a relationship between the total efficiency of the process and the efficiency of each sub-process by regression analysis. The managers of IMI can monitor the efficiency score of the main process and sub-processes during the planning horizon which can help to improve inefficient sub-process.

In today’s competitive environment completing a project within time and budget, is very challenging task for the project managers. This aim of this study is to develop a model that finds a proper trade-off between time and cost to expedite the execution process. Critical path method (CPM) is used to determine the longest duration and cost required for completing the project and then the time-cost trade–off problem (TCTP) is formulated as a linear programming model. Here, LINDO program is used to determine the solution of the model. To implement the proposed model, necessary data were collected through interviews and direct discussion with the project managers of Chowdhury Construction Company, Dhaka, Bangladesh. The analysis reveals that through proper scheduling of all activities, the project can be completed within 120 days from estimated duration of 140 days. Reduction of project duration by 17% is achieved by increasing cost by 3.73%, which is satisfactory.

In this paper, a Multi-Choice Stochastic Bi-Level Programming Problem (MCSBLPP) is considered where all the parameters of constraints are followed by normal distribution. The cost coefficients of the objective functions are multi-choice types. At first, all the probabilistic constraints are transformed into deterministic constraints using stochastic programming approach. Further, a general transformation technique with the help of binary variables is used to transform the multi-choice type cost coefficients of the objective functions of Decision Makers(DMs). Then the transformed problem is considered as a deterministic multi-choice bi-level programming problem. Finally, a numerical example is presented to illustrate the usefulness of the paper.

In this paper, we develop a new mathematical model that integrates layout configuration and production planning in the design of dynamic distributed layouts. The model incorporates a number of important manufacturing attributes such as demand fluctuation, system reconfiguration, lot splitting, work load balancing, alternative routings, machine capability and tooling requirements. In addition, the model allows several cost elements to be optimized in an integrated manner. These costs are associated with material handling, machine relocation, setup, inventory carrying, in-house production and subcontracting needs. Numerical examples of different sizes are presented to illustrate the nature of the developed model and shed light on several managerial insights.