Juman Abdeen

Linear Programming Problem is about minimizing the production cost of t-shirts of the production plant while satisfying its limitations. This paper presents a large scale Linear Programming Model to provide a fully functional Cost Effective System finding optimum number of machine operators and workers in each of its departments as well as finding optimum raw material for the entire t-shirts production. The model is tested by applying to an apparel production plant (Silk Line (pvt) Ltd). The solution of the model is found using the commercial software package called “ LINGO SOLVER ”. Moreover, a sensitivity analysis is performed to complete the target (entire t-shirts production) within a given specific period of time.

In order to proceed with a minimal total cost solution technique, it is necessary to start with an initial feasible solution (IFS). Thus IFS acts as a foundation to a minimal total cost solution technique to the transportation problem. Generally, better is the initial feasible solution lesser is the number of iterations of obtaining the minimal total cost solution. Here, first we demonstrate a deficiency of a recently developed method in obtaining the minimal total cost solution to this problem. Then we develop a better polynomial time (O(N3) (N, higher of the numbers of source and destination nodes)) heuristic solution technique to obtain a better initial feasible solution to the transportation problem. The developed heuristic is coded using C++ programming language. Comparative studies of this heuristic with the best available ones in the literature on results of some numerical problems are carried out to show better performance of the current one. Our heuristic is found to lead to the minimal total cost solution in most cases (88.89%) of the studied numerical problems. We develop a better heuristic to obtain a better IFS to the transportation problem.We find that 88.9% of the solved problems by JHM led to the optimal solution.We demonstrated that the ZSM does not provide the optimal solution all the time.The developed JHM is coded using C++ programming language. Transportation of products from sources to destinations with minimal total cost plays an important role in logistics and supply chain management. All algorithms start with an initial feasible solution in obtaining the minimal total cost solution to this problem. Generally, better is the initial feasible solution lesser is the number of iterations of obtaining the minimal total cost solution. Here, first we demonstrate a deficiency of a recently developed method in obtaining the minimal total cost solution to this problem. Then we develop a better polynomial time (O(N3) (N, higher of the numbers of source and destination nodes)) heuristic solution technique to obtain a better initial feasible solution to the transportation problem. Because of the intractability of carrying out enormous calculations in this heuristic technique without a soft computing program, this technique is coded using C++ programming language. Comparative studies of this heuristic with the best available ones in the literature on results of some numerical problems are carried out to show better performance of the current one. Our heuristic is found to lead to the minimal total cost solution in most cases (88.89%) of the studied numerical problems.

Transportation of products from sources to destinations with minimal total cost plays an important role in logistics and supply chain management. All algorithms start with an initial feasible solution in obtaining the minimal total cost solution to this problem. Generally, better is the initial feasible solution lesser is the number of iterations of obtaining the minimal total cost solution. Here, first we demonstrate a deficiency of a recently developed method in obtaining the minimal total cost solution to this problem. Then we develop a better polynomial time (O(N 3) (N, higher of the numbers of source and destination nodes)) heuristic solution technique to obtain a better initial feasible solution to the transportation problem. Because of the intractability of carrying out enormous calculations in this heuristic technique without a soft computing program, this technique is coded using C++ programming language. Comparative studies of this heuristic with the best available ones in the literature on results of some numerical problems are carried out to show better performance of the current one. Our heuristic is found to lead to the minimal total cost solution in most cases (88.89%) of the studied numerical problems.

Transportation of a product from multi-source to multi-destination with minimal total transportation cost
plays an important role in logistics and supply chain management. Researchers have given considerable
attention in minimizing this cost with fixed supply and demand quantities. However, these quantities
may vary within a certain range in a period due to the variation of the global economy. So, the concerned
parties might be more interested in finding the lower and the upper bounds of the minimal total costs with
varying supplies and demands within their respective ranges for proper decision making. This type of transportation
problem has received attention of only one researcher, who formulated the problem and solved it
by LINGO. We demonstrate that this method fails to obtain the correct upper bound solution always. Then
we extend this model to include the inventory costs during transportation and at destinations, as they are
interrelated factors. The number of choices of supplies and demands within their respective ranges
increases enormously as the number of suppliers and buyers increases. In such a situation, although the
lower bound solution can be obtained methodologically, determination of the upper bound solution
becomes anNP hard problem. Herewecarry out theoretical analyses on developing the lower and the upper
bound heuristic solution techniques to the extended model. A comparative study on solutions of small size
numerical problems shows promising performance of the current upper bound technique. Another comparative
study on results of numerical problems demonstrates the effect of inclusion of the inventory costs.