In this paper the concept of the Minimum Universal cost Flow (MUCF) for an  infeasible flow network is introduced. A new mathematical model in which the objective function includes the total costs of changing arc capacities and sending flow is built and analyzed. A polynomial time algorithm is presented to find the MUCF.    

In the GA approach the parameters that influence its performance include population size, crossover rate and mutation rate. Genetic algorithms are suitable for traversing large search spaces since they can do this relatively fast and because the mutation operator diverts the method away from local optima, which will tend to become more common as the search space increases in size. GA’s are based in concept on natural genetic and evolutionary mechanisms working on populations of solutions in contrast to other search techniques that work on a single solution. An important aspect of GA’s is that although they do not require any prior knowledge or any space limitations such as smoothness, convexity or unimodality of the function to be optimized, they exhibit very good performance in most applications. The Minimum cost flow problem is formulated as genetic algorithm and simulated annealing. This paper shows genetic algorithms and simulated annealing are much easier to implement for solving transportation problems compared with constructing mathematical programming formulations. Finally, a new empirical study for the effect of parameters on the rate of convergence of the GA and SA are demonstrated.

We apply a primal-dual simplex algorithm for solving the biobjective min imum cost-time network flow problem such that the total shipping cost and the total shipping fixed time are considered as the first and second objective functions, respectively. To convert the proposed model into a single-objective parametric one, the weighted sum scalarization technique is commonly used. This problem is a mixed-integer programming, which the decision variables are directly dependent together. Generally, the previous works have consid ered the linear biobjective problem with the traditional network flow con straints, while in this paper, corresponding to each flow variable, a binary variable is defined. These zero-one variables are utilized to describe a fixed shipping time for positive flows. The proposed method is successful in finding all supported efficient solutions of a real numerical example.

The traditional method for studying non-stationary signals is spectrogram based on the short-time Fourier transform (STFT). The well known limitation of the STFT is the inherent trade-off between time and frequency resolution. The Wigner-Ville (WV) distribution has the best time-frequency resolution, but its draw back is generating cross-terms. The matching pursuit (MP) distribution based on using the Gaussian atom is always positive, does not include crossterm, and has convenient resolution. In this paper, we have shown in addition to the known properties, the MP distribution can also remove the additive noise inherently. On the other words, we are able to remove the noise just by limiting the algorithm iterations and without paying any additional cost. Although the MP distribution based on using the Gaussian atoms is always positive and it has convenient resolution, according to the MP the time marginal and the frequency marginal will not be obtained accurately. In this paper, it has been shown that by implementing the Minimum cross entropy (MCE) technique according to the MP distribution as a priory positive distribution, the new extracted distribution has the most similarity to the MP distribution and it also satisfies the correct time and frequency marginal.

One of the important JIT assumptions is the setup time reduction so that an ideal lot size of one unit is possible. Setup time reduction is rather a technical problem than a production planning problem and it is not readily possible. Therefore if maximum effort to reduce set-up time has resulted in a fixed batch size in accordance with the EOQ model, batch manufacturing occurs. This paper is to obtain JIT scheduling of parts while minimizing the overtime cost of resource in the multi-product batch manufacturing. The problem is formulated as two models. From the first model, a mixed integer programming with Minimum WIP cost objective, just-in-time production scheduling of batches is obtained. This inventory minimizing approach produces the right parts, in the right quantity and at the right time. However the achievement of Minimum inventory may be at the expense of significant workload variability. Since the first model provides multiple optimum solutions, the second model allows us to select the best solution with regard to Minimum overtime resource cost. Hence JIT production with Minimum resource overtime cost is realized.