A Software Based on Modelling Solution Using Weibull Distribution and Depreciation, Applicable in MSM e-Business and e-Commerce Industry

Abstract

AbstractThe present model is an extension of the previously developed models which considered a constant rate of deterioration and a linearly price-dependent demand. These assumptions are quite unrealistic. A three-parameter Weibull distribution to represent the distribution of time is more realistic. Also, it improves the generalization of the nonlinear price-dependent demand considered in previous theories. Both these realistic factors are taken into account in developing the present model. Sensitivity analysis is used to reflect the extent to which the solution of a model is affected by changes or errors in the values of the input parameters associated with the model. The appendix of the algorithms used in model is stated. The results are lastly elaborated through numerical illustration and sensitivity analysis results for better understanding and future development. Researchers, so far, have dealt with only two variations on demand-time variations that mean direct and descriptive variations. The line variance reflects a constant change in the demand rate for each unit of product time, which is a realistic and unambiguous assumption in any real industry. For example, the demand for the latest technology, chips, computers, etc., is growing rapidly against the technology used and gadgets. Some researchers also refer to this variation in the classification class as an increase or decrease in function in relation to a time unit. From the researcher’s point of view, the level of diversity is very high, and finding satisfaction is actually a demand in the real market. Therefore, a realistic approach that is consistent with the research ideas and market conditions itself is not equal and does not reflect but quadratic variations in demand and time indications of growth in both the direction and direction of demand. The problem is solved and structured in the form of a model and explained using sensitivity analysis. An attempt is done to research and discuss a production policy for stock with rate of depreciation in one-parameter Weibull distribution and also having a foresaid characteristics: (i) Product is Weibull distributed. (ii) Total time for planning is finite. (iii) Demand is exponential. (iv) Limited rate of production. (v) Backlogging and shortages are allowed. Objective is to find the optimized number of cycles, required to get minimum average cost of production system. The model is further illustrated using a numerical example and then carry out the sensitivity analysis of the optimized solution obtained.KeywordsDepreciationTime distributionPriceDemand