Stochastic production scheduling with weibull rate of production for deteriorating items

Scheduling production process is a prime concern for optimal utilization of resources. Much work has been reported in production scheduling with the assumptions that the production is having finite rate and deterministic. But in many production processes, in particular for deteriorating items the production rate is not deterministic due to various random factors such as availability of raw material, transportation, power supply, manpower and maintenance. The production is random and follows a probability distribution. In addition to this for deteriorating items the deterioration is random. For modelling this phenomenon it is needed to consider the stochastic production scheduling problem with variable rates of production as well as deterioration. This paper addresses this problem by characterizing the production and the life time of commodity with two parameters and three parameters of Weibull distributions respectively. Using the differential calculus, the instantaneous state of inventory is derived the expected total cost function is derived for power pattern demand. By minimizing the expected total cost per unit time, the production start up time, shutdown time and optimal production quantity are derived for without shortages. This model is extended to the case of shortages, where shortages allow and fully backlogged. The sensitivity of the model with respective to variation in input parameters and costs is studied in both the models. The optimal production schedules are sensitive to the changes in the parameters and costs. It is also observed that the deterioration parameters have significant influence on optimal production, uptime and downtime. It is also observed that the model with shortages is having less expected total cost per unit time than that of the model without shortages.