Process quality adjusted lot sizing and marketing interface in JIT environment

Lots exist even in a JIT environment. However, there is a continuous effort to decrease set up time, and employees are empowered to signal quality problems. When signaled quality problems are not fixed inside the cycle time the assembly line stops and is resumed again after the correction. But good JIT systems are pragmatic, and sometimes products with known quality problems go through the assembly line. They are separated (in the clinic area), where they wait to be fixed. In this paper both the number of cars leaving the assembly line and the number of cars entering the clinic area are considered random variables. All possible outcomes of these two random variables are identified and the appropriate inventory positions are determined in order to calculate the expected values of the inventory costs and the cycle length respectively. Using these values we gain new lot- sizing formulas measuring the optimal lot size and the total costs. In a JIT environment orders are usually frozen before the time period when production is scheduled and production plans (demand) is smoothed as much as possible. Thus, demand practically is deterministic and constant throughout the month, while the production volume of a shift is stochastic. The paper analyzes the characteristics of the total cost as a function of demand, and suggests how to determine the optimum volume (the demand) in the contracts. It is shown that the minimum point of the total cost as a function of demand decreases in backlogging cost.