Optimizing a Production Line

Abstract

The simple production line considered in this chapter is shown in Fig. 20.1. This problem has been adapted from an example in [1]. This situation is a little different from those in the previous chapters because items moving through the system are the workers in the production line. We begin with n workers arriving at the first station labelled A in Fig. 20.1. Our first decision variable is n and we are to find the optimal value for n. Let us call the item we are producing a “zapper”. The parts, pieces, raw materials for one zapper are provided at station A and each worker uses these items to assemble one zapper. The assembly time is modelled by the normal distribution. After assembly the worker takes the zapper to the next station labelled O in the figure. At O the zapper is painted and baked and this station will be called an oven. The oven processes only one zapper at a time and the workers must queue up in front of the oven waiting to place their zapper in the oven. The service time at O is also modelled by the normal probability distribution. Our second decision variable is k which is the number of ovens to be placed at station O. Two or more ovens will be modelled as identical and parallel servers. The worker must wait at the oven until it has finished and after the zapper leaves the oven the worker places it in the finished box and returns to A to assemble another zapper. The items moving through the system are the workers.