Plant supply logistics : balancing delivery and stockout costs

INTRODUCTION Transporting raw materials to a production facility would seem to be almost trivial when the final product requires only one primary raw material. While the process is not as involved as a multi-level bill of materials system, there are still a number of variables with which one must deal, particularly in the logistics system. In this case, the raw material, peanuts, are transported from a sheller near Columbus, Georgia, to Portsmouth, Virginia, to be converted into peanut butter. The transportation is via railroad--a distance of about 700 miles. The manufacturer is currently required to lease rail cars, which are then moved from Georgia to Virginia full of raw, shelled peanuts, and returned to Georgia empty. The question the plant manager faces on a regular basis is how many rail cars to lease? Analytically, the system faced by the plant manager is a circular queueing system. As explained in Appendix A, this is a special case of a Jackson network (see Figure 1). In the usual queueing process, customers enter the system, are served and leave the system. In our case, the rail cars leased by the company moved in a continuous loop. The rail cars are "served"' in Georgia when they were loaded with peanuts, in Virginia when they are unloaded at the plant and en route in both directions. Appendix A describes briefly the analytical construction of the problem. [FIGURE 1 OMITTED] There are numerous examples in the literature of analytic solutions to rail car scheduling (Cordeau, Soumis, and Derosiers, 2000; Luub-becke and Zimmermann, 2003; and Sherali and Maguire, 2000). Although the objective here was to solve for the optimal number of rail cars, an analytical solution was not a practical option for several reasons. The first is the limitation of Jackson networks for predictive purposes (see Appendix A); the second is the nature of the data. The probability distributions of service times were empirical distributions. Using theoretical distributions would have made the problem computationally more attractive, but less realistic. Third, the company did not want to release cost figures. Therefore, results could only be stated as trade-offs in terms of numbers of rail cars and number of days the plant would be shut down. Given the results, however, the company could easily calculate the corresponding total costs. Finally, the company wanted the flexibility to test easily a variety of scenarios. For these reasons, it was decided to use simulation as the method of dealing with The travel time between the sheller and the plant (and the return trip) varied widely. The rail cars were sent from the sheller to a rail yard, where they waited until a northbound the problem. It was also easier to explain the process and results to the plant manager. Further, the plant manager could watch the outcomes develop as the simulation was running and could run the simulation with various scenarios. THE PROBLEM The peanut butter manufacturer in Virginia (VA) required an average of 180,000 pounds of peanuts per day to keep the line running. Rail cars carrying 190,000 pounds of peanuts each supplied the plant. The rail cars queued up at the plant waiting to be unloaded. Any time the queue was empty, the plant had to be shut down at a corresponding substantial cost. If there were too many rail cars in the queue, it could cause a problem, especially in the summer. Peanuts are a live organic product and could spoil if left sitting in the sun too long. Although the com-pany could provide no specific data for this problem, management asked that the solution tell them the length of the queue at the plant and the mean number of days in the queue. The peanuts are purchased from a sheller in Georgia (GA). The sheller buys raw peanuts from the farmers, shells them, and loads them in the hopper cars. Since the sheller maintains an inventory of peanuts, there is virtually no queue at the sheller except on weekends. …