Job scheduling in petrochemical production: Two-stage processing with finite intermediate storage

Abstract

In the following paper a new heuristic for product scheduling in a semicontinuous production environment is presented. A two-stage processing structure with a finite number of processors at each stage is assumed wherein intermediate tank storage of limited capacity exists between stages. Product output consists of both simple final products and blends. The objective in scheduling is to achieve as small a makespan as possible—that is, to produce a schedule with near-optimum throughput. Scheduling techniques for related applications tend to position jobs as early as possible in the schedule horizon with the result of producing high resource utilization near the beginning of the schedule and a significant drop in resorce utilization towards the schedule's end. The heuristic method herein starts with an initial schedule which is to be modified through a balancing of the use of available resources, this being accomplished by the identification and repositioning of sets of critical jobs. Evaluation of results from a battery of test problems suggests that notable reductions in schedule makespans can be achieved through use of the strategy described. In this paper we have outlined a model for the two-stage flowshop scheduling problem with multiple processors and finite intermediate storage. In this model feed products are processed through state 1 processing units and the output—i.e. the intermediates—are stored in tanks until stage 2 processing is begun. The scheduling objective is to order jobs so that the time required to get all jobs through the system is minimized. There are, in general, more final products than intermediates (reflecting a processing structure that might be typical of blending operations), so that predecessor/successor product relationships impose a significant constraint on scheduling. To produce scheduling solutions we have introduced a heuristic which represents a modification to an exchange algorithm developed earlier for application to other resource-constrained scheduling problems. The algorithm is initiated with a starting schedule and employs a strategy focused on reduction of the variance in resource utilization over the scheduling horizon. The first step in the rescheduling strategy involves identification of promising “Targets” and related jobs whose positioning in the schedule strongly influence the makespan. These jobs are removed from the schedule, and other jobs competing for resources with the target group over the time interval of concern are right-shifted as far as possible without increasing the current schedule makespan. The target-associated group is then reinserted at an earlier point in the schedule, and jobs occurring to the right of the group are left-shifted to the degree that resource constraints allow. It is through this last move that resource utilization is leveled and the makespan, hopefully, reduced. At every step only feasible schedules are produced, and no iteration delivers a schedule with makespan inferior to that of the previous iteration. Two dispatching rules, judged to provide good initial schedules, were used to generate starting solutions for the exchange heuristic in a series of test problems. Starting schedules, whether produced from method M1 or M2, apppear to lead to final schedules which, on average, are of approximately equal quality. In either case significant reductions in schedule makespans are achieved through application of the exchange algorithm, with final solutions having a mean percentage deviation from estimated makespan optima of about 18% (calculated over all 140 test problems). Problems with 50 final products—the largest number in our battery of tests—required an average of 2 min computing time on a 386-class PC to produce solutions. We believe that problems involving about 100 products are amenable to solution on high- speed PCs, estimated solution times being on the order of perhaps 5–10 min. Very large problems with hundreds of final products would likely require computing speeds typical of mainframe facilities. As a final word on extensions to the work presented here, the authors are now studying a related problem model for which the physical processing structure is similar to that discussed in this paper. However, an additional level of complexity is introduced by way of stage 2 product due dates. In this case, the performance objective will be either minimization of the number of tardy jobs or minimization of the conditional mean tardiness. The type of resource constraints involved are essentially identical, but modification of the exchange heuristic is necessary and will center chiefly on target identification and redefinition of the boundaries for job movement.