(521b) A General Resource-Constrained Short-Term Scheduling Model for Multipurpose Batch Plants Using Synchronous Slots

Short-term scheduling is an important and routine problem in multipurpose batch plants, for which several continuous-time formulations exist in the literature. These formulations can be broadly classified into two types based on the binary variables used for assignment. They are (i) Formulations with decoupling^1-3 and (ii) ones without decoupling⁴. The former rely on the postulation that decoupling the tasks from units reduces the number of assignment binaries. In contrary, the latter do not decouple the tasks from units but use the assignment binaries as such. In this work, we present a new, simpler and more efficient continuous-time mixed integer linear programming (MILP) formulation based on our proven opinion that formulations without decoupling necessarily require the same number of binaries that formulations with decoupling do. We extend our previous work⁴ to a more general model that can account for various resources in the plant, different storage policies, and several operational constraints.

Some recent attempts^1-3 at scheduling multipurpose batch plants have one thing in common. They all base their formulations on the idea that decoupling of tasks from units reduces the number of binary variables. The only difference between the non-decoupled binaries and the decoupled binaries is that the former display the unit information explicitly, while the latter hide the same. The number of necessary binary variables per event/time point must however be the same; otherwise the formulation cannot give the optimal solution. In the previous work⁴, we prove that decoupling of tasks from units does not help reducing the assignment binaries. Furthermore, the proposed model of the previous work does not decouple tasks from units, but still has fewer binaries, constraints and nonzeros than the recent best decoupling-based model².

We consider a multipurpose batch plant or production facility (F) that produces multiple products using a variety of shared resources (production units, raw materials, utilities and manpower) that constrain the plant operation. We describe the production in F using Generalized Recipe Diagrams (GRDs), which we feel are a more straightforward extension of Process Flow Diagram (PFD) concept to a batch process. In a GRD, nodes represent the tasks, arcs represent the various resources (materials, manpower, utilities etc.), and arc directions represent the task precedence. In this work, we propose a general formulation for scheduling multipurpose plants, which incorporates several features such as limitations on resource usage, different storage policies and shared storages, variable or fixed batch sizes and processing times, batch splitting and mixing, and sequence dependent changeover times. We divide the scheduling horizon into a number of variable length slots. To handle the sharing of resources easily and ensure the balance on each resource at any point in horizon, we synchronize the slots on all units.

Some features of our proposed formulation are noteworthy and distinct from the previous work. First, we use a novel balance on units besides that on mass and resource. Second, in contrast to all the existing continuous-time decoupling-based models^1-3, our formulation has absolutely no big-M constraints. We believe that this is significant, because our experience shows that eliminating the big-M constraints generally improves MILP formulations. We consider several examples both from the literature and of our own to illustrate the performance of our model and compare with the best recent general models^2,3. For the sake of fair comparison, we implement all the models using the same hardware and software.

Keywords: scheduling, resource constraints, multipurpose, batch plants, continuous-time formulation, MILP, synchronous slots

Reference:

(1) Giannelos, N.F., Georgiadis, M.C. A simple new continuous-time formulation for short-term scheduling of multipurpose batch processes. Ind. Eng. Chem. Res., 2002, 41, 2178-2184.

(2) Maravelias, C.T., Grossmann, I.E. New general continuous-time state-task network formulation for short-term scheduling of multipurpose batch plants. Ind. Eng. Chem. Res., 2003, 42, 3056-3074.

(3) Janak, S.L., Lin, X., Floudas, C.A. Enhanced continuous-time unit-specific event-based formulation for short-term scheduling of multipurpose batch processes: Resource constraints and mixed storage policies. Ind. Eng. Chem. Res., 2004, 43, 2516-2533.

(4) Sundaramoorthy, A, Karimi, I.A. A simpler better slot-based continuous-time formulation for short-term scheduling in multipurpose batch plants. Chem. Eng. Sci., 2005, 60, 2679-2702.