An embedding formulation for the optimal scheduling and design of multipurpose batch plants

Abstract

Summary of the Basic StepsThe basic steps in the suggested procedure for the optimal design of multi-purposebatch plants can be summarized as follows:1. List the candidate product groups.2. Obtain the super-structure that contains the candidate groups.3. Derive the horizon constraints..4. Examine the horizon constraints. If at least one horizon constraintimplicitly contains all the time periods, complete the merged formulationand solve the MINLP given in Equations (38) to (44) with the correspondinghorizon constraints. Otherwise, go to step 5.5. Select a product(s) that breaks the loop(s) in the super-structure. Treat thechosen product(s) as two or more artificial products.6. Revise the super-structure to include the additional products. Verify thatthe loop is broken. If this condition is met, go to step 7. Otherwise,return to step 5 and modify the products chosen for splitting.7. Derive the multi-period form of the constraints for the product(s) that aresplit into its (their) values for the time periods in which it (they) appear.Formulate the merged representation of the model for the rest of theproducts, including the horizon constraints. At least one horizonconstraint will contain implicitly all the time periods.Example 2The seven product, ten stage example problem of Suhami and Mah (1982) has beensolved to illustrate the design of a large multi-purpose batch plant. From the super-structure of this problem (Figure 4), the horizon constraints shown in Table II arederived.Using these constraints, the example has been solved with the merged formulation.Data for this problem appears in Table III. In addition, the following specificationshave been used: H = 6200 hr, a = 250 SFr, fi = 0.6, 1 < N <, 3, and 250 < V£ 10,000. As seen in Table IV, the MINLP formulation involves 48 variables and 67constraints. MINOS/Augmented (Murtagh and Saunders, 1980) required 16.09 secondsof CPU-time on a DEC-20 computer to solve the relaxed nonlinear program.