The capital, operating, and overall costs of a dedicated continuous manufacturing process to synthesize an active pharmaceutical ingredient (API) and formulate it into tablets are estimated for a production scale of 2000 t of tablets per year, with raw material cost, production yield, and API loading varied over broad ranges. Costs are compared to batch production in a dedicated facility. Synthesis begins with a key organic intermediate three synthetic steps before the final API; results are given for key intermediate (KI) costs of $100 to $3000/kg, with drug loadings in the tablet of 10 and 50 wt %. The novel continuous process described here is being developed by an interdisciplinary team of 20 researchers. Since yields are not yet well-known, and continuous processes typically have better yields than batch ones, the overall yields of the continuous processes with recycling were set equal to that of the batch process. Without recycling, yields are 10% lower, but less equipment is required. The continuous process has not been built at large scale, so Wroth factors and other assumptions were used to estimate costs. Capital expenditures for continuous production were estimated to be 20 to 76% lower, depending on the drug loading, KI cost, and process chosen; operating expenditures were estimated to be between 40% lower and 9% higher. The novel continuous process with recycling coupled to a novel direct tablet formation process yields the best overall cost savings in each drug loading/KI price scenario: estimated savings range from 9 to 40%. Overall cost savings are also given assuming the yield in the continuous case is 10% above and 10% below that of the batch process. Even when yields in the continuous case are lower than in the batch case, savings can still be achieved because the labor, materials handling, CapEx, and other savings compensate.

A series of tubes: The continuous manufacture of a finished drug product starting from chemical intermediates is reported. The continuous pilot-scale plant used a novel route that incorporated many advantages of continuous-flow processes to produce active pharmaceutical ingredients and the drug product in one integrated system.

Abstract. Theory and implementation for the global optimization of a wide class of algorithms is presented via convex/affine relaxations. The basis for the proposed relaxations is the systematic construction of subgradients for the convex relaxations of factorable functions by McCormick [Math. Prog., 10 (1976), pp. 147-175]. Similar to the convex relaxation, the subgradient propagation relies on the recursive application of a few rules, namely, the calculation of subgradients for addition, multiplication, and composition operations. Subgradients at interior points can be calculated for any factorable function for which a McCormick relaxation exists, provided that subgradients are known for the relaxations of the univariate intrinsic functions. For boundary points, additional assumptions are necessary. An automated implementation based on operator overloading is presented, and the calculation of bounds based on affine relaxation is demonstrated for illustrative examples. Two numerical examples for the global optimization of algorithms are presented. In both examples a parameter estimation problem with embedded differential equations is considered. The solution of the differential equations is approximated by algorithms with a fixed number of iterations. 1. Introduction. The development of deterministic algorithms based on continuous and/or discrete branch-and-bound [10,17,18] has facilitated the global optimization of nonconvex programs. The basic principle of branch-and-bound, and related algorithms such as branch-and-cut [19] and branch-and-reduce [27], is to bound the optimal objective value between a lower bound and an upper bound. By branching on the host set, these bounds become tighter and eventually converge. For minimization, upper bounds are typically obtained via a feasible point or via a local solution of the original program. For the lower bound, typically a convex or affine relaxation of the nonconvex program is constructed and solved to global optimality via a convex solver. Convex and concave envelopes or tight relaxations are known for a variety of simple nonlinear terms [1,33,35], and this allows the construction of convex and concave relaxations for a quite general class of functions through several methods [21,2,33,12]. Simple lower bounds from interval analysis are also widely used in global optimization, e.g., [6,7,25]. Such bounds are often weaker but less computationally expensive to evaluate than relaxation-based bounds. For instance, for a box-constrained problem, no linear program (LP) or convex nonlinear program (NLP) needs to be solved.The majority of the literature on global optimization considers nonconvex programs for which explicit functions are known for the objective and constraints. A more

This article presents an optimization formulation for the synthesis of heat exchanger networks where pressure levels of process streams can be adjusted to improve heat integration. Especially important at subambient conditions, this allows for the interconversion of work, temperature, and pressure-based exergy and leads to reduced usage of expensive cold utility. Furthermore, stream temperatures and pressures are tuned for close tracking of the composite curves yielding increased exergy efficiency. The formulation is showcased on a simple example and applied to a case study drawn from the design of an offshore natural gas liquefaction process. Aided by the optimization, it is demonstrated how the process can extract exergy from liquid nitrogen and carbon dioxide streams to support the liquefaction of a natural gas stream without additional utilities. This process is part of a liquefied energy chain, which, supplies natural gas for power generation while facilitating carbon dioxide sequestration.

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