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This paper addresses an integral optimization of fermentation processes. The behavior of the fermentors is described by a set of algebraic and differential equations written as finite-difference equations in an equation-oriented environment. Unconventional constraints related to the number of batch items and connections among them, detailed kinetic models and operating costs corresponding to inoculum, and different available substrates are included in the model. The optimal number of units to be used in the process, their optimal operation policy (i.e., connected in series or in parallel working out of phase), as well as the optimal volume and operation of each unit, are determined simultaneously. The model is formulated as a sequence of nonlinear programming (NLP) problems.

In this paper, a heuristic method is presented for the simultaneous solution of the synthesis and design problems of batch plants. A detailed nonlinear program (NLP) model is developed that considers a superstructure to represent all the configuration options for the plants. Usually, similar works in this area assume as a hard constraint the use of single-product campaigns. In this work, mixed campaigns are introduced to pose problems where this is a significant condition. Specific scheduling constraints are formulated, and a resolution strategy is presented to solve the problem. This formulation is valid for multiproduct batch plants and a special type of multipurpose plants where products follow different production paths sharing some but not all the stages. The approach is implemented for a Torula yeast, brandy, and bakery yeast production plant. To assess the method, different mixed campaigns are modeled. Economical and synthesis, design, and operational results are also reported.

Most previous approaches for the design of multiproduct batch plants have assumed the simplest scheduling policy. In order to simplify the formulation and take into account that many times demands are uncertain, they have used single product campaigns to determine the plant configuration and select the unit sizes. From the commercial point of view, this production mode is not realistic: for example, huge inventories should be kept to support this approach. However, when a stable context can be assured, the simultaneous resolution of design and a more detailed scheduling allows assessing different trade-offs. This article presents a new mixed integer linear programming (MILP) formulation assuming mixed product campaigns. Now, the composition and the sequence of the batches in the campaign must be determined as well as the assignment of batches to units when parallel units are used. Taking into account that the plant configuration is simultaneously obtained, the scheduling problem must be solved without knowing the number of available units and their sizes. Several examples are presented in order to show the performance of the proposed approach.

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In this work, mixed integer linear programming models for scheduling multistage multiproduct batch plants operating under campaign mode are proposed. It is assumed that each plant stage includes identical parallel units operating out of phase. Given the plant topology and the number of batches of each product to be processed in the campaign, the objective is assigning batches to units in each stage in order to minimize the cycle time of the campaign. An asynchronous slot-based continuous-time representation for modeling the assignment of batches to units is used. These formulations require postulating a priori a suitable number of production slots for each unit that integrates the plant, which severely affects the model computational performance. Then, to reduce the computational effort, a solution strategy is proposed where a simplified model, which includes preordering constraints, is first solved. Finally, a detailed scheduling model is posed where the optimal cycle time of simplified model is used as bound for the cycle time and a novel expression for the number of proposed slots for each unit is considered. The strategy is highlighted through examples that show how the computational burden is reduced.

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