Single Product Campaign Research Articles

Differential Adaptive Diffusion: Understanding Diversity and Learning whom to Trust in Viral Marketing

Viral marketing mechanisms use the existing social network between customers to spread information about products and encourage product adoption. Existing viral marketing models focus on the dynamics of the diffusion process, however they typically: (a) only consider a single product campaign and (b) fail to model the evolution of the social network, as the trust between individuals changes over time, during the course of multiple campaigns. In this work, we propose an adaptive viral marketing model which captures: (1) multiple different product campaigns, (2) the diversity in customer preferences among different product categories, and (3) changing confidence in peers’ recommendations over time. By applying our model to a real-world network extracted from the Digg social news website, we provide insights into the effects of network dynamics on the different products’ adoption. Our experiments show that our proposed model outperforms earlier nonadaptive diffusion models in predicting future product adoptions. We also show how this model can be used to explore new viral marketing strategies that are more successful than classic strategies which ignore the dynamic nature of social networks.

The design and scheduling of chemical batch processes: Computational complexity studies

Summary The pharmaceutical industry is quite restrictive concerning quality and safety, the manufacturing disruptions often lead to drug shortages in despite of the high costs involved. Due to the minimization of equipment costs, the design and scheduling of chemical batch processes (DSCBP) is a well-known problem, and various sub-problems are selected from the literature because they were successively enlarging the design and schedule policies: single machine or multiple machines (S or M) in each stage; and single product campaigns or multiple products campaigns (SPC or MPC). In this paper, four problems are studied (by combinatorics: SS, MS, SM, and MM) and it is shown that they are all NP-hard in strong sense through polynomial reduction. This study can support innovative algorithms and methodologies for solving DSCBP problems, in a way to improve equipments sizing and configurations design, and thereby contributing to curb disruptions within pharmaceutical supply chains (PharmSC).

Simultaneous design and scheduling of a semicontinuous/batch plant for ethanol and derivatives production

The interest on renewable fuels has greatly increased in the last years. Particularly, ethanol production arises as a good solution to many current economic-environmental problems. Yeast production from the ethanol residuals constitutes a sustainable alternative. Usually, this kind of plants is designed using single product campaigns. However, since yeast degradation is fast and a continuous supply must be assured, the mixed product campaign policy is the most appropriate. Besides, a stable context can be assumed to justify this approach that takes advantage of the special structure of the plant. Therefore, in this paper, a mixed integer linear programming model is formulated for simultaneous design and scheduling of a semicontinuous/batch plant for ethanol and derivatives production. The optimal plant configuration, unit sizes, number of batches of each product in the campaign and its sequencing is obtained in order to fulfill the ethanol and yeast demands minimizing the investment cost.

Differential Adaptive Diffusion: Understanding Diversity and Learning Whom to Trust in Viral Marketing

Viral marketing mechanisms use the existing social network between customers to spread information about products and encourage product adoption. Existing viral marketing models focus on the dynamics of the diffusion process, however they typically: (a) only consider a single product campaign and (b) fail to model the evolution of the social network, as the trust between individuals changes over time, during the course of multiple campaigns. In this work, we propose an adaptive viral marketing model which captures: (1) multiple different product campaigns, (2) the diversity in customer preferences among different product categories, and (3) changing confidence in peers’ recommendations over time. By applying our model to a real-world network extracted from the Digg social news website, we provide insights into the effects of network dynamics on the different products’ adoption. Our experiments show that our proposed model outperforms earlier non-adaptive diffusion models in predicting future product adoptions. We also show how this model can be used to explore new viral marketing strategies that are more successful than classic strategies which ignore the dynamic nature of social networks.

Detailed Design of Multiproduct Batch Plants Considering Production Scheduling

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.

Heuristic Method for the Optimal Synthesis and Design of Batch Plants Considering Mixed Product Campaigns

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.

Batch process optimization in a multipurpose plant using Tabu Search with a design-space diversification

Problem formulations for the purpose of optimization typically represent a simplification of the real physical systems that are modeled. In order to obtain solutions that are robust to criteria not considered in the objectives and constraints definition, we propose to include in the results list additional solutions that are not necessarily optimal but have very different characteristics in the solution space than the optima. To this effect, we present a novel feature for optimization frameworks, namely a solution-space diversification. We present this feature on a backdrop of batch process design. We developed a method that optimizes the design of a new chemical process to be implemented in an existing multi-purpose batch plant operating in single product campaign mode and that takes into account the special requirements and constraints in the corresponding production facilities. In the optimization, several objectives with different priorities are considered. A flexible meta-heuristic algorithm, Tabu Search, has been implemented to solve this multi-objective combinatorial non-linear problem. This approach is particularly suited for the identification of the Pareto set of non-dominated solutions, to which designs with a pronounced structural diversity are added. For this purpose an indicator of the structural difference between two designs has been defined that takes into account the position and nature of material transfers between equipment units. Three case studies are used to illustrate how the novel approach delivers extended Pareto-sets with a high variability in the design space. It has been shown why diversification in the design space is relevant to obtain solutions representing a robust set of alternatives in order to deal with potential constraints and limitations that are not covered in the problem formulation. Such an extended Pareto-set maximizes the probability that at least one of the proposed solutions will be suitable for industrial implementation.

Process performance models in the optimization of multiproduct protein production plants.

In this work we propose a model that simultaneously optimizes the process variables and the structure of a multiproduct batch plant for the production of recombinant proteins. The complete model includes process performance models for the unit stages and a posynomial representation for the multiproduct batch plant. Although the constant time and size factor models are the most commonly used to model multiproduct batch processes, process performance models describe these time and size factors as functions of the process variables selected for optimization. These process performance models are expressed as algebraic equations obtained from the analytical integration of simplified mass balances and kinetic expressions that describe each unit operation. They are kept as simple as possible while retaining the influence of the process variables selected to optimize the plant. The resulting mixed-integer nonlinear program simultaneously calculates the plant structure (parallel units in or out of phase, and allocation of intermediate storage tanks), the batch plant decision variables (equipment sizes, batch sizes, and operating times of semicontinuous items), and the process decision variables (e.g., final concentration at selected stages, volumetric ratio of phases in the liquid-liquid extraction). A noteworthy feature of the proposed approach is that the mathematical model for the plant is the same as that used in the constant factor model. The process performance models are handled as extra constraints. A plant consisting of eight stages operating in the single product campaign mode (one fermentation, two microfiltrations, two ultrafiltrations, one homogenization, one liquid-liquid extraction, and one chromatography) for producing four different recombinant proteins by the genetically engineered yeast Saccharomyces cerevisiae was modeled and optimized. Using this example, it is shown that the presence of additional degrees of freedom introduced by the process performance models, with respect to a fixed size and time factor model, represents an important development in improving plant design.

Ant colony framework for optimal design and scheduling of batch plants

This paper presents a new co-operative search approach, the ant colony optimisation paradigm, for the optimal design of batch chemical processes and illustrates it by solving (1) the combinatorial optimisation problem of multiproduct batch scheduling and (2) the continuous function optimisation problem for the design of multiproduct batch plant with single product campaigns and horizon constraints. The ant algorithm is simple to implement and results of the case studies show its ability to provide speedy and accurate solutions.

Design of single‐product campaign batch plants under demand uncertainty

AbstractA new method is introduced for optimally designing multiproduct batch plants under the single‐product campaign (SPC) production mode. Uncertain future product demands are described with normal probability distributions, and more than one processing unit of equal size are allowed per stage. A t the expense of imposing the normality assumption for product demand uncertainty and the SPC production mode, the original two‐stage stochastic optimization problem is transformed into a deterministic mixed‐integer nonlinear programming problem without relying on implicit or explicit discretization of the uncertain variables. This is accomplished through the explicit solution of the inner problem and the analytical integration overall product demand realizations. This problem representation and solution strategy result in savings of orders of magnitude over existing methods in computational requirements.

Design of multiproduct batch plants under demand uncertainty with staged capacity expansions

This paper addresses the staged capacity expansion of multiproduct batch plants operating in single product campaign (SPC) mode and in the presence of product demand uncertainty. This extends previous work by the authors on the design problem. Staged capacity expansions are modeled as additions of extra units of equal size at each stage at the end of each time period. The normality assumption is employed for the uncertain product demands. The problem formulation involves an inner stage which identifies the optimum production levels and an outer stage which establishes the design/capacity expansion decisions by maximizing the net present value (NPV) of the plant. This two-stage stochastic optimization problem for capacity expansion is equivalently recast as a deterministic mixed-integer nonlinear programming (MINLP) problem. Finally, the proposed formulation and solution strategy are illustrated with an example problem.

New MILP Models for Scheduling of Multiproduct Batch Plants under Zero-Wait Policy

This paper presents a new mixed-integer linear programming (MILP) model in which makespan is minimized for the multiproduct batch plants. In particular, the zero-wait (ZW) scheduling with transfer and setup times is analyzed. Not only idle times between the successive products but also heads and tails are used to select a possible production sequence with the minimum makespan. To determine the suitable head and tail, new binary variables are defined and aggregated to the assignment constraints of traveling salesman problems (TSPs). Although the number of binary variables increases, the mathematical formulation can yield a very compact MILP model. The effectiveness of the proposed model is demonstrated through several examples. The proposed model is extended to solve the scheduling problems for productions with single product campaigns (SPCs) and mixed product campaigns (MPCs) explained by Birewar and Grossmann (Ind. Eng. Chem. Res. 1989b, 28, 1333). The solutions by the proposed method are compared with the solutions obtained from the rigorous solution method by Birewar and Grossmann. The proposed model is formulated as a compact size and leads to a significant reduction in solution times.

Optimal scheduling of cyclic batch processes for heat integration—I. Basic formulation

Abstract Significant savings in the utility cost of batch plants can be obtained by heat integration coupled with the rescheduling of operation times. In this work, efficient scheduling models are developed for maximization of heat recovery for the case of no intermediate storage with holding time (NIS) in cyclically operated single-product campaigns. In this development, the product recipe network is assumed to take the form of an arborescence and each unit is assumed to be assigned to a single task. A mixed integer linear programming (MILP) formulation is proposed to determine the operating schedule for maximum heat integration between the batch streams to reduce the utility consumption. Solution of this formulation can be readily obtained with a commercial MILP solver. Numerical examples are presented to illustrate the scope of the problems which can be handled with the formulation.

Simulation and queueing network modeling of single-product production campaigns

A two-stage approach to modeling single-product campaigns in specialty chemical production facilities has been developed. In the first stage a simple analytical queueing network model is formulated. In some instances this approximate model is accurate enough for its intended applications (e.g. debottlenecking, capacity planning or scheduling). If it is not, the results indicate which portions of the process must be subjected to more detailed modeling, and a general-purpose simulation language is used for that purpose. In an illustrative application of the approach, a queueing network model was developed for a single-product campaign in an existing multiproduct pharmaceutical plant, and a SLAM II simulation model was subsequently used to model finite intermediate storage and non-Markovian arrival and service times. The final model was validated and used to explore alternative production procedures to reduce the campaign duration and yield additional production capacity.

An outer-approximation method for multiperiod design optimization

We address the development of an efficient optimization method for convex nonlinear and mixed-integer nonlinear multiperiod design optimization problems. An outer-approximation-based decomposition method for solving these problems is proposed. The method is applied to multiperiod multiproduct batch plant problems operating with single product campaigns. Multiperiod models are presented for the design and future capacity expansions of such plants. Numerical results are compared with existing general solution methods such as MINOS and SQP for the nonlinear programming case and DICOPT++ for the mixed-integer nonlinear programming case

Scheduling of multipurpose batch chemical plants. 1. Formation of single-product campaigns

The single-product campaign formation problem is defined and a mixed integer nonlinear programming (MINLP) formulation is presented. The difficulties encountered in solving this formulation are discussed, a decomposition strategy to solve the problem is presented, and the effectiveness of the solution procedure is illustrated with an example

Scheduling of multipurpose batch chemical plants. 2. Multiple-product campaign formation and production planning

The single-product campaign formation decomposition algorithm, which is presented in part I, is extended to identify dominant multiple-product campaign based on the same linear dominance property used by Mauderli and Rippin. A production planning formulation for multipurpose batch plants is presented that selects from the set of previous by identified dominant campaigns and accounts for changeover and startup times of the production lines in each campaign. The dominant campaigns are then identified for the example multipurpose plant from Mauderli and Rippin, and several production planning problems are solved to illustrate the improvement in plant performance using the optimal dominant campaigns compared with the campaigns identified by Mauderli and Rippin

Design of multiproduct batch processes with finite intermediate storage

A heuristic procedure for the preliminary design of batch processes with or without intermediate storage tanks and for which the objective is the minimization of total equipment cost is presented. The processes may be operated in either the multiproduct or the multipurpose mode, but in which multiple products are accommodated through sequential single-product campaigns. The procedure which carries out a sequence of single variable fine searches to obtain a solution to the design problem is easy to code and use. The solutions yielded by the procedure are on an average within 1% of the optimal solutions and are obtained with small computational effort. The results obtained from the test problems also indicate that sizeable reductions in the capital cost of the equipment can be achieved by the insertion of intermediate storage tanks at appropriate locations in a plant.