Multiproduct Processes Research Articles

Path modeling and process control

Many production processes are carried out in stages. At the end of each stage, the production engineer can analyze the intermediate results and correct process parameters (variables) of the next stage. Both analysis of the process and correction to process parameters at next stage should be performed regarding the foreseeable output property y, and with respect to an admissible range of correcting actions for the parameters of the next stage. In this paper the basic principles of path modeling is presented. The mathematics is presented for processes having only one stage, having two stages and having three or more stages. The methods are applied to a process control of a multi-stage production process having 25 variables and one output variable. When moving along the process, variables change their roles. It is shown how the methods of path modeling can be applied to estimate variables of the next stage with the purpose of obtaining optimal or almost optimal quality of the output variable. An important aspect of the methods presented is the possibility of extensive graphic analysis of data that can provide the engineer with a detailed view of the multi-variate variation in data.

Bioprocessing of avian eggshells and eggshell membranes using lactic acid bacteria

Lactic acid fermentation combined with chemical treatments is a new alternative to chemical extraction of by-products from organic wastes such as prawn and krill shells. This study investigated the potential of whole eggshells (WES) and eggshell membranes (ESM) fermentation to provide a multi-product process, thereby eliminating waste and generating revenue. Dry WES and dry ESM were treated separately in a 2-L reactor using a glucose solution, with and without citric acid solution (CA) and commercial lactic acid bacteria as inoculants, to determine the protein and carbohydrate contents from the final products. Through this process, protein and calcium removal is achieved by enzymatic action on the tissues and by dissolving of calcium by organic acids, respectively. The best fermentation condition was obtained by including CA in the process. Mass balances from the WES and ESM treatments were carried out to identify the phases with major amount of protein, carbohydrate and calcium. In the WES treatments with/without CA, the liquid phase turned out to contain the major amount of protein (85.4 and 73.2%) from the final product. On the other hand, the solid phase turned out to contain mainly ash (80.47 and 80.49%), with high calcium content, from the final product. The high-solubility dialysed liquid phase (LP1) from the ESM treatment turned out to contain the major amount both of soluble protein (88.3%) and of exopolysaccharides expressed as carbohydrates (4.3%) and the low-solubility dialysed liquid phase (LP2) turned out to contain the major amount of insoluble protein (60.2%) from the final product. In addition, the first-precipitation solid phase (SP1) from the ESM treatment turned out to contain the major amount of ash (60.5%) from the final product. The foamy phase and the liquid phase from the WES treatment using CA were analysed by SDS–PAGE, two-dimensional electrophoresis and electrospray ionisation ion-trap mass spectrometry. Four proteins related to the hen eggshells were identified from these phases: chicken heat shock protein (Gallus gallus), glucose-regulated protein precursor, calcyclin and 60s acidic ribosomal protein p2 were identified in the liquid phase and a protein homologous with calmodulin, a ubiquitous intracellular Ca2+ receptor, was identified in the foamy phase. Copyright © 2006 Society of Chemical Industry

An autonomous decentralized supply chain planning system for multi-stage production processes

In this paper, we propose an autonomous decentralized optimization system for multi-stage production processes. The proposed system consists of a Material Requirement Planning subsystem, a Distribution Planning subsystem and Decentralized Scheduling subsystems belonging to each production stage that constitute the entire plant. In the proposed system, each subsystem repeats both optimization of the schedule at each subsystem and data exchange among the subsystems. Computational results demonstrate that the results of the proposed planning system are superior to those of the hierarchical planning system, despite the fact that the proposed system has wide flexibility for adding the constraints and modifying the criterion of performance evaluation.

Cascading flowlines and layout modules: Practical strategies for machine duplication in facility layouts

The standard approach for design of a layout for a high-variety low-volume (HVLV) manufacturing facility has been to use either a from-to chart or a multi-product process chart to design a process layout or a cellular layout, respectively, for the facility. Considerable research has focused on making a go-no go decision to implement any one of these two traditional layouts as the preferred layout for an HVLV manufacturing facility. This paper introduces a variety of Hybrid Cellular Layouts (HCLs) which integrate the attributes of the traditional functional, cellular and flowline layouts. The mathematical models and methods for design of two HCLs—cascading flowline layout and modular layout—are discussed in detail. Unlike the standard models in the literature, the design of the cascading flowline layout introduces a novel string-to-graph aggregation and planar graph embedding method that allows machine duplication in the layout. Similarly, the design of the Modular layout introduces a substring clustering method instead of the standard method of cluster analysis to form part families using the complete routings of the parts. For each HCL, results from an industry project are presented to demonstrate the real-world viability of the concepts, methods and software developed to support the design of HCLs for high-variety low-volume manufacturing facilities.

International interdependence and the welfare effects of monetary policy

A vertical chain of production and trade along this chain have been found to be a characteristic feature of globalized markets. This paper examines how a multistage production process that involves more than one country affects the transmission of monetary policy changes. We assume that imported and domestic inputs are required to produce final consumption goods. Monetary policy may have adverse beggar-thyself effects if the mutual dependence between countries is considerably high. The foreign country benefits from a home monetary expansion unless the competitiveness of markets is too low.

Rapidity spectra analysis in terms of non-extensive statistic approach

We provide the description of rapidity spectra of particles produced in pp̄ collisions using the anomalous diffusion approach to account for their non-equilibrium character. In particular, we exhibit connections between multiproduction processes and anomalous diffusion described through the nonlinear Focker-Planck equation with a nonlinearity given by the nonextensivity parameter q describing the underlying Tsallis q-statistics. We demonstrate how this leads to the Feynman scaling violation in these collisions. The q parameter obtained in this way turns out to be closely connected to the parameter 1 k converting the original poissonian multiplicity distribution to its observed Negative Binomial form. The inelasticity of the reaction has also been calculated and found to slightly decrease with increasing reaction energy.

Plantwide Control of Continuous Multiproduct Processes: Three-Product Process

A previous paper (Kapilakarn, K.; Luyben, W. L. Ind. Eng. Chem. Res. 2003, 42, 1890−1904) explored the design and plantwide control of a continuous process in which two reversible reactions produced two desired products M and D. Because chemical equilibrium established the amounts of the products leaving the reactor, the use of product recycle was required to operate over a range of product ratios M/(M + D). This paper extends the previous work to consider the more complex system in which there are three reactions producing components M, D, and T. Desired product ratios can span the entire ternary distribution space (M/D/T), depending on market conditions. Both steady-state design and dynamic control are explored for this three-product process, which features one reactor, four distillation columns, and two recycle streams. Several conventional control structures are studied in which the flow rates of the fresh feed streams are fixed or manipulated by level or composition/temperature controllers and the pr...

Plantwide Control of Continuous Multiproduct Processes: Two-Product Process

Plantwide Control of Continuous Multiproduct Processes: Two-Product Process

Scale, indivisibilities and production function in data envelopment analysis

This paper critically re-examines the concept of returns to scale vis-à-vis economies of scale since the writings of Adam Smith by relating the former to the concept of production unit and the latter to the concept of firm. Though to date some valuable progress has been made exploring the economic theory underlying DEA models, these developments have remained in their infancy and have not found enough application. An attempt is made here to examine the DEA model of efficiency measurement and its application from an economic viewpoint. We show here that the presence of indivisibilities in all multi-stage production processes makes the technology structure non-convex, and therefore, the standard convex DEA production models (e.g., CCR and BCC) fail to exhibit increasing returns due to indivisibilities. However, the non-convex technology embedded in FDH model helps revealing process indivisibilities arising from task-specific processes whereas a homogeneous characterization of production function fails to do so.

A Method for Determining Economic Order Quantities of Procurement Parts in Multistage Production Processes

A Method for Determining Economic Order Quantities of Procurement Parts in Multistage Production Processes

Scheduling a Two-Stage Multiproduct Process with Limited Product Shelf Life in Intermediate Storage

Many commonly occurring multistage facilities in noncontinuous chemical industries can be modeled as a two-stage process with intermediate storage. A two-step mixed-integer linear programming (MILP) approach is developed for such a class of problems with real and complex features such as limited shelf-lives of intermediate products, batch splitting at the storage, a batch filling multiple orders, and general product specifications. Step 1 forms optimal lots and batches to meet the orders, while step 2 schedules them. Twelve new formulations based on several novel constraint sets to assign consecutive orders to a unit are proposed and evaluated using several examples involving up to 90 batches. These sets are useful even for multistage scheduling problems other than the present problem. For this problem, minimizing setups and tardiness together seems easier and better than minimizing tardiness alone.

Scheduling of Single-Stage and Continuous Processes on Parallel Lines with Intermediate Due Dates

This paper addresses scheduling problems in single-stage and continuous multiproduct processes on parallel lines with intermediate due dates and especially restrictions on minimum run lengths. Whereas previous approaches require predetermined time slots or a maximum number of time slots to which only one task should be assigned, the proposed formulation does not use time slots within a time period. Therefore, the size of a model and its computation time are significantly reduced, with restrictions on several realistic situations, such as minimum run lengths, idle times of processes, and tests/maintenance, that are addressed in previous literature. Our approach is illustrated with various examples presented in the literature.

Scheduling Continuous Multi-Product Processes in Compliance with Process Dynamics and Changing Market Conditions

Advanced process control and optimization is believed to be the key in enabling more flexible operation of continuous multi-product plants. A major benefit of increased operating flexibility is to be able to respond faster to changing market conditions. To investigate how this can be realized, we consider the problem of production scheduling in compliance with plant dynamics and changing market conditions. Plant dynamics are included via the introduction of transition tasks, the attributes of which can be calculated using dynamic optimization. A discretized description of company-market interaction is introduced which enables to include most relevant aspects of market behavior.

Scheduling of non-sequential multipurpose batch processes under finite intermediate storage policy

In this study, we present a mathematical model for optimal scheduling of non-sequential multipurpose batch processes under finite intermediate storage (FIS) policy. In non-sequential multipurpose batch processes, the production routes of products may be different from one another and may be in opposite direction. Consequently, in order to reduce idle time of units and to raise the efficiency of process, we have to make operation sequences of products in each unit different by considering the production route of each product. For the formulation of this problem, we represented the starting and finishing time of a task in each unit with two coordinates. One is based on products, and the other is based on operation sequences. Then, we matched the variables used in the two coordinates into one with binary variables and logical constraints. We formulated this problem as an MILP model. Compared with Jung, J. H., Lee, H., Yang, D. R. and Lee, I. (1994) [Completion times and optimal scheduling for serial multi-product processes with transfer and setup times in zero wait (ZW) policy. Computers & Chemical Engineering, 18(6), 537] and Kim, M. S., Jung, J. H. and Lee I. (1996) [Optimal scheduling of multiproduct batch processes for various intermediate storage policies. Industrial Engineering & Chemical Research, 27, 1840] who used an MINLP model for multiproduct scheduling problems, we su9ggest an MILP model, even though we handle sequence dependent setup times in multipurpose processes. Therefore, the proposed model can guarantee the optimality of the solutions. We applied this model to two examples to show the effectiveness of the model. The MILP solver we used to solve these problems is GAMS/ OSL and H/W is IBM RS/6000 (model 350).

Multi-cyclic flow shop scheduling: An application in multi-stage, multiproduct production processes

This paper focuses primarily on multi-cyclic flow shop scheduling. Multi-cyclic scheduling is a generalization of common cycle scheduling in which the cycle time for each product is required to be an integer multiple of the base cycle time. After reviewing the literature, this paper presents an efficient heuristic procedure which generates near-optimal multi-cyclic schedules for a flow shop production environment under deterministic and stationary conditions. This heuristic accounts for all inventory costs including in-process inventory and idle time. The proposed heuristic is then implemented and tested at CONMAT Inc. CONMAT Inc. is a construction materials company based in Pennsylvania, USA. The solution procedure compared to the performance of the current production process at CONMAT proved to be very cost and time efficient.

A hybrid system of heuristics and simulated annealing for large size scheduling problems of batch processes with pipeless intermediate storage

This paper describes a new scheduling solution for large number multi-product batch processes with complex intermediate storage system. Recently many batch chemical industries have turned their attention to a more efficient system known as a pipeless batch system. But existing plants need to change their systems to pipeless systems, piece by piece. In this case, current systems are changed to pipeless systems by way of non critical process operations such as through the use of intermediate storage. We have taken the conventional batch plant with a pipeless storage system as an objective process. Although the operation of a pipeless storage system becomes more complex, its efficiency is very high. With this system, all of the storage should be commonly used by any batch unit. For this reason, solving the optimal scheduling problem of this system with a mathematical method is very difficult. Despite the attempts of many previous researches, there has been no contribution which solves the scheduling of intermediate storage for complex batch processes. In this paper, we have developed a hybrid system of heuristics and Simulated Annealing (SA) for large multi-product processes using a pipeless storage system. The results of this study show that the performance and computational time of this method are superior to that of SA and Rapid Access Extensive Search (RAES) methods.

A dynamical supervisor strategy for multi-product processes

Competing in the global marketing place puts additional burden on multi-product manufacturing processes. Each transition to a different product grade must be made efficiently with the simultaneous objectives of minimal off-spec product and feed stock waste, and non-violation of safety and environmental constraints. In this work, a hybrid, dynamical supervisory control strategy is presented to address transition control of multi-product processes. The scheme involves the selection of the best setpoint controller, from an existing family of feedback controllers so as to cause the output to track the desired setpoint. The performance of the supervisory control strategy is demonstrated on an exothermic reactor.

Production scheduling of single-stage multi-product batch chemical processes with fixed batch sizes

We address the problem of scheduling a single-stage multi-product batch chemical process with fixed batch sizes. We present a mixed-integer nonlinear programming model to determine the schedule of batches, the batch size, and the number of overtime shifts that satisfy the demand at minimum cost for this process. We introduce a polynomial-time algorithm to solve the problem when the processing times of all batches are identical and the setup and cleaning times are sequence-independent. The solution procedure is based on recognizing that the optimal fixed batch size is a member of a set whose cardinality is polynomial. Given a batch size, the problem may be formulated as an assignment problem. Thus, an optimal solution may be found by iteratively solving a polynomial number of assignment problems. This work was motivated by a pesticide manufacturing company in the design of a new plant where the assumptions of a single bottleneck machine, fixed batch sizes, sequence-independent setup times, and identical batch processing times are all valid. An example is developed for this application.

Operating regime-based controller strategy for multi-product processes

A hybrid, dynamical supervisory control strategy is introduced to control multi-product processes. The scheme involves the selection of the best setpoint controller, from an existing family of feedback controllers, to be placed into feedback with the process so as to cause the output to track the desired setpoint. This task is performed without exhaustive trial and error, by minimizing a specific normed output estimation error that relates the process output to a shared controller state. The performance of the supervisory control strategy is demonstrated on a continuous-stirred tank reactor that can be operated at three different conversion levels. However, the most desirable operating point is open-loop unstable. Linear controllers are designed for each operating region and the role of the supervisory control strategy will be to determine the switching logic as different scheduling policies are demanded.

Production scheduling of single-stage multi-product batch chemical processes with fixed batch sizes

We address the problem of scheduling a single-stage multi-product batch chemical process with fixed batch sizes. We present a mixed-integer nonlinear programming model to determine the schedule of batches, the batch size, and the number of overtime shifts that satisfy the demand at minimum cost for this process. We introduce a polynomial-time algorithm to solve the problem when the processing times of all batches are identical and the setup and cleaning times are sequence-independent. The solution procedure is based on recognizing that the optimal fixed batch size is a member of a set whose cardinality is polynomial. Given a batch size, the problem may be formulated as an assignment problem. Thus, an optimal solution may be found by iteratively solving a polynomial number of assignment problems. This work was motivated by a pesticide manufacturing company in the design of a new plant where the assumptions of a single bottleneck machine, fixed batch sizes, sequence-independent setup times, and identical batch processing times are all valid. An example is developed for this application.