Ho-Kyung Lee

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

Abstract 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).

Capacity expansion problem of multisite batch plants with production and distribution

Abstract In this study we develop a capacity expansion model of an integrated production and distribution system comprised of multisite batch plants and several warehouses. Such an integration of the production and distribution system can generate significant savings by trading off the costs associated with the whole, rather than minimizing production and distribution costs separately. The study presented here to be considered as two or more multiproduct batch plants producing several products to supply several warehouses. An objective function is defined as a net profit in a chemical company — total expected selling price minus the cost of new units and the expected shipping cost. We determine a revised plant configuration, sizes and operating modes of newly illustrated with two case studies. The case studies are solved with GAMS/DICOPT + +.

Generalized retrofit design of multiproduct batch plants

Abstract The problem of a generalized retrofit design of multiproduct batch plants is considered in this paper. Unlike previous research on this topic, which concerns only the ways to add a new unit which will be operated in-phase or out-of-phase with the existing units, we get a better result by altering the existing operating mode between existing units (or between new units). Disposing of the useless existing units and replacing outworn equipment with new are also considered. We present a new generalized superstructure with a concept of ‘group’, a collection of units operated in-phase, then formulate it as an MINLP problem with an implicit or explicit group expression. Five examples will verify the effectiveness of this method.

Completion times algorithm of multi-product batch processes for common intermediate storage policy (CIS) with nonzero transfer and set-up times

Abstract Common intermediate storage policy (CIS) is suggested for flexible use of various intermediate storage policies. CIS can accomplish the complete flexible intermediate storage operations to satisfy more frequent changes of ordered item sets by customers. In this paper, two kinds of CIS system are discussed. One is a conventional pipe-valve, pump intermediate storage system and the other is a pipeless scheme of intermediate storage system. A completion time algorithm of the CIS system is also developed with two steps and it is applicable to both kinds of CIS systems. At the first step, we suggest a simplified CIS operation to make the problem easier, and in the second step we proposed the complete CIS operation as a complete flexible intermediate storage policy by inserting the ZW block in the simplified CIS operation system. Finally, we develop the completion time algorithm for the CIS policies with nonzero transfer, set-up times.

An evolutionary approach to optimal synthesis of multiproduct batch plant

Abstract In case of adding new equipment in parallel to the synthesized batch processes, there are two operating modes for the added equipment. One is “out-of-phase (in-sequence)” mode and the other is “in-phase” mode. However, previous approaches in solving the synthesis problem as a MINLP (Mixed Integer NonLinear Programming) problem so far have considered only the out-of-phase mode. In this paper, using MINLP, heuristics and NLP (nonlinear programming) formulation, we deal with the problems where the in-phase mode is also considered. The effectiveness of this approach is verified by solving three literature problems.

Developing a heuristics for glass cutting process optimization: A case of two-dimensional two-stage guillotine cutting with multiple stock sizes

This paper presents a heuristic algorithm for a two-dimensional two-stage guillotine cutting problem with multiple stock sizes by allowing the rotation of items by 90°. The proposed algorithm generates levels or strips where the first item or base item is selected according to the length of the strip and packs the next items beside the base item in the strip. For each type of item, strips are generated for packing each type of item in a base item. The best n orders in a yield of strips or the best n strips are selected for each type of item. The selected best n strips are packed in one type of bin. For the other types of bins, another best n strips are selected and packed in each type of bin. The best yield in all types of bins is then selected. This iteration is executed until the number of item demands in the overall demands is less than the number of item demands in the bin. Four numerical examples generated from actual industries are illustrated to highlight the applicability of the proposed algorithm with some comments.

A Mathematical Programming for Supply Chain Network Design

Supply chain network design is a classical problem in operations research area since it was invented during the Second World War. A large-scale supply chain network design problem, which is originated from industrial need in restructuring a companys supply chain network, is introduced. The supply chain network includes multiple-warehouses, and large number of customers. Designing supply chain network is a semi-permanent decision that cannot be changed easily once the decision has been made. Furthermore, it also requires investment that should be retrieved in reasonable period by improved supply chain operations based on the design decision. Due to importance of the design decision, a mathematical model for the problem is developed for considering various aspects of the problem, operation cost and customer service level besides the investment cost. The optimization model is solved for real-world business decision making to decide locations, and sizes of multiple-warehouses

A synthesis of multiproduct batch plants considering both in-phase and out-of-phase modes

Abstract A heuristic procedure using a NLP(NonLinear Programming) is developed for the preliminary design of multiproduct batch plants. The procedure determines equipment volumes/batch sizes and allows structural features such as in-phase and out-of-phase modes of operation and nonidentical parallel units in a stage. The previous approaches in solving the synthesis problem as MINLP(Mixed Integer NonLinear Programming) problem so far, have considered only out-of-phase mode. In this paper, using a NLP formulation combined with heuristics, we deal with the problems where in-phase mode and out-of-phase mode are simultaneously considered. The first step of our procedure, by heuristics and table analyses, is to determine how the parallel equipment operates every stage for each product. And then, using a NLP formulation, we determine the unit volumes and batch sizes. This paper demonstrates the effectiveness of our approach in solving two problems of batch plant design.

MILP scheduling model for multipurpose batch processes considering various intermediate storage policies

MILP (Mixed Integer Linear Programming) scheduling models for non-sequential multipurpose batch processes are presented. Operation sequences of products have to be made in each unit differently by considering production route of each product under a given intermediate storage policy to reduce idle time of units and to raise the efficiency of the process. We represent the starting and finishing time of a task in each unit with two coordinates for a given storage policy. One is based on products, and the other is based on operation sequences. Then, using binary variables and logical constraints, we match the variables used in the two coordinates into one. We suggest MILP models considering sequence dependent setup times to guarantee the optimality of the solutions. Two examples are presented to show the effectiveness of the suggested models.

MINLP formulations for solving strip packing problems in LCD mother glass production

Abstract Mother glass production for liquid crystal displays involves the cutting of small rectangles from a large rectangle (strip) to minimize the length of the strip used. This is called the strip packing problem. The main concept for formulating this problem is to generate cutting patterns that can be used to produce items from the strip. This problem is a non-convex mixed integer nonlinear programming (MINLP) problem due to the bilinear terms in the demand and objective function. To obtain global optimal solutions, this problem should be transformed into several linear forms. Numerical examples based on the strip packing problem in LCD mother glass production are provided. Different objective functions for two problems are presented and compared.