• Journal of Institute of Control, Robotics and Systems
• /
• v.21 no.11
• /
• pp.1076-1080
• /
• 2015

An inventory control system was developed for a distribution system consisting of a single multiproduct warehouse serving a set of customers and purchasing products from multiple vendors. Purchase orders requesting multiple products are delivered to the warehouse in a process. The receipt of customer orders by the warehouse proceeded in order intervals and in order quantities that are subject to random fluctuations. The objective of warehouse operation is to minimize the total cost while maintaining inventory levels within the warehouse capacity by adjusting the purchase order intervals and quantities. An adaptive model predictive control algorithm was developed using a periodic square wave model to represent the material flows. The adaptive concept incorporated a stabilized minimum variance control-type input calculation coupled with input/output stream parameter predictions. The effectiveness of the scheme was demonstrated using simulations.

• Management Science and Financial Engineering
• /
• v.1 no.1
• /
• pp.39-66
• /
• 1995

This article presents a new model called the periodic square wave(PSW) to describe the material flow of periodic processes involving an intermediate buffer. The material flows into and out of the intermediate buffer are assumed to be periodic square shaped. By using this model, It is proved that the classical economic lot size model with finite supply rate, the so-called EPQ model, can be applicable to the arbitrary periodic demand case. This new model relaxes the original assumption of the constant demand. It is shown, as a unique application example, that the explicit solution for determining both upstream and downstream economic lot size can be obtained with the aid of the PSW model. The PSW model provides more accurate information on analyzing the inventory and production system than the classical approach, without losing simplicity and increasing the computational burden.

• Journal of Institute of Control, Robotics and Systems
• /
• v.3 no.4
• /
• pp.398-405
• /
• 1997

This article presents a new model which is called Periodic Square-Wave(PSW) to describe the material flow of the periodic processes involving intermediate buffer. The material flows incoming into and outgoing from the intermediate buffer are assumed to be periodic square shaped. PSW model gives the same result as that of Economic Production Quantity(EPQ) model for determining optimal lot size of single stage batch storage system. However, for batch storage serial train system, PSW model gives a different optimal solution of about 6 % reduced total cost. PSW model provides the more accurate information on inventory and production system than the classical approach by maintaining simplicity and increasing computational burden.

• Journal of Institute of Control, Robotics and Systems
• /
• v.3 no.5
• /
• pp.532-541
• /
• 1997

This article derives an analytic solution to determine the optimal size of multiple noncontinuous process and storage units. The total cost to be minimized consists of the setup cost of noncontinuous processing units and the inventory holding cost of feedstock/product storages. A novel approach, which is called PSW(Periodic Square Wave) model, is applied to represent the material flow among non-continuous units and storages. PSW model presumes that the material flow between unit and storage is periodic square wave shaped. The resulting optimal unit size has similar characteristics with the classical economic lot sizing model such as EOQ(Economic Order Quantity) or EPQ(Economic Production Quantity) model in a sense that the unit size is determined as the balance between setup and inventory holding cost. However, the influence of inventory holding cost of PSW model is different from that of EOQ/EPQ model. EOQ/EPQ model includes only the product inventory holding cost but PSW model includes all inventory holding costs around the non-continuous unit with proportional contribution. PSW model is suitable for analyzing interlinked process-storage system. The optimal lot size of PSW model is smaller than that of EOQ/EPQ model. This is quitea remarkable result considering that the EOQ/EPQ model has been is widely used since last half century.

• Journal of Institute of Control, Robotics and Systems
• /
• v.22 no.12
• /
• pp.1040-1045
• /
• 2016

An inventory control system was developed for multiproduct batch plants with an arbitrary number of batch processes and storage units. Customer orders are received by the plant at intervals and in quantities that are subject to random fluctuations. The objective of the plant operation is to minimize the total cost while maintaining inventory levels within the storage or warehouse capacity by adjusting the startup times, the quantities of raw material orders, and production batch sizes. An adaptive model-based control algorithm was developed that uses a periodic square wave model to represent the flows of material between the processes and the storage units. The effectiveness of this approach was demonstrated by performing simulations.

• The Pure and Applied Mathematics
• /
• v.9 no.1
• /
• pp.19-30
• /
• 2002

We consider one class of bursting oscillation models, that is square-wave burster. One of the interesting features of these models is that periodic bursting solution need not to be unique or stable for arbitrarily small values of a singular perturbation parameter $\epsilon$. Recent results show that the bursting solution is uniquely determined and stable for most of the ranges of the small parameter $\epsilon$. In this paper, we present a condition of uniqueness and stability of periodic bursting solutions for all sufficiently small values of $\epsilon$ > 0.

• Journal of Institute of Control, Robotics and Systems
• /
• v.4 no.6
• /
• pp.802-810
• /
• 1998

The purpose of this study is to find the analytic solution of determining the optimal capacity of processes and storages to meet the product demand. Recent trend to reduce product delivery time and to provide high quality product to customer requires the increasing capacity of storage facilities. However, the cost of constructing and operating storage facilities is becoming substantial because of increasing land value, environmental and safety concern. Therefore, reasonable decision making about the capacity of processes and storages is important subject for industries. The industrial solution for this subject is to use the classical economic lot sizing method, EOQ(Economic Order Quantity) model, trimmed with practical experience but the unrealistic assumption of EOQ model is not suitable for the chemical plant design with highly interlinked processes and storages. This study, a first systematic attempt for this subject, clearly overcomes the limitation of classical lot sizing method. The superstructure of the plant consists of the network of serially and/or parallelly interlinked processes and storages. A novel production and inventory analysis method, PSW(Periodic Square Wave) model, is applied. The objective function of optimization is minimizing the total cost composed of setup and inventory holding cost. The advantage of PSW model comes from the fact that the model provide a set of simple analytic solution in spite of realistic description of material flow between process and storage. The resulting simple analytic solution can greatly enhance the proper and quick investment decision for the preliminary plant design confronting diverse economic situation.

• Journal of the Optical Society of Korea
• /
• v.17 no.3
• /
• pp.262-268
• /
• 2013

We study the focusing properties of a two-dimensional square-lattice photonic crystal (PC) comprising silica and germanium partitioned cylinders in air background. The finite difference time domain (FDTD) method with periodic boundary condition is utilized to calculate the dispersion band diagram and the FDTD method incorporating the perfectly matched layer boundary condition is employed to simulate the image formation. In contrast to the common square PCs in which the negative refraction effect occurs in the first photonic band without negative phase propagation, in our suggested model system, the frequency with negative refraction exists in the second band and in near-infrared region. In this case, the wave propagates with a negative phase velocity and the evanescent waves can be supported. We also discuss the dependency of the image resolution and its location on surface termination, source location, and slab thickness. According to the simulation results, spatial resolution of the proposed PC lens is below the radiation wavelength.

• Journal of Institute of Control, Robotics and Systems
• /
• v.19 no.6
• /
• pp.563-568
• /
• 2013

The purpose of this study is to find the analytic solution for determining the optimal capacity (lot-size) of a batch-storage network to meet the finished product demand under infrequent shutdowns. Batch processes are bound to experience random but infrequent operating time losses. Two common remedies for these failures are duplicating another process or increasing the process and storage capacity, both of which are very costly in modern manufacturing systems. An optimization model minimizing the total cost composed of setup and inventory holding costs as well as the capital costs of constructing processes and storage units is pursued with the framework of a batch-storage network of which flows are susceptible to infrequent shutdowns. The superstructure of the plant consists of a network of serially and/or parallel interlinked batch processes and storage units. The processes transform a set of feedstock materials into another set of products with constant conversion factors.A novel production and inventory analysis method, the PSW (Periodic Square Wave) model, is applied. The advantage of the PSW model stems from the fact it provides a set of simple analytic solutions in spite of a realistic description of the material flow between processes and storage units. The resulting simple analytic solution can greatly enhance a proper and quick investment decision at the early plant design stagewhen confronted with diverse economic situations.

• Journal of Institute of Control, Robotics and Systems
• /
• v.18 no.9
• /
• pp.854-862
• /
• 2012

The optimal design of batch-storage network by using periodic square wave model provides analytical lot sizing equations for a complex supply chain network characterized as multi-supplier, multi-product, multi-stage, non-serial, multi-customer, cyclic system including recycling and/or remanufacturing. The network structure includes multiple currency flows as well as material flows. The processes are represented by multiple feedstock/product materials with fixed composition which are very suitable for production processes. In this study, transportation processes that carry multiple materials with unknown composition are added and the time frame is changed from single period into multiple periods in order to represent nonperiodic parameter variations. The objective function of the optimization involves minimizing the opportunity costs of annualized capital investments and currency/material inventories minus the benefit to stockholders in the numeraire currency. The expressions for the Kuhn-Tucker conditions of the optimization problem are reduced to a multiperiod subproblem for average flow rates and analytical lot-sizing equations. The multiperiod lot sizing equations are different from single period ones. The effects of corporate income taxes, interest rates and exchange rates are incorporated.