• Proceedings of the Korea Society of Information Technology Applications Conference
• /
• 2005.11a
• /
• pp.311-314
• /
• 2005

Supply chain optimization is one of the most important components in the optimization of a company's value chain. This paper considers the problem of designing the supply chain for a product that is represented as an assembly bill of material (BOM). In this problem we are required to identify the locations at which different components of the product arc are produced/assembled. The objective is to minimize the overall cost, which comprises production, inventory holding and transportation costs. We assume that production locations are known and that the inventory policy is a base stock policy. We first formulate the problem as a 0-1 nonlinear integer programming model and show that it can be reformulated as a 0-1 linear integer programming model with an exponential number of decision variables.

• Journal of Korean Society of Industrial and Systems Engineering
• /
• v.32 no.4
• /
• pp.53-62
• /
• 2009

Lee[15] examined quantity discount contracts between a manufacturer and a retailer in a stochastic, two-period inventory model where quantity discounts are provided based on the previous order size. During the two periods, the retailer faces stochastic (truncated Poisson distributed) demands and he/she places orders to meet the demands. The manufacturer provides for the retailer a price discount for the second period order if its quantity exceeds the first period order quantity. In this paper we extend the above two-period model to a k-period one (where k < 2) and propose a stochastic nonlinear mixed binary integer program for it. In order to make the program tractable, the nonlinear term involving the sum of truncated Poisson cumulative probability function values over a certain range of demand is approximated by an i-interval piecewise linear function. With the value of i selected and fixed, the piecewise linear function is determined using an evolutionary algorithm where its fitness to the original nonlinear term is maximized. The resulting piecewise linear mixed binary integer program is then transformed to a mixed binary integer linear program. With the k-period model developed, we suggest a solution procedure of receding horizon control style to solve n-period (n < k) order decision problems. We implement Lee's two-period model and the proposed k-period model for the use in receding horizon control style to solve n-period order decision problems, and compare between the two models in terms of the pattern of order quantities and the total profits. Our computational study shows that the proposed model is superior to the two-period model with respect to the total profits, and that order quantities from the proposed model have higher fluctuations over periods.

• Journal of the Korean Institute of Navigation
• /
• v.22 no.4
• /
• pp.15-19
• /
• 1998

This paper concerns a bulk or semibulk cargo ship scheduling problem with a single loading port. This type of ship scheduling problem is frequently needed in real world for carrying minerals or agricultural produce from a major single production zone to many destinations scattered over a large area of the world. The first optimization model for this problem was introduced by Ronen (1986) as a nonlinear mixed integer program. The model developed in this paper is an improvement of his model in the sense that nonlinearities and numerous unnecessary integer variables have been eliminated. By this improvement we could expect real world instances of moderate sizes to be solved optimal solutions by commercial integer programming software. Similarity between the ship scheduling model and the capacitated facility location model is also discussed.

• Journal of the Korean Operations Research and Management Science Society
• /
• v.31 no.1
• /
• pp.91-103
• /
• 2006

Given a bill of materials (BOM) tree T labeled by the breadth first search (BFS) order from node 0 to node n and a general network ${\Im}=(V,A)$, where V={1,2,...,m} is the set of production facilities and A is the set of arcs representing transportation links between any of two facilities, we assume that each node of T stands for not only a component. but also a production stage which is a possible stocking point and operates under a periodic review base-stock policy, We also assume that the random demand which can be achieved by a suitable service level only occurs at the root node 0 of T and has a normal distribution $N({\mu},{\sigma}^2)$. Then our integrated model of facility location problems and safety stock optimization problem (FLP&SSOP) is to identify both the facility locations at which partitioned subtrees of T are produced and the optimal assignment of safety stocks so that the sum of production cost, inventory holding cost, and transportation cost is minimized while meeting the pre-specified service level for the final product. In this paper, we first formulate (FLP&SSOP) as a nonlinear integer programming model and show that it can be reformulated as a 0-1 linear integer programming model with an exponential number of decision variables. We then show that the linear programming relaxation of the reformulated model has an integrality property which guarantees that it can be optimally solved by a column generation method.

• Journal of the Korean Operations Research and Management Science Society
• /
• v.13 no.2
• /
• pp.34-46
• /
• 1988

This paper deals with design problem of unit load automated storage/retrieval systems (AS/RS). We propose an optimal design model in which the investment and maintenance costs of AS/RS, operating under dual command model is minimized over a time horizon satisfying the warehouse dimensional constraints. The model is formulated as an integer nonlinear program and an algorithm is proposed to find an optimum solution. The valididty of the solution algorithm is illustrated through an example.

• The Pure and Applied Mathematics
• /
• v.3 no.1
• /
• pp.73-81
• /
• 1996

Multiple objective programming has been a popular research area since 1970. The pervasiveness of multiple objective in decision problems have led to explosive growth during the 1980's. Several approaches (interactive methods, feasible direction methods, criterion weight space methods, Lagrange multiplies methods, etc) have been developed for solving decision problems having multiple objectives. However there are still many mathematically challengings including multiple objective integer, nonlinear optimization problems which require further mathematically oriented research. (omitted)

• 전기의세계
• /
• v.23 no.1
• /
• pp.73-78
• /
• 1974

Digital simulation algorithms and program for multimachine dynamic stability have been developed which represent the effects of machines much more complety than have been available previously. Emphasis is given to the savings of the memory spaces required, thus making it possible to use a small computer with limited capacity of core storage (without auxiliary storage). Both d- and q- aris quantities are fully represented, and the speed-governing and voltage-regulating system available are ertensive, thus allowing a very close approximation to any physical system. Facilities for dynamic and nonlinear loads are also included. The computational algorithms and program developed have been shown to be extensive and complete, and are very desirable features minimizing memory spaces for stability calculations. The capabilities have been demonstrated by several case studies for an actual power system of 44 generators, 22 loads and 33 buses. About 13-K words of memory spaces have been required for the case studies on the basis of two words per real variable and a word per integer variable.

• Korean Management Science Review
• /
• v.10 no.1
• /
• pp.193-205
• /
• 1993

This paper presents a mathematical model for a class of vertical integration decisions. The problem structure of interest consists of raw material vendors, components suppliers, components processing plants, final product (assembly) plants and external components buyers. Economic feasibility of operating components plants instead of keeping outside suppliers is our major concern. The model also determines assignment of product lines and production volumes to each open plant considering the cost impacts of economies of scale and plant complexity. The problem formulation leads to a concave, mixed integer mathematical program. Given the state of the art of nonlinear programming techniques, it is often not possible to find global optima for reasonably sized such problems. We developed an optimization solution algorithm within the framework of Benders decomposition for the case of a piecewise linear concave cost function. It is shown that our algorithm generates optimal solutions efficiently.

• Journal of Korean Institute of Industrial Engineers
• /
• v.19 no.4
• /
• pp.97-104
• /
• 1993

This paper deals with the design problem of a man-on-board(MOB) storage and retrieval warehousing system which is suitable for storing items of small size and light weight. It is assumed that the operator carries out a sequence of retrieving(or storing) operations traveling on a specially designed truck. Considering the operating characteristics of the man-on-board system, an optimal design model is developed in which the investment and maintenance costs of the system are minimized over a time horizon satisfying a set of constructional restrictions. The model is formulated as a nonlinear integer program and a search algorithm is proposed to find an optimum solution.

• Journal of Korean Society of Industrial and Systems Engineering
• /
• v.20 no.43
• /
• pp.25-36
• /
• 1997

The purpose of this paper is to structure a new integrated model that can minimize the total cost for the transportation and inventory systems between m origin points, where origin i has a supply of a commodity, such as distribution centers or warehouses, and n destination points, where destination j requires the commodity. In this case, demands of the destination points are assumed random variables which have a known probability distribution. We will find optimal distribution centers which transport the commodity to the destination points and suggest optimal inventory policy to the selected distribution center which find the optimal pair $$ and safety stock level that minimize total cost with back-ordered case. This new model is formulated as a 0-1 nonlinear integer programming problem. To solve the problem, this paper proposes heuristic computational procedures and program and provides numerical examples.