• 대한산업공학회지
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• 제33권1호
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• pp.26-32
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• 2007

This study deals with waiting-time dependent backordering rate during stock-out period in the EconomicProduction Quantity (EPQ) model. Assuming that the backordering rate follows an exponentially decreasingfunction of the waiting time, the backorder rate is developed under First-Come-First-Served (FCFS) andLast-Come-First-Served (LCFS) Policy. The mathematical models are developed based on differential equations.Through numerical examples, the validity of the developed models is illustrated.

• 한국경영과학회지
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• 제13권1호
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• pp.10-23
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• 1988

This paper examines a deterministic, discrete-time, finite-horizon, production/distribution problem for a one-plant multi-retailer system. Production may occur at the plant in each time period. Customer demands at each retailer over a finite number of periods are known and must be met without backlogging. The plant as well as the retailers can serve as stocking points. The problem is to find a minimum-cost production/distribution schedule satisfying the known demands. We show that under a certain cost structure a nested policy is optimal, and present an efficient algorithm to find such an optimal policy. Planning horizon results and some computational saving schemes are also presented.

• 한국경영과학회지
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• 제34권3호
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• pp.71-84
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• 2009

This paper considers a remanufacturing and purchasing planning problem, in which either used products(or wastes) are remanufactured or remanufactured products(or final products) are purchased to satisfy dynamic demands of remanufactured products over a discrete and finite time horizon. Also, as remanufactured products are purchased more than or equal to a special quantity Q, a discount price policy is applied. The problem assumes that the related cost(remanufacturing and inventory holding costs of used products, and the purchasing and inventory holding costs of remanufactured products) functions are concave and backlogging is not allowed. The objective of this paper is to determine the optimal remanufacturing and purchasing policy that minimizes the total cost to satisfy dynamic demands of remanufactured products. This paper characterizes the properties of the optimal policy and then, based on these properties, presents a dynamic programming algorithm to find the optimal policy. Also, a network-based procedure is proposed for the case of a large quantity of low cost used products. A numerical example is then presented to demonstrate the procedure of the proposed algorithm.

• 한국경영과학회:학술대회논문집
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• 대한산업공학회/한국경영과학회 2000년도 춘계공동학술대회 논문집
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• pp.61-64
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• 2000

This paper analyzes a dynamic lot-sizing problem, in which the order size of multiple products and a single container type are simultaneously considered. In the problem, each order (product) placed in a period is immediately shipped immediately by containers in the period and the total freight cost is proportional to the number of each container type employed. Also, it is assumed that backlogging is not allowed. The objective of this study is to determine the lot-sizes and the shipping policy that minimizes the total costs, which consist of ordering costs, inventory holding costs, and freight costs. Because this problem is NP-hard, we propose a heuristic algorithm with an adjustment mechanism, based on the optimal solution properties. The computational results from a set of simulation experiment are also presented.

• 한국경영과학회지
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• 제14권2호
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• pp.67-74
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• 1989

This paper considers single-product production and inventory management problem where cumulative demands up to each time period are mutually independent random variables(known) having continuous probability distributions and the associated cost-minimizing production schedule (when to produce and how much to produce) need be determined in rolling horizon environment. For the problem, both the production cost and the inventory holding and backlogging costs are included in the whole system cost. The probability distributions of these costs are expressed in terms of random demands, and utilized to exploit a solution procedure for a production schedule which minimizes the expected unit time system cost and also reduces the probability of rist that, for the first-period of each production cycle (rolling horizon), the cost of the "production" option will exceed that of the "non-production" one. Numerical examples are presented for the solution procedure illustration.cedure illustration.

• 한국경영과학회지
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• 제4권1호
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• pp.25-31
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• 1979

We consider the optimal ordering policy for a single-product two-stage inventory system where the main assumptions are as follows: (i) constant continuous demand only at stage 2, (ii) constant input (production) rate at stage 1, (iii) instantaneous delivery (transportation) from stage 1 to stage 2, (iv) backlogging is allowed only at stage 2, (v) an infinite planning horizon. Costs considered are ordering and linear holding costs at both stages, and linear shortage cost only at stages 2. By solving 9 different case problems, we have observed the general from of the optimal ordering policies for our model which minimizes the total cost per unit time. It is noticeable from this observation that the questionable but more often than not adopted assumption by many authors in determining the optimal potimal policy for multistage inventory systems, that the ordering (lot) sizes at each stage remain constant thruout the planning horizon, is not valid.

• 산업공학
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• 제13권2호
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• pp.217-224
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• 2000

This paper analyzes the effects of setup cost reduction in a dynamic lot-sizing model for a single-facility multi-product problem. In the model, demands for each product are known, no backlogging is allowed, and a single resource is employed. Also, setup cost is defined as a function of capital expenditure to invest in setup cost reduction. Furthermore, in each production period the facility (or plant) produces many products, each representing a fixed part of the involved production activity (or input resource quantity). In this paper, the structure of the optimal solution is characterized and an efficient algorithm is proposed for simultaneously determining the optimal lot size with reduced setup cost and the optimal investment in setup cost reduction. Also, the proposed algorithm is illustrated by a numerical example with a linear and an exponential setup reduction functions.

• 대한산업공학회지
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• 제24권1호
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• pp.157-165
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• 1998

This paper considers the single-product production and transportation problem with discrete time, dynamic demand and finite time horizon, an extension of classical dynamic lot-sizing model. In the model, multiple freight container types are allowed as the transportation mode and each order (product) placed in a period is shipped immediately by containers in the period. Moreover, each container has type-dependent carrying capacity restriction and at most one container type is allowed in each shipping period. The unit freight cost for each container type depends on the size of its carrying capacity. The total freight cost is proportional to the number of each container type employed. Such a freight cost is considered as another set-up cost. Also, it is assumed in the model that production and inventory cost functions are dynamically concave and backlogging is not allowed. The objective of this study is to determine the optimal production policy and the optimal transportation policy simultaneously that minimizes the total system cost (including production cost, inventory holding cost, and freight cost) to satisfy dynamic demands over a finite time horizon. In the analysis, the optimal solution properties are characterized, based on which a dynamic programming algorithm is derived. The solution algorithm is then illustrated with a numerical example.

• 한국경영과학회지
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• 제27권4호
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• pp.185-205
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• 2002

In this study, we consider infinite supply of raw materials and backlogged demands as given two boundary conditions. And we need not make any specific assumptions about the inter-arrival of external demand and service time distributions. Under these situations, the ultimate objective of this study is to prove the variability propagation principle in a pull serial line and is to measure it in terms of the first two moments of the inter-departure process subject to number of cards in each cell. Two preparations are required to achieve this objective : The one is to derive a true lower bound of variance of the inter-departure process. The other is to establish a constrained discrete minimax problem for the no backorder (backlogging) probabilities in each cell. We may get some fundamental results necessary to a completion for the proof through the necessary and sufficient conditions for existence of optimal solution of a constrained discrete minimax problem and the implicit function theorem. finally, we propose a numeric model to measure the variability propagation principle. Numeric examples show the validity and applicability of our study.

• 한국시뮬레이션학회논문지
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• 제12권3호
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• pp.31-40
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• 2003

This paper studies an optimal policy for a certain class of (s, S) inventory control systems, where the demands are characterized by the renewal arrival process. To minimize the average cost over a simulation period, we apply a stochastic optimization algorithm which uses the gradients of parameters, s and S. We obtain the gradients of objective function with respect to ordering amount S and reorder point s via a combined perturbation method. This method uses the infinitesimal perturbation analysis and the smoothed perturbation analysis alternatively according to occurrences of ordering event changes. The optimal estimates of s and S from our simulation results are quite accurate. We consider that this may be due to the estimated gradients of little noise from the regenerative system simulation, and their effect on search procedure when we apply the stochastic optimization algorithm. The directions for future study stemming from this research pertain to extension to the more general inventory system with regard to demand distribution, backlogging policy, lead time, and inter-arrival times of demands. Another direction involves the efficiency of stochastic optimization algorithm related to searching procedure for an improving point of (s, S).