• Journal of Korean Society of Industrial and Systems Engineering
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• v.32 no.4
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• pp.53-62
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• 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 military operations research society of Korea
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• v.23 no.2
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• pp.72-84
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• 1997

In this paper, we consider an economic order quantity(EOQ) and an optimal discount pricing policy for the monopsony related to the weapon system acquisition. In the monopsony case, a buyer wishes to maximize the profit. However, a seller wants to minimize the total inventory related cost since a buyer can determine the purchase price for the product. We develop a generalized version of EOQ model for the monopsony, including one seller-one buyer model and two seller-one buyer model. A model of buyer reaction to any given pricing scheme is developed to show that there exits a unified pricing policy which motivates the buyer to increase its ordering quantity per order, thereby reducing the joint(buyer and seller) ordering and holding costs in the system.

• Journal of Korean Institute of Industrial Engineers
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• v.27 no.4
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• pp.345-351
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• 2001

We are concerned with a multiple replenishment contract with a purchase price discount in a supply chain. The chain is composed of one supplier, one buyer and consumers for a product. The replenishment contract is based upon the well-known (s, Q) policy but allows contracting several firmed orders at a time with a price discount. Due to a larger forecast error of the future demand, the buyer should keep a higher level of safety stock to provide the same level of service of the usual (s, Q) policy but can reduce his purchase cost by placing larger quantity. Thus there exists a trade-off between the price discount and inventory holding cost. We present a model for the contract and an algorithm to find the optimum number of the firmed orders. Computer experiments show that the algorithm finds the global optimum solution very fast.

• The Research Journal of the Costume Culture
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• v.3 no.2
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• pp.409-424
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• 1995

This study intends to investigate the actual state and problems of Outlet, and the research consumer's perception of Outlet. It affords a effective way to get rid of inventories for manufacture and to economize and rational buying for consumer. Ultimately trying to find a effective managing method of Outlet for both manufacturers and consumers. The result about research the actual sate of Outlet, there are affluent assortment, generous amount of merchandise and high discount rate in Kuro-dong Outlet stores, but stores' location is scattered that makes shopping environment inconvenient. It is not good condition of assortment, quantity and freshness of merchandise in Mungung-dong Outlet stores, but close proximity between stores and fancy shopping place make convenient shopping possible. Multi-discount stores dilute the fundumental of Qutlet with poor quantity and assortment of merchandise make man choices possible for consumer, but discount rate is lower for high management cost. The result about research the consumer's perception of Outlet shows that consumer have enough interest in Outlet, and intention to continue shopping in Outlet. Therefore we can expect continuous growth of Outlet. Also consumer is satisfied with price and quality of merchandise, but they are not satisfied with assortment of merchandise, expecially poorness in sizes.

• Journal of Korean Institute of Industrial Engineers
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• v.15 no.1
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• pp.17-21
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• 1989

The problem to determine Economic Order Quantity(EOQ) occurs when price discounts or uncharged additions are offered for the purchase in the unit of package. It is found that the annual inventory cost needs to be evaluated for at most three alternative order sizes to find EOQ, which is easier than the case of all-unit or incremental quantity discount. Numerical examples are presented.

• Journal of the Korean Operations Research and Management Science Society
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• v.34 no.3
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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.

• Proceedings of the Korean Operations and Management Science Society Conference
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• 2002.05a
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• pp.378-384
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• 2002

In this paper, we propose a mixed integer optimization approach for solving the inventory problem with variable lead time, reorder point, crashing cost and price -quantity discount. Chang and Chang[15] study a continuous review inventory model in which lead time is a decision variable under price-quantity discount. However, their study cannot find the optimal solution due to the flaws in the modeling and the solution procedure. We present a complete procedure to find the optimal solution for the model. In addition to the above contribution, we also apply the minimax distribution free approach to the model to devise a practical procedure which can be used without specific information on demand distribution.

• Industrial Engineering and Management Systems
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• v.6 no.2
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• pp.136-145
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• 2007

The selection of suppliers and the determination of order quantities to be placed with those suppliers are important decisions in a supply chain. In this research, a non-linear mixed integer programming model is presented to select suppliers and determine the order quantities. The model considers the purchasing cost which takes into account quantity discount, the cost of transportation, the fixed cost for establishing suppliers, the cost for holding inventory, and the cost of receiving poor quality parts. The capacity constraints for suppliers, quality and lead-time requirements for the parts are also taken into account in the model. Since the purchasing cost, which is a decreasing step function of order quantities, introduces discontinuities to the non-linear objective function, it is not easy to employ traditional optimization methods. Thus, a heuristic algorithm, called particle swarm optimization (PSO), is used to find the (near) optimal solution. However, PSO usually generates initial solutions randomly. To improve the PSO solution quality, a heuristic procedure is proposed to find an initial solution based on the average unit cost including transportation, purchasing, inventory, and poor quality part cost. The results show that PSO with the proposed initial solution heuristic provides better solutions than those with PSO algorithm only.

• Journal of the Korean Operations Research and Management Science Society
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• v.14 no.1
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• pp.51-58
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• 1989

A joint economic ordering problem between supplier and customer has been formulated where a supplier has to pay the freight cost which follows the principle of economy of scale. An algorithm is given to determine order size and price simultaneously which give gains to both parties. A scenario is presented within which both parties come to a mutual agreement on the revised order size and price by utilizing quantity discount schedule.

• Proceedings of the Safety Management and Science Conference
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• 2002.05a
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• pp.237-241
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• 2002

This paper deals with the problem of determining the buyer's economic lot sizing policy for exponentially deteriorating products under trade credit. It is also assumed that the ordering cost consists of a fixed set-up cost and a freight cost, where the freight cost has a quantity discount offered due to the economies of scale. We formulate the mathematical model and the solution algorithm is developed based on the properties of an optimal solution.