• Journal of the Korean Operations Research and Management Science Society
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• v.31 no.4
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• pp.125-138
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• 2006

This paper considers a periodic review, two-echelon inventory system with one central warehouse and several re-tailers facing normally distributed demand. The goal is to attain target fill rates, while the systemwide total holding costs are minimized. An important aspect of this problem is material rationing in the case of shortages. If a central warehouse has insufficient inventory to deliver all replenishment orders to retailers, all order quantities are should be adjusted according to some rationing rule. A simple but efficient rationing rule is proposed and compared with the Balanced Stock (BS) rationing as introduced by Heijden which is known to be the best rationing policy in the literature. Numerical results show that the proposed rationing rule is more cost effective than BS rationing, especially for the differences in holding costs between retailers are large.

• Industrial Engineering and Management Systems
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• v.8 no.2
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• pp.80-92
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• 2009

This paper addresses the inventory rationing issue embedded in the regional supply chain inventory replenishment problem (RSIRP). The concerned supply chain, which was fed by the national supply chain, consisted of a single warehouse distributing a single product to multiple stores (M-stores) with independent and normally distributed customer demand. It was assumed that the supply chain operated under the order-up-to level inventory replenishment system and had only one truck at the regional warehouse. The truck could make one replenishment trip to one store per period (a round trip per period). Based on current inventories and the vehicle constraint, the warehouse must make two decisions in each period: which store in the region to replenish and what was the replenishment quantity? The objective was to position inventories so as to minimize lost sales in the region. The warehouse inventory was replenished in every fixed-interval from a source outside the region, but the store inventory could be replenished daily. The truck destination (store) in each period was selected based on its maximum expected shortage. The replenishment quantity was then determined based on the predetermined order-up-to level system. In case of insufficient warehouse inventories to fulfill all projected store demands, an inventory rationing rule must be applied. In this paper, a new inventory rationing rule named Expected Cost Minimization (ECM) was proposed based on the practical purpose. The numerical results based on real data from a selective industry show that its performance was better and more robust than the current practice and other sharing rules in the existing literature.

• Journal of Korean Institute of Industrial Engineers
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• v.41 no.5
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• pp.447-452
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• 2015

This paper considers a two-stage make-to-stock production system. The first stage produces a single-component and the second stage produces a make-to-stock product using components. In addition to internal demands, the first stage faces external demands with the option of accepting or rejecting. To ration component inventory, the manufacturer adopts a static rule. This paper analyzes the production controls at both facilities that maximizes the manufacturer's profit. Using the Markov decision process model, we characterize the optimal production policy by two monotonic switching curves.

• Journal of Korea Water Resources Association
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• v.54 no.6
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• pp.443-452
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• 2021

The authors obtained the discrete hedging rule for a reservoir's water supply operation by applying mixed-integer programming to save more water by earlier rationing of water supply for a drought period. The 'water supply adjustment guide' is the current operational method applied to the multipurpose reservoirs, and it was derived by a simulation method. Applying the two rules to the Hapcheon multipurpose dam's reservoir simulations with the inflow record from 2003 to 2018, the water supply deficit occurred for the long drought from 2015 to 2018. Especially, the no water supply or intermittent water supply persisted for the second half of 2017. The water supply adjustment guide had the 'normal water supply recovery threshold on storage,' which resulted in the water supply being unavailable in July 2017; then, the water supply suspension occurred until January 2018, when the reservoir storage was greater than the normal water supply recovery threshold. Despite the storage increasing due to the inflow of water into the reservoir, the suspension occurrence needs to be improved in practice. The current water supply adjustment guide and the discrete hedging rule for a reservoir's water supply operation are useful and realistic as the reservoir operation guide, which shows the concept of reducing water supply during the drought phase as scientific figures. However, to improve the reservoir simulation results, which do not provide any or intermittent water for several months, it is necessary to increase the current water supply reduction for drought phases.

• Journal of Korea Port Economic Association
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• v.29 no.2
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• pp.1-17
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• 2013

This paper aims to review the fairness of carriers' incentive schemes at Gwangyang port in 2010 and to show the desirable incentive allocation rules using the proportional and egalitarian rules under cooperative game theory. The carriers' incentive schemes at Gwangyang port in 2010 did not meet the no-envy and the efficiency, and satisfy the symmetry axiom. According to the research findings, the equal surplus method satisfies the axioms of equity, efficiency, symmetry, and progressivity. However, the uniform losses method meets the axioms of equity, efficiency, symmetry, and regressivity. We use a single allocation criterion of the total throughput to show the regressivity and the symmetry principles into the incentive scheme instead of using multiple criteria such as total throughput, increased volume, and coastal volume. The uniform losses method based on the total throughput can distribute the incentive amount according to the intent of the incentive schemes. Hence, we need to establish a rationing system to allocate reasonably the total amount of different types of incentives, avoiding the temptation to adjust the volume shipped between the ports of carriers considering the efficiency of allocation.