• Journal of the military operations research society of Korea
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• v.5 no.2
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• pp.15-25
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• 1979

Single-period inventory problems such as the newspaper boy problem having quadratic cost functions for both shortages and overage are examined to determine the optimal order level under various principles of choice such as minimum expected cost, aspiration level, and minimax regret. Procedures for finding the optimum order levels are developed for both continuous and discrete demand patterns.

• Management Science and Financial Engineering
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• v.21 no.1
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• pp.11-17
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• 2015

Min-max stochastic optimization is an approach to address the distribution ambiguity of the underlying random variable. We present a unified approach to the problem which utilizes the theory of convex order on the random variables. First, we consider a general framework for the problem and give a condition under which the convex order can be utilized to transform the min-max optimization problem into a simple minimization problem. Then extremal distributions are presented for some interesting classes of distributions. Finally, applications to the single-period inventory control problems are given.

• IE interfaces
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• v.16 no.3
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• pp.280-290
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• 2003

Many firms are trying to optimize their production and distribution functions separately, but possible savings by this approach may be limited. Nowadays, it is more important to analyze these two functions simultaneously by trading off the costs associated with the whole. In this paper, I treat a production and distribution planning problem for single-period inventory products comprised of a single production facility and multiple customers, with the aim of optimally coordinating important and interrelated decisions of production sequencing and vehicle routing. Then, I propose a hybrid genetic algorithm incorporating several local optimization techniques, HGAP, for integrated production-distribution planning. Computational results on test problems show that HGAP is effective and generates substantial cost savings over Hurter and Buer's decoupled planning approach in which vehicle routing is first developed and a production sequence is consequently derived. Especially, HGAP performs better on the problems where customers are dispersed with multi-item demand than on the problems where customers are divided into several zones based on single-item demand.

• Proceedings of the Korean Operations and Management Science Society Conference
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• 2005.05a
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• pp.904-913
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• 2005

This paper deals with an integrated problem of inventory control and dynamic pricing strategies for a commodity with price and sales-period dependent demand pattern, where a seller and customers have complete information of each other. The problem consists of two parts; one is each buyer's benefit problem which makes the best decision on price and time for buyer to purchase items, and the other one is a seller's profit problem which decides an optimal sales strategy concerned with inventory control and discount schedule. The seller's profit function consists of sales revenue and inventory holding cost functions. The two parts are closely related into each other with some related variables, so that any existing general solution methods can not be applied. Therefore, a simplified model with single seller and two customers in considered first, where demand for multiple units is allowed to each customer within a time limit. Therewith, the model is generalized for a n-customer-classes problem. To solve the proposed n-customer-set problem, a dynamic programming algorithm is derived. In the proposed dynamic programming algorithm, an intermediate profit function is used, which is computed in case of a fixed initial inventory level and then adjusted in searching for an optimal inventory level. This leads to an optimal sales strategy for a seller, which can derive an optimal decision on both an initial inventory level and a discount schedule, in $O(n^2)$ time. This result can be used for some extended problems with a small customer set and a short selling period, including sales strategy for department stores, Dutch auction for items with heavy holding cost, open tender of materials, quantity-limited sales, and cooperative buying in the on/off markets.

• Journal of Korean Society of Industrial and Systems Engineering
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• v.36 no.3
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• pp.43-50
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• 2013

In this paper, the single-period inventory problem, what is called newsboy problem, has been revisited with two different conditions, uncertain supply and risk-averseness. Eeckhoudt et al. [5] investigated the effect of risk-averseness of a newsboy on the optimal order quantity in a stochastic demand setting. In contrary to Eeckhoudt et al. [5] this paper investigates the effect of risk-averseness in a stochastic supply setting. The findings from this investigation say that if ${\alpha}^*$ represents the optimal order quantity without risk-averseness then the risk-averse optimal order quantity can be greater than ${\alpha}^*$ and can be less than ${\alpha}^*$ as well.

• Journal of Korean Institute of Industrial Engineers
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• v.40 no.3
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• pp.313-320
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• 2014

We consider the problem to find economic inventory quantity of a single commodity under stochastic demands and order cancellation. In contrast to the traditional economic production quantity (EPQ) model, we assume that once the amount of inventory reaches to a predetermined level of quantity then the production is not halted but its production speed decreases until the inventory level drops to zero. We establish two probabilistic models representing the behaviors of both the high-production period and low-production period, respectively, and derive the relationship between the level of inventory and costs of production, cancellation, and holding, from which the quantity of economic inventory is obtained.

• 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.13 no.1
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• pp.1-10
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• 1987

This paper deals with a single-facility multiproduct lot-size model requiring consideration of setup costs. Each product is demanded at the constant rate per unit time in the next particular period. Due to the limitation of the production capacity, some productions of total demand requirement in that period must be pre-produced. The aim of this project is to determine when and how much of each product to make in order to minimize the total setup costs and inventory carrying-costs of all products. Also this paper contains the further realistic treatment of inventory carrying-costs.

• Journal of the Korean Operations Research and Management Science Society
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• v.14 no.2
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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.

• Journal of Korean Society of Industrial and Systems Engineering
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• v.36 no.1
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• pp.36-43
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• 2013

Many retailer store managers are experiencing the situation where some customers balk at purchasing products if the stock is low. In this paper, we extend the single period newsvendor model in an environment of customer balking behavior occurring at double threshold inventory levels assuming the chance of sales during balking is a discrete function of inventory level. Our analysis is based on the assumption that only the mean and the variance of demand are known, without assuming any specific distributional form. We derive the explicit general expression of optimal order quantity with unknown distribution of demand with double threshold inventory levels of customer balking. Then, we illustrate the concepts developed here through simple numerical examples and conclude the future research topics under balking situation.