• Journal of Korean Society of Industrial and Systems Engineering
• /
• v.36 no.3
• /
• pp.43-50
• /
• 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 Society of Industrial and Systems Engineering
• /
• v.37 no.1
• /
• pp.50-59
• /
• 2014

In this paper, we develop an efficient approach to solve a multiple-item budget-constraint newsboy problem with a reservation policy. A conventional approach for solving such problem utilizes an approximation for the evaluation of an inverse of a Gaussian cumulative density function when the argument of the function is small, and a heuristic method for finding an optimal Lagrangian multiplier. In contrast to the conventional approach, this paper proposes more accurate method of evaluating the function by using the normalization and an effective numerical integration method. We also propose an efficient way to find an optimal Lagrangian multiplier by proving that the equation for the budget-constraint is in fact a monotonically increasing function in the Lagrangian multiplier. Numerical examples are tested to show the performance of the proposed approach with emphases on the behaviors of the inverse of a Gaussian cumulative density function and the Lagrangian multiplier. By using sensitivity analysis of different budget constraints, we show that the reservation policy indeed provides greater expected profit than the classical model of not having the reservation policy.

• Proceedings of the Korean Operations and Management Science Society Conference
• /
• 1993.04a
• /
• pp.225-225
• /
• 1993

• Journal of the Korean Operations Research and Management Science Society
• /
• v.26 no.3
• /
• pp.105-117
• /
• 2001

This paper models supply uncertainty in the dynamic Newsboy problem context. The system consists of one supplier and one retailer who places an order to the supplier every period to meet stochastic demand. Supply uncertainty is modeled as the uncertainty in quantities delivered by the supplier. That is, the supplier delivers exactly the amount ordered by the retailer with probability of $\beta$ and the amount minus K with probability of (1-$\beta$). We formulate the problem as a dynamic programming problem and prove that retailer’s optimal replenishment policy is a stationary base-stock policy. Through a numerical study, we found that the cost increase due to supply uncertainty is significant and that the costs increase more rapidly as supply uncertainty increases. We also identified the effects of various system parameters. One of the interesting results is that as retailer’s demand uncertainty, the other uncertainty in our model, increases, the cost increase due to supply uncertainty becomes less significant.

• Journal of the Korean Operations Research and Management Science Society
• /
• v.30 no.3
• /
• pp.81-93
• /
• 2005

This paper models supply chain uncertainties in the dynamic Newsboy Problem context. The system consists of one supplier and one retailer who place an order to the supplier every period. Demand uncertainty is modeled as stochastic period demand, and supply uncertainty as the uncertainty in quantities delivered by the supplier. The supplier delivers exactly the amount ordered by the retailer with probability of $\beta$ and the amount minus K with probability of $(1-\beta)$ We formulate the problem as a dynamic programming problem and derive the first-order optimality condition. Through a numerical study, we measure the extent to which the cost decrease due to the reduction in supply uncertainty depends on the level of demand uncertainty. One of the most important findings In this paper is that this cost decrease is relatively small if demand uncertainty is kept high, and vice versa. We also backup this numerical result by analyzing the distribution of ending Inventory under the supply and demand uncertainties.

• Management Science and Financial Engineering
• /
• v.7 no.1
• /
• pp.1-26
• /
• 2001

Assume a company sells two products (a and B) in a retail market. the company adopts a specific promotion mechanism, Tie-in Promotion, in which product A's promotional discount coupon is distributed whenever a consumer purchases product B. Product A will later e sold at a markdown price when consumers eventually take the opportunity to redeem the coupon. in the integrated tie-in promotion and stocking policy, we assume managers of two products coordinate by sharing information on the demand forecast and deciding the order quantities and tie-in promotion program to maximize joint profits. The optimal integrated tie-in policy is analyzed. The integrated tie-in promotion model is then compared with two other base models: (1) a decentralized Newsboy model in which no promotion is considered, and (2) an individual promotion model in which managers design a promotion program to promote one of the two products directly. The factors that make an integrated tie-in promotion a better approach are studied.

• Management Science and Financial Engineering
• /
• v.6 no.2
• /
• pp.1-28
• /
• 2000

Supply chain management issues faced by a manufacturing company are considered in this paper. The supply chain consists of a manufacturing company and its suppliers. The manufacturer produces multiple products with inputs (e.g., raw materials) from the suppliers, but each product needs a different mix of these inputs. The market demand for the products is uncertain. We develop a mathematical model and algorithm, which can help the manufacturer to solve its procurement decision problem: how much of raw material to order from which supplier. The model incorporates such factors as market demand uncertainty, product's input requirement, supplier's as well as manufacturer's capacity, plus other costs comparable with those in a typical newsboy problem. Numerical examples are presented to see the interacting effects among critical parameters and variables.

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

• Journal of Korean Society for Quality Management
• /
• v.40 no.4
• /
• pp.441-452
• /
• 2012

Purpose: In this paper, we have considered a problem of newsvendor model in an environment of random yields in quality and customer balking behavior, in which only the mean and the variance of the demand are known. In practice, the distributional information of the demand is very limited and only the mean and variance are guessed by experience. In addition, due to the customers balking behavior occurring when the available inventory level decreases, the product's demand becomes a function of inventory level so that the classical newsvendor's optimal order quantity is no longer optimal. Methods: We have developed an optimal order quantity model that enables us to incorporate the random yield of a product and the customer balking information such as a threshold inventory level of balking and the corresponding probability of a sale during the balking. Results: We illustrated the concepts developed here through simple numerical examples and showed the robustness of our model in a various setting of parameters. Conclusion: This paper provides a useful analysis showing that our distribution-specific and distribution-free approach to the optimal order quantity in the newsboy model can act as an effective tools to match supply with demand for these product lines.

• Management Science and Financial Engineering
• /
• v.11 no.2
• /
• pp.1-17
• /
• 2005

In this article we consider a supply chain consisting of a risk-sensitive manufacturer and a riskneutral retailer. The manufacturer maximizes her individual expected profit by designing a supply chain coordinating returns contract (SCRC) that consists of (i) a channel coordinating returns policy that maximizes the supply chain joint expected profit, and (ii) a profit sharing arrangement that gives the retailer an expected profit only slightly higher than that in the no returns case so that it is just enough to induce the retailer to accept the SCRC. Thus, the manufacturer captures as high a percentage as possible of the jointly maximum supply chain profit. However, this contract can sometimes lead to the manufacturer's resulting realized profit being lower than that in the no returns case when demand is lower than expected. In this context, even though profit is sufficiently attractive on average, will the risk-sensitive manufacturer ever consider applying a SCRC? Our research raises this question and focuses on designing a SCRC that can significantly increase the probability of the manufacturer's resulting realized profit being at least higher than that in the no returns case.