• Proceedings of the Korean Operations and Management Science Society Conference
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• 2001.10a
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• pp.395-398
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• 2001

Studies on quantity discounts have been in two directions since Buchanen[1] published that suppliers provide quantity discounts for price discrimination and for channel efficiency. The quantity discounts for price discrimination have been treated in economics. On the contrary, the quantity discounts for channel efficiency have been studied in production management with assumptions and focuses different from economics. In this paper, the differences in each area are analyzed and purchasing situations that supplier's motivation on quantity discounts occurs is analyzed and the purchasing situations for two-stage quantity discounts are specified. In conclusion, we suggest that suppliers can enhance channel coordination through two stage quantity discounts in these purchasing situations.

• Journal of the Korean Operations Research and Management Science Society
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• v.37 no.1
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• pp.1-18
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• 2012

The present study provides some extensions over a recent work in Won (2011) which investigates properties of the static newsvendor problem under a schedule involving progressive multiple discounts under the assumption that demand is given exogenously. Khouja (1995, 1996) formulated the extended versions over the classical newsvendor model with various discount policies including all-units discount and/or multiple discounts and found that the extended newsvendor models with discount schedules yield higher optimal expected profits than the classical newsvendor model with no-discounts. In this study, we establish a robust conjecture as a stronger statement than Khouja's findings with regard to the general relationship among the expected profits of newsvendor models in the sense that the conjecture holds for every order quantity as well as the optimal order quantity. The conjecture encourages the newsvendor facing quantity discounts to safely implement her own discounts policy to customer or accept quantity discounts offered by the supplier even if the optimal order quantity cannot be ordered due to additional restrictions such as budget or warehouse capacity constraints because the newsvendor models with quantity discounts always yield higher expected profit than the classic newsvendor model without quantity discounts regardless of the order quantity. Results from wide experiments with various probability distributions of demand strongly support our conjecture.

• Management Science and Financial Engineering
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• v.16 no.3
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• pp.21-47
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• 2010

Quantity discounts provide a practical foundation for supply chain inventory policies, improving the supplier's profit and reducing the buyer's inventory cost simultaneously. Traditional quantity-discount research, which deals with inventory coordination between a buyer and a supplier, is extended to a stationary stochastic environment. This research shows that the magnitude of the optimal discounts scheduled by the deterministic quantity discount models may not be large enough to cover the buyer's additional inventory stocking risks under uncertain conditions. As a result, the buyer's total inventory cost may often increase rather than decrease. In contrast, the proposed model allows the supplier to identify the discount level, which shares the buyer's amplified risk associated with temporary overstocking and ensures that both buyer and supplier benefit economically. The performance of the proposed model was tested in the continuous review environments via numerical experiments. The experimental results support the proposed method as a feasible alternative in coordinating inventory decisions under stochastic demand.

• Journal of the Korean Operations Research and Management Science Society
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• v.36 no.3
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• pp.27-43
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• 2011

This paper investigates properties of the newsvendor problem under a schedule involving progressive multiple discounts compared with the standard newsvendor problem under a no-discounts schedule. Unlike most conventional approaches using the criticial fractile to analyze the retailer and/or supplier behavior(s) in the newsvendor problem, our approach uses riskless profit. From the properties revealed through a series of computational experiments, two conjectures regarding the relationship between the expected profits of both newsvendor problems as a generalization over Khouja's argument (1995) are raised. Those conjectures encourage newsvendors who may face budget or warehouse capacity restriction to use the extended model under a multiple-discounts schedule rather than the standard model with no-discounts schedule because they apply for every order quantity as well as the optimal order quantity. In addition to the conjectures, some insightful results are found to justify the implementation of a multiple-discounts schedule from the computational experiments and a new interpretation for implementation of a multiple-discounts schedule that has not been addressed in Khouja is provided.

• Journal of the Korean Operations Research and Management Science Society
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• v.37 no.3
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• pp.13-21
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• 2012

In this note, a recent work in Won (2011) which investigates properties of the newsvendor model under progressive multiple discounts is revisited and a complete proof is provided for the conjecture on the consistent advantage of progressive multiple discounts over no-discounts in terms of the expected profit. The proof considers the generalized newsvendor model under progressive multiple discounts extended with positive shortage cost and salvage value which have not been considered in the previous newsvendor models under progressive multiple discounts. Without relying on derivatives, we prove that the expected profit under progressive multiple discounts are consistently greater than or equal to the one under no-discounts for every order quantity as far as her multiple discounts do not decrease customer demand, and therefore, the optimal expected profit under progressive multiple discounts is always greater than or equal to the one under no-discounts. As by-products from the proof, some interesting features of the generalized newsvendor model under progressive multiple discounts are revealed.

• 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 Korean Institute of Industrial Engineers
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• v.16 no.1
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• pp.27-36
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• 1990

This study deals with the dynamic transportation-inventory model for a single product from which the optimal procurement quantities and the transportation modes are determined simultaneously over a finite planning horizon. Moreover, it covers the situation where quantity discounts are applied to the transportation cost as well as the purchase cost and disposals of the excess are possible at the end of each period. For a relevant mathematical model formulated, the theorems and properties of an optimal solution are discussed to present the efficient algorithm. A numerical example is solved to illustrate the algorithm developed.

• Management & Information Systems Review
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• v.31 no.1
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• pp.247-272
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• 2012

This study scarcity of recent online message promotion limited quantity of messages and time the message is limited controlled variable message whose regulatory focus and promotional discounts depending on the presence of any differences in attitudes and purchase intention appears, was to verify empirically. The results of this study, first, if limited quantity of messages focus on prevention rather than focusing on messages promoting promotion attitudes and purchase intention was higher. Second, the scarcity message is simply, as well as adjust the focus, such as price discounts and promotional activities can be controlled by a variety of points were identified. If the message is particularly limited quantity discounts are not present, rather than the message, the message is presented when the discount promotional attitudes and purchase intention, except that the amplification has been demonstrated. If the message is limited time, however, these discounts are worth the extra promotion on attitudes and purchase intentions are least likely to affect the thing that was found.

• Journal of the Korean Operations Research and Management Science Society
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• v.40 no.1
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• pp.35-55
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• 2015

In this research, we analyze the effects of price discounts and scarcity message (both quantity limitation message and time limitation message) on the purchase intention in the smart-phone environment. The purchase intention becomes higher at high discount rate and with scarcity message (both quantity limitation message and time limitation message). We also analyze the moderating effects of consumer's shopping value and distance between the consumer and the store on the effects of price discounts and scarcity message (both quantity limitation message and time limitation message) on the purchase intention. On average, the effects of price discount, time limitation message and quantity limitation message on the purchase intention become the highest levels for consumers pursuing hedonic shopping value. The effects of price discount, time limitation message and quantity limitation message on the purchase intention become higher when they are offered within a short distance between the coupon provider and the target customer.

• Journal of Korean Institute of Industrial Engineers
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• v.12 no.2
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• pp.77-87
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• 1986

This paper presents a heuristic method for solving the discrete-time ordering problem with quantity discounts and deterministic, time-varying demand. This algorithm utilizes a variation of the incremental cost approach(ICA) to determine a near optimal solution. The ICA is the method which reduces the total cost with reduction of the number of orders by one. In order to reduce the number of orders, if the incremental cost for one of the periods is negative, the demand of the period should be purchased in its immediate preceding period. In order to test the performance of this algorithm, an experiment is conducted that involves a large number of test problems covering a wide variety of situations. The result of the experiment shows that the proposed algorithm has 80.5% better solutions than the adjusted part period algorithm(APPA), which is known to be the best heuristic method.