Implementation of the Newsvendor Model with Clearance Pricing: How to (and How Not to) Estimate a Salvage Value

The newsvendor model is designed to decide how much of a product to order when the product is to be sold over a short selling season with stochastic demand and there are no additional opportunities to replenish inventory. There are many practical situations that reasonably conform to those assumptions, but the traditional newsvendor model also assumes a fixed salvage value: all inventory left over at the end of the season is sold off at a fixed per-unit price. The fixed salvage value assumption is questionable when a clearance price is rationally chosen in response to the events observed during the selling season: a deep discount should be taken if there is plenty of inventory remaining at the end of the season, whereas a shallow discount is appropriate for a product with higher than expected demand. This paper solves for the optimal order quantity in the newsvendor model, assuming rational clearance pricing. We then study the performance of the traditional newsvendor model. The key to effective implementation of the traditional newsvendor model is choosing an appropriate fixed salvage value. (We show that an optimal order quantity cannot be generally achieved by merely enhancing the traditional newsvendor model to include a nonlinear salvage value function.) We demonstrate that several intuitive methods for estimating the salvage value can lead to an excessively large order quantity and a substantial profit loss. Even though the traditional model can result in poor performance, the model seems as if it is working correctly: the order quantity chosen is optimal given the salvage value inputted to the model, and the observed salvage value given the chosen order quantity equals the inputted one. We discuss how to estimate a salvage value that leads the traditional newsvendor model to the optimal or near-optimal order quantity. Our results highlight the importance of understanding how a model can interact with its own inputs: when inputs to a model are influenced by the decisions of the model, care is needed to appreciate how that interaction influences the decisions recommended by the model and how the model’s inputs should be estimated

オムニチャネル小売業におけるファッション商品の品切れに対する対応のモデル化分析

筑波大学 (University of Tsukuba)201

Inventory Model with Seasonal Demand: A Specific Application to Haute Couture

In the stochastic multiperiod inventory problem, a vast majority of the literature deals with demand volume uncertainty. Other dimensions of uncertainty have generally been overlooked. In this paper, we develop a newsboy formulation for the aggregate multiperiod inventory problem intended for products of short sales season and without replenishments. A distinguishing characteristic of our formulation is that it takes a time dimension of demand uncertainty into account. The proposed model is particularly suitable for applications in haute couture, i.e., high fashion industry. The model determines the time of switching primary sales effort from one season to the next as well as optimal order quantity for each season with the objective of maximizing expected profit over the planning horizon. We also derive the optimality conditions for the time of switching primary sales effort and order quantity. Furthermore, we show that if time uncertainty and volume uncertainty are independent, order quantity becomes the main decision over the interval of the primary selling season. Finally, we demonstrate that the results from the two-season case can be directly extended to the multi-season case and the limited resource multiple-item case

Optimal pricing strategy:How to sell to strategic consumers?

Technological advances are preparing consumers to plan their purchases strategically. Selling to strategic consumers at a fixed price forgoes the profit from salvaging inventory, whereas high-low pricing, as a ubiquitous pricing strategy, is costly due to the offered markdown discount. This research explores the overall impact of consumer's strategic buying behaviour on a pricing strategy, and identifies conditions where fixed pricing, strategic high pricing, or high-low pricing is the best approach by analytically comparing the profits of the three pricing strategies. Our results show that high-low pricing is appropriate only if the offered markdown discount is relatively small. If strategic consumers have a small population and the needed markdown discount is relatively large, retailers can ignore strategic buying behaviour and sell products at a fixed price. Our results emphasize that the markdown discount for clearance sales and the market structure of heterogeneous consumers play vital roles in determining the optimal pricing strategy

Multi-product budget-constrained acquistion and pricing with uncertain demand and supplier quantity discounts

We consider the joint acquisition and pricing problem where the retailer sells multiple products with uncertain demands and the suppliers provide all unit quantity discounts.The problem is to determine the optimal acquisition quantities and selling prices so as to maximize the retailer’s expected profit, subject to a budget constraint. This is the first extension to consider supplier discounts in the constrained multi-product newsvendor pricing problem. We establish a mixed integer nonlinear programming (MINLP) model to formulate the problem, and developaLagrangian based solution approach.Computational results for the test problems involving up to thousand products are reported, which show that the Lagrangian based approach can obtain high-quality solutions in a very short time

Improving supply chain efficiency through wholesale price renegotiation

In a decentralized supply chain, double marginalization is an important source of inefficiency. We suggest in this paper a simple mechanism to reduce it that uses a wholesale price contract and renegotiation. Our mechanism only requires repeated interaction, and rational behavior from the players. Specifically, over T rounds of negotiation, the supplier proposes different prices in each round, and the buyer places orders at the quoted price. Even though prices are decreasing in time, the buyer places a positive order, to force the supplier to reduce its price in the following round. This interaction results in higher profits for both supplier and buyer. We solve the buyer and supplier problems and show that, as T increases, supply chain efficiency tends to 100%, and the sub-optimality gap decreases with 1/T. Finally, we discuss how these results can be applied to design negotiation processes.strategic customer; dynamic pricing; supply chain;

Revenue Management and Demand Fulfillment: Matching Applications, Models, and Software

Recent years have seen great successes of revenue management, notably in the airline, hotel, and car rental business. Currently, an increasing number of industries, including manufacturers and retailers, are exploring ways to adopt similar concepts. Software companies are taking an active role in promoting the broadening range of applications. Also technological advances, including smart shelves and radio frequency identification (RFID), are removing many of the barriers to extended revenue management. The rapid developments in Supply Chain Planning and Revenue Management software solutions, scientific models, and industry applications have created a complex picture, which appears not yet to be well understood. It is not evident which scientific models fit which industry applications and which aspects are still missing. The relation between available software solutions and applications as well as scientific models appears equally unclear. The goal of this paper is to help overcome this confusion. To this end, we structure and review three dimensions, namely applications, models, and software. Subsequently, we relate these dimensions to each other and highlight commonalities and discrepancies. This comparison also provides a basis for identifying future research needs.Manufacturing;Revenue Management;Software;Advanced Planning Systems;Demand Fulfillment

Inventory and pricing decisions in a single-period problem involving risky supply

Cataloged from PDF version of article.We explore an extension of the single-period (newsboy) inventory problem when supply is uncertain. We look into the negotiations between a newsvendor (retailer) and a manufacturer when there is competition from a second supplier. There is a chance that the second supplier will not be able to deliver the product. The retailer can maximize his expected profit by optimally allocating his order between the two suppliers. The retailer’s ordering problem is analyzed in conjunction with the manufacturer’s related pricing problem. The effects of demand and supply uncertainties on the optimal decisions of the parties are explored using numerical examples. We also explore extension of the retailer’s problem to the cases of order cancellation, price-dependent demand, and demand-dependent supply availability. & 2008 Elsevier B.V. All rights reserve

Supply chain contracting coordination for fresh products with fresh-keeping effort

Purpose – Fresh product loss rates in supply chain operations are particularly high due to the nature of perishable products. This paper aims to maximize profit through the contract between retailer and supplier. The optimized prices for the retailer and the supplier, taking the fresh-keeping effort into consideration, are derived. Design/methodology/approach – To address this issue, we consider a two-echelon supply chain consisting of a retailer and a supplier (i.e., wholesaler) for two scenarios: centralized and decentralized decision-making. We start from investigating the optimal decision in the centralized supply chain and then comparing the results with those of the decentralized decision. Meanwhile, a fresh-keeping cost-sharing contract and a fresh-keeping cost- and revenue-sharing contract are designed. Numerical examples are provided, and managerial insights are discussed at end. Findings – The results show that (a) the centralized decision is more profitable than the decentralized decision; (b) a fresh product supply chain can only be coordinated through a fresh-keeping cost- and revenue-sharing contract; (c) the optimal retail price, wholesale price and fresh-keeping effort can all be achieved; (d) the profit of a fresh product supply chain is positively related to consumers’ sensitivity to freshness and negatively correlated with their sensitivity to price. Originality/value – Few studies have considered fresh-keeping effort as a decision variable in the modelling of supply chain. In this paper, a mathematical model for the fresh-keeping effort and for price decisions in a supply chain is developed. In particular, fresh-keeping cost sharing contract and revenue-sharing contract are examined simultaneously in the study of the supply chain coordination problem

판매촉진을 도입한 수요 불확실성 재고관리 모형

학위논문 (박사) -- 서울대학교 대학원 : 공과대학 산업공학과, 2020. 8. 문일경.As the globalization of markets accelerates competition among companies, sales promotion, which refers to short-term incentives promoting sales of products or services, plays a prominent role. Although there are various types of sales promotions, such as price reduction, buy-x-get-y-free, and trade-in program, the common purpose is to induce the purchase of customers by offering benefits. This successful strategy has caught the attention of researchers, including operations management and supply chain management. Thus, various studies have been conducted to examine strategies for ongoing operations and to demonstrate the effects of the sales promotion, which are based on the strategic level. However, research at the tactical or operational level has been conducted insufficiently. This dissertation examines the inventory models considering (i) markdown sale, (ii) buy one get one free (BOGO), and (iii) trade-in program. First, the newsvendor model is considered. By introducing the decision variable, which represents the start time of markdown sale, the retailer can obtain the optimal combination of the start time of a markdown sale and an order quantity. Under certain conditions in a decentralized system, however, the start time of a markdown sale where the retailer obtains the highest profit is the least profitable for the manufacturer. To avoid irrational ordering behavior by a retailer against a manufacturer, a revenue-sharing contract is proposed. Second, the mobile application, ``My Own Refrigerator'', is considered in the inventory model. It enables customers to store BOGO products in their virtual storage for later use. That is, customers can drop by the store to pick up the extra freebies in the future. The promotion involves a high degree of uncertainty regarding the revisiting date because customers who buy the product do not need to take both products on the day of purchase. To deal with this uncertainty, we propose a robust multiperiod inventory model by addressing the approximation of a multistage stochastic optimization model. Third, the trade-in program is considered. It is one of the sales promotions that companies collect used old-generation products from customers and provide them with new-generation products at a discount price. It also helps to acquire the additional products which are required for the refurbishment service. A multiperiod stochastic inventory model based on the closed-loop supply chain system is proposed by incorporating the trade-in program and refurbishment service simultaneously. The stochastic optimization model is approximated to the robust counterpart, which features a deterministic second-order cone program.시장의 세계화에 따른 기업 간의 경쟁이 가속화됨에 따라, 단기 인센티브를 통해 고객의 제품 또는 서비스 구매를 유도하는 판매촉진의 역할이 중요해졌다. 가격 인하, 행사상품 증정, 트레이드인프로그램과 같은 다양한 유형의 판매촉진 전략이 존재하지만, 공통된 주요 목적은 기업이 고객에게 혜택을 제공하여 고객의 수요를 증대시키는 것이다. 판매촉진의 성공적인 전략은 경영과학 또는 공급망관리 분야를 포함한 관련 학계의 관심을 이끌었다. 지속적인 운영을 위한 전략을 검토하고 전략적 수준 계획을 기반으로 하는 판매 촉진의 효과를 입증하기 위한 다양한 연구가 수행되었습니다. 하지만 운영 수준의 소매업체 입장에서의 연구는 미흡한 실정이다. 본 논문에서는 (i) 마크 다운 (ii) buy one get one free (BOGO), 및 (iii) 트레이드인프로그램을 고려한 재고관리모형을 다룬다. 먼저, 신문가판원 모형에 마크 다운 시작 시점을 나타내는 결정 변수를 도입하여 최적의 마크 다운 시작 시점과 주문량의 조합을 제공하는 모형을 제안한다. 분산 시스템의 특정 조건에서는 소매업자가 가장 높은 이익을 얻는 시점이 제조업자에게 낮은 수익성을 야기할 수 있다. 따라서 본 연구는 제조업자에 대한 소매업자의 비합리적 주문을 막기 위한 이익분배계약을 제안한다. 이익분배계약을 통한 중앙집권화 시스템은 분산 시스템에서 얻은 이익에 비해 소매업자와 제조업자의 이익을 향상시킴을 수치실험을 통해 확인하였다. 둘째, 모바일 어플리케이션 ``나만의 냉장고''를 고려한 재고모형을 고려한다. 이 앱을 통해 BOGO 행사제품을 구매한 고객은 증정품을 구매 당일 날 가져가지 않고 미래에 재방문하여 수령할 수 있는 혜택을 받는다. 하지만 소매업자 입장에서는 고객이 증정품을 언제 수령해 갈 지에 대한 불확실성이 존재하며 이는 기존의 재고관리 운영방식에는 한계점이 있음을 시사한다. 본 연구에서는 고객의 재방문에 대한 불확실성을 고려한 복수기간 추계계획 재고모형을 수립하며 이를 효율적으로 계산하기 위한 강건최적화 모형으로 근사화하였다. 셋째, 리퍼서비스와 트레이드인프로그램을 고려한 폐회로 공급망 시스템 기반의 복수기간 재고관리모형을 제안한다. 신세대 제품, 리퍼서비스 및 트레이드인프로그램에 대한 세 가지 유형의 불확실한 수요에 대한 상관관계를 반영함에 따라 복수기간 추계계획 재고모형이 수립된다. 복수기간 추계계획 재고모형의 계산이 어렵다는 한계를 극복하고자 강건최적화 모형으로 근사화하였다.Chapter 1 Introduction 1 1.1 Sales promotion 1 1.2 Inventory management 3 1.3 Research motivations 6 1.4 Research contents and contributions 8 1.5 Outline of the dissertation 10 Chapter 2 Optimal Start Time of a Markdown Sale Under a Two-Echelon Inventory System 11 2.1 Introduction and literature review 11 2.2 Problem description 17 2.3 Analysis of the decentralized system 21 2.3.1 Newsvendor model for a retailer 21 2.3.2 Solution procedure for an optimal combination of the start time of the markdown sale and the order quantity 25 2.3.3 Profi t function of a manufacturer 25 2.3.4 Numerical experiments of the decentralized system 27 2.4 Analysis of a centralized system 35 2.4.1 Revenue-sharing contract 35 2.4.2 Numerical experiments of the centralized system 38 2.5 Summary 40 2.5.1 Managerial insights 41 Chapter 3 Robust Multiperiod Inventory Model with a New Type of Buy One Get One Promotion: "My Own Refrigerator" 43 3.1 Introduction and literature review 43 3.2 Problem description 51 3.2.1 Demand modeling 52 3.2.2 Sequences of the ordering decision 54 3.3 Mathematical formulation of the IMMOR 56 3.3.1 Mathematical formulation of the IMMOR under the deterministic demand 58 3.3.2 Mathematical formulation of the IMMOR under the stochastic demand 58 3.3.3 Distributionally robust optimization approach for the IMMOR 60 3.4 Computational experiments 76 3.4.1 Experiment 1: tractability of the RIMMOR 77 3.4.2 Experiment 2: robustness of the RIMMOR 78 3.4.3 Experiment 3: e ect of duration of the expiry date under the different customers' revisiting propensities 78 3.5 Summary 83 3.5.1 Managerial insights 83 Chapter 4 Robust Multiperiod Inventory Model Considering Refurbishment Service and Trade-in Program 85 4.1 Introduction 85 4.2 Literature review 91 4.2.1 Effects of the trade-in program and strategic-level decisions for the trade-in program 91 4.2.2 Inventory or lot-sizing model in a closed-loop supply chain system 94 4.2.3 Distinctive features of this research 97 4.3 Problem description 100 4.3.1 Demand modeling 103 4.3.2 Decision of the inventory manager 105 4.4 Mathematical formulation 108 4.4.1 Mathematical formulation of the IMRSTIP under the deterministic demand model 108 4.4.2 Mathematical formulation of the IMRSTIP under the stochastic demand model 110 4.4.3 Distributionally robust optimization approach for the IMRSTIP 111 4.5 Computational experiments 125 4.5.1 Demand process 125 4.5.2 Experiment 1: tractability of the RIMRSTIP 128 4.5.3 Experiment 2: approximation error from the expected value given perfect information 129 4.5.4 Experiment 3: protection against realized uncertain factors 130 4.5.5 Experiment 4: di erences between modeling demands from VARMA and ARMA 131 4.5.6 Experiments 5 and 6: comparisons of backlogged refurbishment service with or without trade-in program 133 4.6 Summary 136 Chapter 5 Conclusions 138 5.1 Summary 138 5.2 Future research 140 Bibliography 142 Chapter A 160 A.1 160 A.2 163 A.3 163 A.4 164 A.5 165 A.6 166 Chapter B 168 B.1 168 B.2 171 B.3 172 Chapter C 174 C.1 174 C.2 174 국문초록 179Docto