Robust Production Plan with Periodic Order Quantity under Uncertain Cumulative Demands

International audienceIn this paper, we are interested in a production planning process in collaborative supply chains. More precisely, we consider supply chains, where actors use Manufacturing Resource Planning process (MRPII). Moreover, these actors collaborate by sharing procurement plans.We focus on a supplier, who applies the Periodic Order Quantity (POQ) rule to plan a production integrating the uncertain procurement plan sent by her/his customer. The uncertainty of the procurement plan is expressed by closed intervals on the cumulative demands. In order to choose a robust production plan, under the interval uncertainty representation, the min-max criterion is applied. We propose algorithms for determining the set of possible costs of a given production plan - due to the uncertainty on the cumulative demands.We then construct algorithms for computing a robust production plan with respect to the min-max criterion: the algorithm based on iterative adding constraints and the polynomial algorithms under certain realistic assumptions

Optimal robust inventory management with volume flexibility: matching capacity and demand with the lookahead peak-shaving policy

We study inventory control with volume flexibility: A firm can replenish using period-dependent base capacity at regular sourcing costs and access additional supply at a premium. The optimal replenishment policy is characterized by two period-dependent base-stock levels but determining their values is not trivial, especially for nonstationary and correlated demand. We propose the Lookahead Peak-Shaving policy that anticipates and peak shaves orders from future peak-demand periods to the current period, thereby matching capacity and demand. Peak shaving anticipates future order peaks and partially shifts them forward. This contrasts with conventional smoothing, which recovers the inventory deficit resulting from demand peaks by increasing later orders. Our contribution is threefold. First, we use a novel iterative approach to prove the robust optimality of the Lookahead Peak-Shaving policy. Second, we provide explicit expressions of the period-dependent base-stock levels and analyze the amount of peak shaving. Finally, we demonstrate how our policy outperforms other heuristics in stochastic systems. Most cost savings occur when demand is nonstationary and negatively correlated, and base capacities fluctuate around the mean demand. Our insights apply to several practical settings, including production systems with overtime, sourcing from multiple capacitated suppliers, or transportation planning with a spot market. Applying our model to data from a manufacturer reduces inventory and sourcing costs by 6.7%, compared to the manufacturer's policy without peak shaving.info:eu-repo/semantics/publishedVersio

Optimal Learning Algorithms for Stochastic Inventory Systems with Random Capacities

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/156225/2/poms13178_am.pdfhttp://deepblue.lib.umich.edu/bitstream/2027.42/156225/1/poms13178.pd

Optimal inventory policies with non-stationary supply disruptions and advance supply information

We consider the production/inventory problem of a manufacturer (or a retailer) under non-stationary and stochastic supply availability. Although supply availability is uncertain, the supplier would be able to predict her near future shortages -and hence supply disruption to (some of) her customers- based on factors such as her pipeline stock information, production schedule, seasonality, contractual obligations, and non-contractual preferences regarding other manufacturers. We consider the case where the information on the availability of supply for the near future, which we refer to as advance supply information (ASI), is provided by the supplier. The customer demand is deterministic but non-stationary over time, and the system costs consist of fixed ordering, holding and backorder costs. We consider an all-or-nothing type of supply availability structure and we show the optimality of a state-dependent (s; S) policy. For the case with no fixed ordering cost we prove various properties of the optimal order-up-to levels and provide a simple characterization of optimal order-up-to levels. For the model with fixed ordering cost, we propose a heuristic algorithm for finding a good ordering strategy. Finally, we numerically elaborate on the value of ASI and provide managerial insights

Optimizing lot sizing model for perishable bread products using genetic algorithm

This research addresses order planning challenges related to perishable products, using bread products as a case study. The problem is how to effi­ci­ently manage the various bread products ordered by diverse customers, which requires distributors to determine the optimal number of products to order from suppliers. This study aims to formulate the problem as a lot-sizing model, considering various factors, including customer demand, in­ven­tory constraints, ordering capacity, return rate, and defect rate, to achieve a near or optimal solution, Therefore determining the optimal order quantity to reduce the total ordering cost becomes a challenge in this study. However, most lot sizing problems are combinatorial and difficult to solve. Thus, this study uses the Genetic Algorithm (GA) as the main method to solve the lot sizing model and determine the optimal number of bread products to order. With GA, experiments have been conducted by combining the values of population, crossover, mutation, and generation parameters to maximize the feasibility value that represents the minimal total cost. The results obtained from the application of GA demonstrate its effectiveness in generating near or optimal solutions while also showing fast computational performance. By utilizing GA, distributors can effectively minimize wastage arising from expired or perishable products while simultaneously meeting customer demand more efficiently. As such, this research makes a significant contri­bution to the development of more effective and intelligent decision-making strategies in the domain of perishable products in bread distribution.Penelitian ini berfokus untuk mengatasi tantangan perencanaan pemesanan yang berkaitan dengan produk yang mudah rusak, dengan menggunakan produk roti sebagai studi kasus. Permasalahan yang dihadapi adalah bagaimana mengelola berbagai produk roti yang dipesan oleh pelanggan yang beragam secara efisien, yang mengharuskan distributor untuk menentukan jumlah produk yang optimal untuk dipesan dari pemasok. Untuk mencapai solusi yang optimal, penelitian ini bertujuan untuk memformulasikan masalah tersebut sebagai model lot-sizing, dengan mempertimbangkan berbagai faktor, termasuk permintaan pelanggan, kendala persediaan, kapasitas pemesanan, tingkat pengembalian, dan tingkat cacat. Oleh karena itu, menentukan jumlah pemesanan yang optimal untuk mengurangi total biaya pemesanan menjadi tantangan dalam penelitian ini. Namun, sebagian besar masalah lot sizing bersifat kombinatorial dan sulit untuk dipecahkan, oleh karena itu, penelitian ini menggunakan Genetic Algorithm (GA) sebagai metode utama untuk menyelesaikan model lot sizing dan menentukan jumlah produk roti yang optimal untuk dipesan. Dengan GA, telah dilakukan percobaan dengan mengkombinasikan nilai parameter populasi, crossover, mutasi, dan generasi untuk memaksimalkan nilai kelayakan yang merepresentasikan total biaya yang minimal. Hasil yang diperoleh dari penerapan GA menunjukkan keefektifannya dalam menghasilkan solusi yang optimal, selain itu juga menunjukkan kinerja komputasi yang cepat. Dengan menggunakan GA, distributor dapat secara efektif meminimalkan pemborosan yang timbul akibat produk yang kadaluarsa atau mudah rusak, sekaligus memenuhi permintaan pelanggan dengan lebih efisien. Dengan demikian, penelitian ini memberikan kontribusi yang signifikan terhadap pengembangan strategi pengambilan keputusan yang lebih efektif dan cerdas dalam domain produk yang mudah rusak dalam distribusi roti

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