A two-stage stochastic programming approach to employee scheduling in retail outlets with uncertain demand

This paper describes an employee scheduling system for retail outlets; it is a constraint-based system that exploits forecasts and stochastic techniques to generate schedules meeting the demand for sales personnel. Uncertain scenarios due to fluctuating demand are taken into account to develop a stochastic operational optimization of staffing levels. Mathematically, the problem is stated as a mixed-integer linear programming problem. Simulations with store data belonging to a major Swiss retailer show the effective performance of the proposed approach. The schedule quality is assessed through comparison with a deterministic scheduling package, which has been used at several outlets in Switzerland.     

Managing High‐Tech Capacity Expansion via Reservation Contracts

We study capacity reservation contracts between a high‐tech manufacturer (supplier) and her OEM customer (buyer). The supplier and the buyer are partners who enter a ‘design‐win” agreement to develop the product, and who share the stochastic demand information. To encourage the supplier for more aggressive capacity expansion, the buyer reserves capacity upfront by paying a deductible fee. As capacity expansion demonstrates diseconomy of scale in this context, we assume convex capacity costs. We show that as the buyer's revenue margin decreases, the supplier faces a sequence of four profit scenarios with decreasing desirability. We examine the effects of market size and demand variability to the contract conditions. We propose two channel coordination contracts, and discuss how such contracts can be tailored for situations where the supplier has the option of not complying with the contract, and when the buyer's demand information is only partially updated during the supplier's capacity lead‐time.     

Stabilized‐Cycle Strategy for Capacitated Lot Sizing with Multiple Products: Fill‐Rate Constraints in Rolling Schedules

In practice, deterministic, multi‐period lot‐sizing models are implemented in rolling schedules since this allows the revision of decisions beyond the frozen horizon. Thus, rolling schedules are able to take realizations and updated forecasts of uncertain data (e.g., customer demands) into account. Furthermore, it is common to hold safety stocks to ensure given service levels (e.g., fill rate). As we will show, this approach, implemented in rolling schedules, often results in increased setup and holding costs while (over‐)accomplishing given fill rates. A well‐known alternative to deterministic planning models are stochastic, static, multi‐period planning models used in the static uncertainty strategy, which results in stable plans. However, these models have a lack of flexibility to react to the realization of uncertain data. As a result, actual costs may differ widely from planned costs, and downside deviations of actual fill rates from those given are very high. We propose a new strategy, namely the stabilized cycle. This combines and expands upon ideas from the literature for minimizing setup and holding costs in rolling schedules, while controlling actual product‐specific fill rates for a finite reporting period. A computational study with a multi‐item capacitated medium‐term production planning model has been executed in rolling schedules. On the one hand, it demonstrates that the stabilized‐cycle strategy yields a good compromise between costs and downside deviations. Furthermore, the stabilized‐cycle strategy weakly dominates the order‐based strategy for both constant and seasonal demands.     

Stochastic Judgments in the AHP: The Measurement of Rank Reversal Probabilities

This paper presents a methodology for analyzing Analytic Hierarchy Process (AHP) rankings if the pairwise preference judgments are uncertain (stochastic). If the relative preference statements are represented by judgment intervals, rather than single values, then the rankings resulting from a traditional (deterministic) AHP analysis based on single judgment values may be reversed, and therefore incorrect. In the presence of stochastic judgments, the traditional AHP rankings may be stable or unstable, depending on the nature of the uncertainty. We develop multivariate statistical techniques to obtain both point estimates and confidence intervals of the rank reversal probabilities, and show how simulation experiments can be used as an effective and accurate tool for analyzing the stability of the preference rankings under uncertainty. If the rank reversal probability is low, then the rankings are stable and the decision maker can be confident that the AHP ranking is correct. However, if the likelihood of rank reversal is high, then the decision maker should interpret the AHP rankings cautiously, as there is a subtantial probability that these rankings are incorrect. High rank reversal probabilities indicate a need for exploring alternative problem formulations and methods of analysis. The information about the extent to which the ranking of the alternatives is sensitive to the stochastic nature of the pairwise judgments should be valuable information into the decision-making process, much like variability and confidence intervals are crucial tools for statistical inference. We provide simulation experiments and numerical examples to evaluate our method. Our analysis of rank reversal due to stochastic judgments is not related to previous research on rank reversal that focuses on mathematical properties inherent to the AHP methodology, for instance, the occurrence of rank reversal if a new alternative is added or an existing one is deleted.     

基于二阶段随机规划的城市医疗废弃物回收网络设计

城市医疗废弃物日益增加,且回收需求量受诸多因素的影响,难以准确预测,假定回收需求为确定值的医疗废弃物网络优化设计不能与实际需求相匹配。本文考虑了离散随机参数环境下,医疗回收网络设计中选址规划、分配计划及运输规划的协同优化问题,建立了以选址成本、运输成本最小为目标,设施与车辆能力限制为约束的二阶段随机规划模型。根据模型特点,设计了基于Benders decomposition的求解算法,同时,设计了一系列加速技术用于提高算法的求解效率。最后,以国内某城市医疗回收网络为背景设计算例,检验本文模型和求解策略的可行性和有效性。结果表明：相比确定性规划,随机规划的解能够节约总成本,结合一系列加速技术的Benders decomposition方法比CPLEX与纯的Benders decomposition更有优势。     

Flexible Servers in Understaffed Tandem Lines

We study the dynamic assignment of cross‐trained servers to stations in understaffed lines with finite buffers. Our objective is to maximize the production rate. We identify optimal server assignment policies for systems with three stations, two servers, different flexibility structures, and either deterministic service times and arbitrary buffers or exponential service times and small buffers. We use these policies to develop server assignment heuristics for Markovian systems with larger buffer sizes that appear to yield near‐optimal throughput. In the deterministic setting, we prove that the best possible production rate with full server flexibility and infinite buffers can be attained with partial flexibility and zero buffers, and we identify the critical skills required to achieve this goal. We then present numerical results showing that these critical skills, employed with an effective server assignment policy, also yield near‐optimal throughput in the Markovian setting, even for small buffer sizes. Thus, our results suggest that partial flexibility is sufficient for near‐optimal performance, and that flexibility structures that are effective for deterministic and infinite‐buffered systems are also likely to perform well for finite‐buffered stochastic systems.     

Portfolio-based airline fleet planning under stochastic demand

Airlines operate their fleet of aircraft over a relatively long time horizon during which the realized stochastic demand has the potential to profoundly impact the airlines’ financial performance. This makes the investment in a fleet of aircraft a highly capital-intensive long-term commitment, associated with inherent risks. We propose an innovative three-step airline fleet planning methodology with the primary objective of identifying fleets that are robust to stochastic demand realizations. The methodology presents two main innovation aspects. The first one is the use of the mean reverting Ornstein–Uhlenbeck process to model the long-term travel demand, which is then combined with discrete-time Markov chain transitions to generate demand scenarios. The second innovative aspect is the adoption of a portfolio-based fleet planning perspective that allows for an explicit comparison of different fleets, in size and composition. Ultimately, the methodology yields for each fleet in the portfolio a distribution of net present values of operating profit across the planning horizon and a list of key financial and operational metrics per year. The robustest fleet can be selected based on the operating profit generating capability across different realizations of stochastic demand. An illustrative case study is presented as a proof of concept. The case study is used to demonstrate the type of results obtained and to discuss the usefulness of the methodology proposed.     

A demand classification scheme for spare part inventory model subject to stochastic demand and lead time

In this study, we aim to develop a demand classification methodology for classifying and controlling inventory spare parts subject to stochastic demand and lead time. Using real data, the developed models were tested and their performances were evaluated and compared. The results show that the Laplace model provided superior performance in terms of service level, fill rate (FR) and inventory cost. Compared with the current system based on normal distribution, the proposed Laplace model yielded significant savings and good results in terms of the service level and the FR. The Laplace and Gamma optimisation models resulted in savings of 82 and 81%, respectively.     

On service degrade at a discount: Capacity, demand pooling, and optimal discounting

In this paper we study the capacity investment decisions and operational strategies of a firm providing two-class services facing uncertain demands. The capacity decisions of the resources are made before demands are observed. Each service can be implemented by its corresponding resource. Should a mismatch between the capacity and the actual demand for the services arise, the low-class resource can be used as a substitute for the high-class service. We introduce an operational strategy called degrade-at-a-discount, where a price discount is offered to motivate customers to accept a lower class service when their original choice is out of capacity. By formulating the problem as a one-period, two-stage stochastic problem, we analyze how to set up the optimal capacity and the optimal discount. We also conduct a comprehensive numerical study to show the benefits of the degrade-at-a-discount strategy.     

Point‐of‐Use Hybrid Inventory Policy for Hospitals

Modern point‐of‐use technology at hospitals has enabled new replenishment policies for medical supplies. One of these new policies, which we call the hybrid policy, is currently in use at a large U.S. Midwest hospital. The hybrid policy combines a low‐cost periodic replenishment epoch with a high‐cost continuous replenishment option to avoid costly stockouts. We study this new hybrid policy under deterministic and stochastic demand. We develop a parameter search engine using simulation to optimize the long‐run average cost per unit time and, via a computational study, we provide insights on the benefits (reduction in cost, inventory, and number of replenishments) that hospitals may obtain by using the hybrid policy instead of the commonly used periodic policies. We also use the optimal hybrid policy parameters from the deterministic analysis to propose approximate expressions for the stochastic hybrid policy parameters that can be easily used by hospital management.      

A Maximum Entropy Joint Demand Estimation and Capacity Control Policy

We propose a tractable, data‐driven demand estimation procedure based on the use of maximum entropy (ME) distributions, and apply it to a stochastic capacity control problem motivated from airline revenue management. Specifically, we study the two fare class “Littlewood” problem in a setting where the firm has access to only potentially censored sales observations; this is also known as the repeated newsvendor problem. We propose a heuristic that iteratively fits an ME distribution to all observed sales data, and in each iteration selects a protection level based on the estimated distribution. When the underlying demand distribution is discrete, we show that the sequence of protection levels converges to the optimal one almost surely, and that the ME demand forecast converges to the true demand distribution for all values below the optimal protection level. That is, the proposed heuristic avoids the “spiral down” effect, making it attractive for problems of joint forecasting and revenue optimization problems in the presence of censored observations.     

Managing Demand Risk in Tactical Supply Chain Planning for a Global Consumer Electronics Company

We consider the problem of managing demand risk in tactical supply chain planning for a particular global consumer electronics company. The company follows a deterministic replenishment‐and‐planning process despite considerable demand uncertainty. As a possible way to formally address uncertainty, we provide two risk measures, “demand‐at‐risk” (DaR) and “inventory‐at‐risk” (IaR) and two linear programming models to help manage demand uncertainty. The first model is deterministic and can be used to allocate the replenishment schedule from the plants among the customers as per the existing process. The other model is stochastic and can be used to determine the “ideal” replenishment request from the plants under demand uncertainty. The gap between the output of the two models as regards requested replenishment and the values of the risk measures can be used by the company to reallocate capacity among different products and to thus manage demand/inventory risk.     

MULTI‐VENDOR SOURCING IN A RETAIL SUPPLY CHAIN*

This paper describes a methodology for managing capacity, inventory, and shipments for an assortment of retail products produced by multiple vendors. The vendors differ in lead times, costs, and production flexibility. Product demand is uncertain and fluctuates over time. We develop an optimization model to choose the production commitments that maximize the retailers expected gross profit, given demand forecasts and vendors capacity and flexibility constraints. The model has been incorporated into a decision support system, developed in collaboration with supply chain planners at a global retailer of seasonal and fashion merchandise. The software has been tested by two major retailers.     

Centralization versus decentralization: Risk pooling,risk diversification,and supply chain disruptions

We investigate optimal system design in a multi-location system in which supply is subject to disruptions. We examine the expected costs and cost variances of the system in both a centralized and a decentralized inventory system. We show that, when demand is deterministic and supply may be disrupted, using a decentralized inventory design reduces cost variance through the risk diversification effect, and therefore a decentralized inventory system is optimal. This is in contrast to the classical result that when supply is deterministic and demand is stochastic, centralization is optimal due to the risk-pooling effect. When both supply may be disrupted and demand is stochastic, we demonstrate that a risk-averse firm should typically choose a decentralized inventory system design.     

Hedging strategic flexibility in the distribution optimization problem

Motivated by the increasing prevalence of flexibility hedging in corporate-level risk management programs, this paper focuses on the treatment of hedging operational risks in the coordinated replenishment and shipment for distribution systems. The forward option pricing model with the generalized autoregressive conditional heteroskedasticity (GARCH) model for stochastic demand forecasting is adopted for constructing inventory volume flexibility. We therefore propose a hedge-based coordinated inventory replenishment and shipment (HCIRS) methodology for flexibly making inventory hedging and optimal routing assignment decisions as well as coordinating replenishment and shipment policies. The HCIRS methodology provides insight into strategic flexibility adopted for a real-life inventory–distribution problem faced by one of the major East Asia food supply networks and turns out to be very efficient. The proposed HCIRS methodology has provided evidence of better results than the traditional operational techniques for the presented case in this paper.     

On certain optimal gas storage policies

A gas distribution company must satisfy at every instant of time an exogenous demand. In order to meet the peak demand in the most economic way, it can resort to storage and peak shaving techniques. For the case of a local distribution company linked to a national gas grid through a connection of bounded transmission capacity, we derive a schedule of drawing gas from the national grid that minimizes the storage capacity required under the assumption of deterministic demand. The storage minimizing schedule is derived through both elementary and optimal control methods. An extension is possible for the case of stochastic demand.     

EVALUATING THE TRADE-OFFS BETWEEN IDLING AND SHUTTING DOWN PRODUCTION LINES IN PROCESS INDUSTRIES

The costs of starting-up and shutting down production lines (and plants) in a process industry are often quite high. Therefore, when a plant's capacity significantly exceeds its forecast demand over an annual planning horizon, a manufacturer must either plan temporary production line shutdowns during the year, or plan to temporarily idle production lines without formally shutting line(s) down. The trade-offs between these two strategies can be complex. In this paper, we propose a methodology to evaluate the impact of both strategies on a plant's production costs by developing an analytical model based on the authors' experience with several process industries.     

Investigating the effect of product variants,and demand distributions on the optimal demand supply network setup

In today's marketplace, consumers are looking for product variety and low prices. In this paper, we investigate how product variation and demand distributions affect demand supply network optimality in a real-life based setting. The research methodology was based on a novel Petri net formulation, which employs reachability analysis to demand supply network optimisation. We found that in our case study localised final assembly is justified with one or two product variants, but a centralised production should be favoured with three or more product variants. We also noted the sensitivity of this result to transport cost/inventory carrying cost tradeoff.     

基于风险偏好下的网上在线拍卖策略设计

针对占线拍卖问题（on-line auction problem）的卖方策略进行了研究,扩展了传统占线拍卖机制中拍卖人风险规避态度的假设,构建了基于风险偏好的风险回报分析框架。进一步,为拍卖人设计了RPS拍卖策略和MPS拍卖策略,结论显示这两种拍卖策略使得拍卖人可以根据自己的风险偏好和对未来的预期进行拍卖数量、拍卖价格的选择,而且两种拍卖策略的竞争性能比优于传统竞争分析框架下的结果。数值算例的分析表明,在风险回报分析框架下,拍卖人的风险忍耐度与拍卖策略的收益成正比。分析还显示,设置多个预期参考价格可以增强拍卖人预测能力,从而提高拍卖策略收益。