Modelling consumer-directed substitution

We discuss the challenges and difficulties arising when approaching and modelling the consumer-directed substitution problem in quick response supply chains. Further, we propose heuristic solutions suited for large problems with complex uncertainty and dependency patterns. Despite the single-period newsvendor model we use, our substitution process is an approximation of the dynamic product choice. To ensure consistency with regard to the information used to establish substitution fractions and information available at the time of optimisation, substitution fraction estimation and inventory/assortment optimisation are discussed simultaneously. The decision-independent substitution preferences applied here do not require inventory or sales transaction data, but reflect understanding on the demand driver attributes. This approach, in turn, leads to increased robustness in assortment planning. Factual substitution is an outcome of the optimisation process, constrained by the available substitutes and unfulfilled demand.Despite being unable to fully describe the dependencies among the substitute choice possibilities, our substitution approach, together with the modelling process, allows handling the most important dependencies, such as negatively correlated substitute choice possibilities and positively/negatively correlated first and second choice possibilities.     

Optimizing the capital rationing decision with uncertain returns

In this article, we develop a new optimization model for capital rationing with uncertain project returns. Our model maximizes the probability of meeting a predefined target return by selecting a feasible set of projects subject to budget constraints in multiple time periods. We employ a mixed-integer nonlinear algorithm recently developed in the optimization field to solve the resulting nonconvex optimization problem to optimality. Our model and solution methods are tested and validated through a comprehensive computational experiment. Several managerial insights are obtained about the impact of available budget and target return on the optimal solutions. Notably, we have found that increasing target return may not necessarily result in an increase in optimal total expected return of the selected projects. Our model and solution method offer a unified and computationally tractable approach to precisely quantify the tradeoff between project returned and risk.     

Optimal production–inventory strategies for a HMMS-type reverse logistics system

The aim of the paper is to find optimal inventory policies in a reverse logistics system with special structure. It is assumed that demand is a known continuous function in a given planning horizon and return rate of used items is a given function. There is a constant delay between the using and return process. We investigate two stores. The demand is satisfied from the first store, where the manufactured and remanufactured items are stored. The returned products are collected in the second store and then remanufactured or disposed. The costs of this system consist of the quadratic holding costs for these two stores and the quadratic manufacturing, remanufacturing and disposal costs.The model is represented as an optimal control problem with two state variables (inventory status in the first and second store) and with three control variables (rate of manufacturing, remanufacturing and disposal). The objective is to minimize the sum of the quadratic deviation from described inventory levels in stores and from described manufacturing, remanufacturing and disposal rates. In this form, the model can be considered as a generalization of the well-known Holt et al. (Planning Production, Inventories, and Work Forces, Prentice-Hall, Englewood Cliffs, NJ, 1960) model with two warehouses. After solving the problem, we give some numerical examples to represent the optimal path in dependence of the demand rates.     

A multi-objective robust optimization model for multi-product multi-site aggregate production planning in a supply chain under uncertainty

Manufacturers need to satisfy consumer demands in order to compete in the real world. This requires the efficient operation of a supply chain planning. In this research we consider a supply chain including multiple suppliers, multiple manufacturers and multiple customers, addressing a multi-site, multi-period, multi-product aggregate production planning (APP) problem under uncertainty. First a new robust multi-objective mixed integer nonlinear programming model is proposed to deal with APP considering two conflicting objectives simultaneously, as well as the uncertain nature of the supply chain. Cost parameters of the supply chain and demand fluctuations are subject to uncertainty. Then the problem transformed into a multi-objective linear one. The first objective function aims to minimize total losses of supply chain including production cost, hiring, firing and training cost, raw material and end product inventory holding cost, transportation and shortage cost. The second objective function considers customer satisfaction through minimizing sum of the maximum amount of shortages among the customers’ zones in all periods. Working levels, workers productivity, overtime, subcontracting, storage capacity and lead time are also considered. Finally, the proposed model is solved as a single-objective mixed integer programming model applying the LP-metrics method. The practicability of the proposed model is demonstrated through its application in solving an APP problem in an industrial case study. The results indicate that the proposed model can provide a promising approach to fulfill an efficient production planning in a supply chain.     

Incorporating uncertainty into a supplier selection problem

Supplier selection is an important strategic supply chain design decision. Incorporating uncertainty of demand and supplier capacity into the optimization model results in a robust selection of suppliers. A two-stage stochastic programming (SP) model and a chance-constrained programming (CCP) model are developed to determine a minimal set of suppliers and optimal order quantities with consideration of business volume discounts. Both models include several objectives and strive to balance a small number of suppliers with the risk of not being able to meet demand. The SP model is scenario-based and uses penalty coefficients whereas the CCP model assumes a probability distribution and constrains the probability of not meeting demand. Both formulations improve on a deterministic mixed integer linear program and give the decision maker a more complete picture of tradeoffs between cost, system reliability and other factors. We present Pareto-optimal solutions for a sample problem to demonstrate the benefits of the SP and CCP models. In order to describe the tradeoffs between costs and risks in an analytical form, we use multi-parametric programming techniques to more completely analyze the alternative Pareto-optimal supplier selection solutions in the CCP model. This analysis gives insights into the robustness of the solutions with respect to number of suppliers, costs and probability of not meeting demand.     

A serial mixed produce-to-order and produce-in-advance inventory model with multiple retailers

We formulate a general mixed produce-to-order and produce-in-advance inventory model having multiple stocking echelons and multiple retailers. We show that the problem to find an optimal inventory policy for such a model with a uniform or a normal demand distribution can be reduced to a general constrained optimization problem.     

Modified critical fractile approach for a class of partial postponement problems

This paper studies a single period partial postponement problem, which is motivated by an inventory planning problem encountered in Reebok NFL replica jersey supply chain. We consider a group of regular products each facing a random demand. There are two stocking options. One is to procure the regular products. The other is to stock a common component which can be customized later to any one of the regular products, after demand realization.We obtain an insightful interpretation of the optimality conditions for this class of problems, and use it to obtain rules of thumb that practitioners can incorporate into their inventory models to determine the stocking levels to minimize the supply chain cost. Instead of proposing a numerical procedure to obtain the optimal solution, we propose an adaptation of the classical critical fractile approach for this class of partial postponement problem. The closed-form formula obtained are surprisingly effective. Our numerical results suggest that this simple approach to inventory planning often comes close to the performance of the optimal solution obtained from numerical method.     

Coordination of planning and scheduling decisions in global supply chains with dual supply modes

We address the problem of coordinating aggregate planning decisions and short-term scheduling decisions in supply chains with dual supply modes. We consider long lead time, less expensive sea shipments that are based on demand forecast, and responsive but costly air shipments that are based on revised forecast closer to the demand period. The planning problem determines the sea shipment order quantity and inventory level, while the scheduling model determines the schedule and quantity of air shipments. Results from our numerical experiments suggest that our model leads to consistent cost improvements over a wide range of operating scenarios.     

A production rate control policy for stochastic repair and remanufacturing systems

We consider the control of a manufacturing system responding to planned demand at the end of the expected life of each individual piece of equipment and unplanned demand triggered by a major equipment failure. The difficulty of controlling this type of production system resides in the variable nature of the remanufacturing process. In practice, remanufacturing operations for planned demand can be executed at different rates, referring to different component replacement and repair strategies. We formulate this problem as a multi-level control problem and propose a suboptimal control policy. The proposed control policy is described by inventory thresholds triggering the use of different execution modes. Determination of the control policy parameters is based on parameter optimization of analytical cost expressions. A numerical example based on a real case is presented. Our analysis demonstrates that the use of the proposed control approach can lead to a significant reduction in the total average cost, as compared to current practices.     

A local search algorithm for the optimization of the stochastic economic lot scheduling problem

This paper describes a model for the stochastic economic lot scheduling problem (SELSP) and a Local Search heuristic to find close to optimal solutions to this model. The SELSP considers multiple products, which have to be scheduled on a single facility with limited capacity and significant setup times and costs. The demand is modeled as a stationary compound renewal process. The objective is to find a schedule that minimizes the long-run average costs for setups and inventories while satisfying a given fill rate. We use a cyclic scheduling approach in which the individual cycle time of each product is a multiple of some basic period (fundamental cycle).For the deterministic version of the SELSP, efficient heuristics have been developed which guarantee the feasibility of the solution by adding an additional constraint to the problem. In our case this is not sufficient, because for the calculation of the average inventory levels and fill rates we need to develop a schedule with detailed timing of the lots. We present an efficient heuristic for this scheduling problem, which can also be used to check the feasibility of the solution. Thereby, the most time-consuming step (the calculation of average inventory levels and fill rates) is only performed for a limited set of candidates.The algorithm was tested on deterministic benchmark problems from literature and on a large set of stochastic instances. We report on the performance of the heuristic in both cases and try to identify the main factors influencing the objective.     

Timing production in LP models in a rolling schedule

We consider an arbitrary supply chain structure under demand uncertainty. We look at a setting where the supply chain planning is executed periodically and where the demand of end items in subsequent periods is stochastic. In contrast to other linear programming-based approaches, we assume constant planned lead times. In this paper we discuss the timing of production during the planned lead times of items. If production starts immediately, the work-in-process inventory costs are higher, but producing later will result in higher safety stocks. We look at the influence of the demand variation, the planned lead time of the items, the utilization rate of resources, and the added value when merging items, on the inventory costs. The results indicate that, for higher utilization rates, producing early is more suitable.     

基于连锁零售企业退货管理的供应链协调机制研究

在对连锁零售企业退货物流网络结构进行分析的基础上,建立了与价格相关的随机需求下存在顾客退货和允许库存结转的单一供应商、单一连锁零售企业、单一产品的供应链模型。根据供应链一体化模式下得到的相关决策变量的一阶条件,论证基于回馈和惩罚的批发价格契约能够实现供应链的协调。研究表明,在给定回馈和惩罚因子的前提下,供应商可以通过调整目标订购数量来实现供应链整体利润的任意分配,并且当目标订购数量和回馈惩罚因子满足一定条件时,供应链的协调才是有效的,从而为连锁零售企业的退货物流管理提供了重要的理论依据。     

Competition under capacitated dynamic lot-sizing with capacity acquisition

Lot-sizing and capacity planning are important supply chain decisions, and competition and cooperation affect the performance of these decisions. In this paper, we look into the dynamic lot-sizing and resource competition problem of an industry consisting of multiple firms. A capacity competition model combining the complexity of time-varying demand with cost functions and economies of scale arising from dynamic lot-sizing costs is developed. Each firm can replenish inventory at the beginning of each period in a finite planning horizon. Fixed as well as variable production costs incur for each production setup, along with inventory carrying costs. The individual production lots of each firm are limited by a constant capacity restriction, which is purchased up front for the planning horizon. The capacity can be purchased from a spot market, and the capacity acquisition cost fluctuates with the total capacity demand of all the competing firms. We solve the competition model and establish the existence of a capacity equilibrium over the firms and the associated optimal dynamic lot-sizing plan for each firm under mild conditions.     

Risk averse retail pricing with robust demand forecasting

Good demand estimates are the key to effective pricing decision-making. However, they are subject to a high degree of uncertainty due to various factors that are unpredictable or difficult to model, thus making pricing decisions risky. This research provides a simple proposal for a robust optimization methodology that incorporates both demand uncertainty and the decision maker's degree of risk aversion. Uncertainty is explicitly considered for two coefficients of a linear demand function, price expressions are derived, and a criterion is proposed for defining the degree of risk aversion. The resulting model is also applied to an exponential demand case to better reflect a more realistic retail setting.     

Supply network capacity planning for semiconductor manufacturing with uncertain demand and correlation in demand considerations

A semiconductor supply network involves many expensive steps, which have to be executed to serve global markets. The complexity of global capacity planning combined with the large capital expenditures to increase factory capacity makes it important to incorporate optimization methodologies for cost reduction and long-term planning. The typical view of a semiconductor supply network consists of layers for wafer fab, sort, assembly, test and demand centers. We present a two-stage stochastic integer-programming formulation to model a semiconductor supply network. The model makes strategic capacity decisions, (i.e., build factories or outsource) while accounting for the uncertainties in demand for multiple products. We use the model not only to analyze how variability in demand affects the make/buy decisions but also to investigate how the correlation between demands of different products affects these strategic decisions. Finally, we demonstrate the value of incorporating demand uncertainty into a decision-making scheme.     

A production/remanufacture model with returns’ subassemblies managed differently

This paper considers a production-remanufacturing inventory model for a single product, where constant demand is satisfied from the inventory of newly produced and remanufactured items. Although the available models in the literature imply that collected used units (or returns) are disassembled for recovery purposes, these models really do not treat them as such. Contrary, the returns are assumed to be recovered as whole units, perhaps, for simplicity. This assumption may not capture the benefits reaped from product recovery programs. This paper addresses this limitation in the literature and assumes that each unit of a used product is collected and disassembled into components, where these components are sorted into subassemblies, which are fed back into the production-remanufacturing process. The returned subassemblies are remanufactured and reassembled to represent a second source of as-good-as-new units of the end-product. For this multi-component inventory problem, the question that needs to be answered is whether, or not, extreme strategies of either pure remanufacturing or pure production are more economical than a mixed strategy (one that combines both strategies). A mathematical model is developed that accounts for the inventories of subassemblies. The results suggested that not accounting for the disassembled components of a product leads to inappropriate inventory decisions that are not environmentally sound.     

An extension to the classical mean–variance portfolio optimization model

Abstract

The purpose of this study is to find a portfolio that maximizes the risk-adjusted returns subject to constraints frequently faced during portfolio management by extending the classical Markowitz mean–variance portfolio optimization model. We propose a new two-step heuristic approach, GRASP & SOLVER, that evaluates the desirability of an asset by combining several properties about it into a single parameter. Using a real-life data set, we conduct a simulation study to compare our solution to a benchmark (S&P 500 index). We find that our method generates solutions satisfying nearly all of the constraints within reasonable computational time (under an hour), at the expense of a 13% reduction in the annual return of the portfolio, highlighting the effect of introducing these practice-based constraints.     

An inventory reservation problem with nesting and fill rate-based performance measures

In many inventory settings companies wish to provide customer-differentiated service levels. These may, for example, be motivated by differences in the perceived customer lifetime value or by specific contractual agreements. One approach to provide differentiated service levels is to reserve some portion of the available inventory exclusively for specific customer classes. Existing approaches to inventory reservation are typically based on the assumption that a company can assign a customer specific revenue or penalty cost to any order or unit of demand filled or unfulfilled. In practice, however, it is usually extremely difficult to accurately estimate (especially long term) monetary implications of meeting or not meeting customer demand and corresponding service level requirements. The research presented in this paper addresses the problem of setting appropriate inventory reservations for different customer classes based on fill rate-based performance measures. We model a single period inventory reservation problem with two customer classes and nesting. We develop exact expressions for two conflicting performance measures: (1) the expected fill rate of high priority customers and (2) the expected loss in the system fill rate induced by inventory reservation. With these expressions a decision maker can analyze the tradeoff between the loss in overall system performance and the higher expected fill rates for prioritized customers. We provide analytical insights into the effects of nesting and the impact of relevant problem parameters on these two performance measures. The analytical insights are illustrated and highlighted through a set of numerical examples. Although we limit our analysis to a single period inventory reservation problem, we expect that our results can be utilized in a wide range of problem settings in which a decision maker has to ration a perishable resource among different classes of customers.     

Uncertainty premia in REIT returns

We provide a systematic study of how financial and real estate uncertainty affect the aggregate return performance of the U.S. REIT market from 1994 to 2017. A temporal causality analysis reveals a negative uncertainty impact on REIT returns. The asset pricing analysis confirms the predictive relation and suggests that REITs are statistically significantly exposed to changes in market-wide uncertainty, for which investors require a return compensation. We also identify economic state variables to explain time-varying uncertainty exposures as well as periodic hedging characteristics of REITs. Finally, we find evidence that the source of uncertainty matters for compensating expected REIT returns.     

The Bias of the RSR Estimator and the Accuracy of Some Alternatives

This paper analyzes the implications of cross-sectional heteroskedasticity in the repeat sales regression (RSR). RSR estimators are essentially geometric averages of individual asset returns because of the logarithmic transformation of price relatives. We show that the cross-sectional variance of asset returns affects the magnitude of the bias in the average return estimate for each period, while reducing the bias for the surrounding periods. It is not easy to use an approximation method to correct the bias problem. We suggest an unbiased maximum likelihood alternative to the RSR that directly estimates index returns, which we term MLRSR. The unbiased MLRSR estimators are analogous to the RSR estimators but are arithmetic averages of individual asset returns. Simulations show that these estimators are robust to time-varying cross-sectional variance and that the MLRSR may be more accurate than RSR and some alternative methods.