Incorporating demand uncertainty and forecast error in supply chain planning models

This paper develops a framework for examining the effect of demand uncertainty and forecast error on unit costs and customer service levels in the supply chain, including Material Requirements Planning (MRP) type manufacturing systems. The aim is to overcome the methodological limitations and confusion that has arisen in much earlier research. To illustrate the issues, the problem of estimating the value of improving forecasting accuracy for a manufacturer was simulated. The topic is of practical importance because manufacturers spend large sums of money in purchasing and staffing forecasting support systems to achieve more accurate forecasts. In order to estimate the value a two-level MRP system with lot sizing where the product is manufactured for stock was simulated. Final product demand was generated by two commonly occurring stochastic processes and with different variances. Different levels of forecasting error were then introduced to arrive at corresponding values for improving forecasting accuracy. The quantitative estimates of improved accuracy were found to depend on both the demand generating process and the forecasting method. Within this more complete framework, the substantive results confirm earlier research that the best lot sizing rules for the deterministic situation are the worst whenever there is uncertainty in demand. However, size matters, both in the demand uncertainty and forecasting errors. The quantitative differences depend on service level and also the form of demand uncertainty. Unit costs for a given service level increase exponentially as the uncertainty in the demand data increases. The paper also estimates the effects of mis-specification of different sizes of forecast error in addition to demand uncertainty. In those manufacturing problems with high demand uncertainty and high forecast error, improved forecast accuracy should lead to substantial percentage improvements in unit costs. Methodologically, the results demonstrate the need to simulate demand uncertainty and the forecasting process separately.     

The effects of demand uncertainty on channel structure

Motivated by the business practice whereby some manufacturers open their own retail stores despite the existence of more efficient independent retailers, this paper examines the distribution channel choice of competing manufacturers under demand uncertainty and resale price maintenance. We characterize the conditions for the equilibrium channel structures. We find that (1) manufacturers tend to distribute products with more design attributes through their own retail stores, (2) manufacturers with highly substitutable products are more likely to use independent retailers, and (3) at least one manufacturer has more incentive to open its own retail stores when facing an increase of the market size asymmetry.     

Two-stage workforce planning under demand fluctuations and uncertainty

We address a multi-category workforce planning problem for functional areas located at different service centres, each having office-space and recruitment capacity constraints, and facing fluctuating and uncertain workforce demand. A deterministic model is initially developed to deal with workforce fluctuations based on an expected demand profile over the horizon. To hedge against the demand uncertainty, we also propose a two-stage stochastic program, in which the first stage makes personnel recruiting and allocation decisions, while the second stage reassigns workforce demand among all units. A Benders’ decomposition-based algorithm is designed to solve this two-stage stochastic mixed-integer program. Computational results based on some practical numerical experiments are presented to provide insights on applying the deterministic versus the stochastic programming approach, and to demonstrate the efficacy of the proposed algorithm as compared with directly solving the model using its deterministic equivalent.     

Using shared sell-through data to forecast wholesaler demand in multi-echelon supply chains

Operational forecasting in supply chain management supports a variety of short-term planning decisions, such as production scheduling and inventory management. In this respect, improving short-term forecast accuracy is a way to build a more agile supply chain for manufacturing companies. Demand forecasting often relies on well-established univariate forecasting methods to extrapolate historical demand. Collaboration across the supply chain, including information sharing, is suggested in the literature to improve upon the forecast accuracy of such traditional methods. In this paper, we review empirical studies considering the use of downstream information in demand forecasting and investigate different modeling approaches and forecasting methods to incorporate such data. Where empirical findings on information sharing mainly focus on point-of-sale data in two-level supply chains, this research empirically investigates the added value of using sell-through data originating from intermediaries, next to historical demand figures, in a multi-echelon supply chain. In a case study concerning a US drug manufacturer, we evaluate different methods to incorporate this data and consider both time series methods and machine learning techniques to produce multi-step ahead weekly forecasts. The results show that the manufacturer can effectively improve its short-term forecast accuracy by integrating sell-through data into the forecasting process and provide useful insights as to the different modeling approaches used. The conclusion holds for all forecast horizons considered, though it is most pronounced for one-step ahead forecasts. Therefore, our research provides a clear incentive for manufacturers to assess the forecast accuracy that can be achieved by using sell-through data.     

Cash management cost reduction using data mining to forecast cash demand and LP to optimize resources

This paper presents a two step model aimed at reducing cash management costs in a bank’s branch. First, data mining was used to forecast daily cash demand, comparing an ARMA-ARCH model with a neural network. Secondly, using the prior result, a linear programming model was solved. The optimal allocation of resources, i.e., cash collections and supplies was estimated showing that the model can be a helpful tool to support the determination of collections and supplies at the bank branch.     

Optimal inventory policy with supply uncertainty and demand cancellation

We consider a periodic review model where the firm manages its inventory under supply uncertainty and demand cancellation. We show that because of supply uncertainty, the optimal inventory policy has the structure of re-order point type. That is, we order if the initial inventory falls below this re-order point, otherwise we do not order. This is in contrast to the work of Yuan and Cheung (2003) who prove the optimality of an order up to policy in the absence of supply uncertainty. We also investigate the impact of supply uncertainty and demand cancellation on the performance of the supply chain. Using our model, we are able to quantify the importance of reducing the variance of either the distribution of yield or the distribution of demand cancellation. The single, multiple periods and the infinite horizon models are studied.     

Production and location on a network under demand uncertainty

The Hakimi theorem is fundamental in location theory. It says that the set of nodes and market-places necessarily contains a profit-maximizing location when the transportation costs are concave in distance. The purpose of this letter is to discuss the validity of this theorem in the context of a two-stage stochastic model of the location of a firm on a network. In the first stage, the firm chooses its location and production level before knowing the exact demands. In the second stage, it observes the realization of the random variables representing the demands and decides upon the distribution of its production. It is shown that the Hakimi theorem still holds in this model when the firm is risk-neutral. On the other hand, in the case of a risk-averse firm, it ceases to be true in that all the points of the network must be considered to obtain an optimal location.     

Channel coordination under two-level trade credits and demand uncertainty

This study considers a decentralized supply chain where a retailer has an opportunity to order a product from a supplier prior to the sales season to satisfy uncertain demand. The retailer provides trade credit to end customers and makes credit period and order quantity decisions to maximize profits. The end demand is both random and credit period-dependent. On the basis of the newsvendor model, this paper focuses on channel coordination when a retailer provides trade credit to end customers. When the supplier also provides trade credit to the retailer, we show that the traditional trade credit contract cannot coordinate the channel. Four composite contracts based on trade credit (trade credit cost sharing with buy back or quantity flexibility; modified trade credit with buy back or quantity flexibility) are provided to induce the retailer to make decisions while optimizing the channel profit. This paper shows that the retailer provides a longer credit period to its customers and orders a larger quantity from the supplier under the composite contracts. With these contracts, the profit sharing between both parties depends on the wholesale price (Pareto improvement) for the fixed retail price and the purchasing cost.     

An analytical approach to the facility location and capacity acquisition problem under demand uncertainty

This article presents an analysis of facility location and capacity acquisition under demand uncertainty. A novel methodology is proposed, in which the focus is shifted from the precise representation of facility locations to the market areas they serve. This is an extension of the optimal market area approach in which market area size and facility capacity are determined to minimize the total cost associated with fixed facility opening, variable capacity acquisition, transportation, and shortage. The problem has two variants depending on whether the firm satisfies shortages by outsourcing or shortages become lost sales. The analytical approach simplifies the problem considerably and leads to intuitive and insightful models. Among several other results, it is shown that fewer facilities are set up under lost sales than under outsourcing. It is also shown that the total cost in both models is relatively insensitive to small deviations in optimal capacity choices and parameter estimations.     

The valuation of options on capacity with cost and demand uncertainty

Options contracts can provide trading partners with enhanced flexibility to respond to uncertain market conditions and allow for superior capacity planning thanks to early information on future demand. We develop an analytical framework to value options on capacity for production of non-storable goods or dated services. The market consists of a sequence of contract and spot market. Reservations are made during the contract market session in period 0, where the buyer’s future demand, the seller’s future marginal costs as well as the future spot price are uncertain, the latter being impacted neither by the buyer nor the seller. During the spot market session in period 1, the buyer may execute his options or satisfy his entire or additional demand from a competing seller in the spot market. The seller allocates reserved capacity now being called and attempts to sell remaining capacity into the spot market. Analytical expressions for the buyer’s optimal reservation quantity and the seller’s tariff are derived, making explicit the risk-sharing benefits of options contracts. The combination of an options contract and a spot market is demonstrated to be Pareto improving as compared to alternative market schemes. An analysis of the determinants of the efficiency gain characterizes industries particularly suitable to the options approach.     

Collaborative production planning of supply chain under price and demand uncertainty

This research is motivated by an automobile manufacturing supply chain network. It involves a multi-echelon production system with material supply, component fabrication, manufacturing, and final product distribution activities. We address the production planning issue by considering bill of materials and the trade-offs between inventories, production costs and customer service level. Due to its complexity, an integrated solution framework which combines scatter evolutionary algorithm, fuzzy programming and stochastic chance-constrained programming are combined to jointly take up the issue. We conduct a computational study to evaluate the model. Numerical results using the proposed algorithm confirm the advantage of the integrated planning approach. Compared with other solution methodologies, the supply chain profits from the proposed approach consistently outperform, in some cases up to 13% better. The impacts of uncertainty in demand, material price, and other parameters on the performance of the supply chain are studied through sensitivity analysis. We found the proposed model is effective in developing robust production plans under various market conditions.     

Robust solutions for network design under transportation cost and demand uncertainty

In many applications, the network design problem (NDP) faces significant uncertainty in transportation costs and demand, as it can be difficult to estimate current (and future values) of these quantities. In this paper, we present a robust optimization-based formulation for the NDP under transportation cost and demand uncertainty. We show that solving an approximation to this robust formulation of the NDP can be done efficiently for a network with single origin and destination per commodity and general uncertainty in transportation costs and demand that are independent of each other. For a network with path constraints, we propose an efficient column generation procedure to solve the linear programming relaxation. We also present computational results that show that the approximate robust solution found provides significant savings in the worst case while incurring only minor sub-optimality for specific instances of the uncertainty.     

Revenue impacts of fare input and demand forecast accuracy in airline yield management

Most airline yield management seat allocation models require inputs of the expected demand by fare class, the variance of this demand, and a revenue value associated with the bookings expected in each class. In this paper, we examine the impacts of errors in the demand forecasts and fare estimates on the revenue performance of some commonly used seat allocation heuristic decision rules. Through simulation analysis of scenarios in which the fare or demand inputs used by the models differ from the ‘actual’ values simulated in the flight booking process, we examine the effects of unexpected variability in the actual fare values, misestimation of the mean fare values of the different booking classes, and forecasting errors in the expected demand for each class. Our findings confirm previous studies that found the accuracy of the demand forecasts to be of greatest importance, but we also uncover some instances where misestimation of the mean demands and/or mean fare values used as inputs to the decision models can actually be beneficial. At the same time, we conclude that the variability of actual fare values around the mean fare values used as inputs does not have a significant impact, given the mathematical characteristics of existing EMSR seat allocation methods.     

Ordering policy and coordination of a supply chain with two-period demand uncertainty

We develop a two-period game model of a one-manufacturer and one-retailer supply chain to investigate the optimal decisions of the players, where stock-out and holding costs are incorporated into the model. The demand at each period is stochastic and price sharply drops in mid-life. We assume the retailer has a single order opportunity, and decides how much inventory to keep in the middle of selling season. We show that both the price-protection mid-life and end-of-life returns (PME) scheme and the only mid-life and end-of-life returns (ME) scheme may achieve channel coordination and access a ‘win-win’ situation under some conditions. The larger the lowest expected profit of the retailer, the lower the possibility of ‘win-win’ situation will be. Combined with the analysis of feasible regions for coordination policies, we find that PME scheme is not always better than ME scheme from the perspective of implementable mechanism. Finally, we find that adopting the dispose-down-to (DDT) policy can bring a larger improvement of the expected channel profit in the centralized setting, and it is interesting that by using DDT policy, double marginalization occurs only at Period 1, and however, does not plague the retailer in Period 2.     

Optimal exit and valuation under demand uncertainty: A real options approach

This paper considers both the optimal exit strategy and the valuation of stochastic cash flows of a firm facing demand uncertainty and potential excess supply. By relying on the standard theory of linear diffusions and ordinary nonlinear programming, we derive the value of the rationally managed firm, and state the necessary condition for optimal exit. In contrast to the standard approaches in the real options literature, our analysis is completely independent of both dynamic programming and the smooth-fit principle. I demonstrate that irreversible exit is optimal only when the value of the future productive opportunities becomes smaller than the value of irreversibly exercising the option to exit and in this way avoid further cumulative losses. I also present the comparative static properties of the optimal exit threshold and demonstrate that increased uncertainty may increase or decrease the optimal exit threshold depending on the sign of the net convenience yield.     

Robust vehicle routing problem with deadlines and travel time/demand uncertainty

In this article, we investigate the vehicle routing problem with deadlines, whose goal is to satisfy the requirements of a given number of customers with minimum travel distances while respecting both of the deadlines of the customers and vehicle capacity. It is assumed that the travel time between any two customers and the demands of the customer are uncertain. Two types of uncertainty sets with adjustable parameters are considered for the possible realizations of travel time and demand. The robustness of a solution against the uncertain data can be achieved by making the solution feasible for any travel time and demand defined in the uncertainty sets. We propose a Dantzig-Wolfe decomposition approach, which enables the uncertainty of the data to be encapsulated in the column generation subproblem. A dynamic programming algorithm is proposed to solve the subproblem with data uncertainty. The results of computational experiments involving two well-known test problems show that the robustness of the solution can be greatly improved.     

A sensitivity analysis to assess the completion time deviation for multi-purpose machines facing demand uncertainty

This paper addresses multi-purpose machine configuration in an uncertain context through sensitivity analysis. The so-called configuration is the machine??s ability to process products, and the uncertain context is modelled as a demand variation affecting the forecast demand. Given a configuration, this work aims at assessing the completion time deviation when the workshop demand is subject to perturbation. Such quantitative information can be used in a robustness approach for selecting the most appropriate configuration. To do so, the configuration impact on the completion time value that can be reached by solving the attached scheduling problem is first investigated. Then, the completion time deviation is written as a piecewise linear function of the magnitude of demand variation. The proposed approach, which is based on the solution of a set of linear programs, is illustrated through a detailed example. It is shown to be polynomial, and fast enough for addressing real-world instances. Finally, how to compare two configurations on the basis of completion time deviation in an uncertain context is demonstrated.     

Preemptive expediting to improve project due date performance

Project expediting is often viewed as a corrective action taken in response to prior scheduling errors and is usually applied in the later stages of projects when it appears that predefined due dates will not be met. However, large-scale projects with uncertain activity durations tend to have numerous probabilistic network paths with complex interactions that require some level of expediting to ensure successful scheduling outcomes. Because potential expediting options are consumed over time, delaying expediting efforts until the later stages of projects is likely to result in higher expediting costs or poorer due date performance. This research introduces a preemptive expediting approach that evaluates the probability of completion before the due date throughout the life of a project and selects expediting options per a prespecified probability tolerance or expediting budget. An experiment demonstrates the benefits of this preemptive approach.