تاثیر شکل توزیع تقاضا در مدل های تصمیم گیری برای مدیریت عملیات

Decision support tools are increasingly used in operations where key decision inputs such as demand, quality, or costs are uncertain. Often such uncertainties are modeled with probability distributions, but very little attention is given to the shape of the distributions. For example, state-of-the-art planning systems have weak, if any, capabilities to account for the distribution shape. We consider demand uncertainties of different shapes and show that the shape can considerably change the optimal decision recommendations of decision models. Inspired by discussions with a leading consumer electronics manufacturer, we analyze how four plausible demand distributions affect three representative decision models that can be employed in support of inventory management, supply contract selection and capacity planning decisions. It is found, for example, that in supply contracts flexibility is much more appreciated if demand is negatively skewed, i.e., has downside potential, compared to positively skewed demand. We then analyze the value of distributional information in the light of these models to find out how the scope of improvement actions that aim to decrease demand uncertainty vary depending on the decision to be made. Based on the results, we present guidelines for effective utilization of probability distributions in decision models for operations management.

Organizations use mathematical models to support decision making in uncertain environments. Such models often account for many uncertain variables: in manufacturing, product demand varies from period to another; cost parameters change over time due to fluctuating raw-material prices or rising wages; and suppliers may not supply as promised due to constrained capacity or quality problems. Uncertain demand, in particular, is a key variable for operations management and supply chain planning: for example, push type supply chains are typically coordinated using a forecast of demand for a given planning period. This demand forecast is built on expert knowledge and/or mathematical forecast and serves as a basis for other supply chain planning activities from operational to strategic level decisions [41]. In principle, accurate forecasts would allow cost-efficient coordination, but forecasting is difficult in turbulent environments. As a result, increasing attention has been paid to the question of how demand and supply uncertainties should be accounted for in supply chain modeling [10]. These uncertainties impact all levels of operations management: strategic (e.g., [14] and [26]), tactical (e.g., [18]) and operational (e.g., [36]). Considerable efforts have been made to develop both stochastic (distribution based) and robust (distribution free) models to support decision making under uncertainty. Such models can be used to derive insights under very general assumptions; for example, they can be used to study how a given supply contract shares demand risk in a supply chain, or how lead time variability reduction can systematically lower inventory levels while keeping the shortage risk constant. But at a more concrete level (such as when implementing decision support systems) detailed assumptions about the uncertainties are required for setting numerical contract parameters or calculating target inventory levels, for example. Thus, the estimation of uncertainties is critical for model implementation. In this paper, we study how the shape of demand distribution can impact the results of decision making models in operations management, and discuss the value of distributional knowledge in these models. In particular, we focus on demand uncertainty and show how seemingly similar but qualitatively different uncertainties impact three widely employed models. We use different demand distributions, which exhibit at least one of the following statistical properties: (i) symmetry, (ii) positive skewness, (iii) negative skewness, and (iv) bimodality. Arguably, these properties can be used to describe the qualitative attributes of a large share of realistic demand types. We assume demands which have identical expected value and variance, but which differ in shape with respect to (i)–(iv). By drawing upon these examples, we also analyze how much value the knowledge about a distribution can offer, compared to a case where the distribution is not known. Similar analysis has been done before for individual decision models, but not extensively for multiple models as we do here. Based on the resulting insights we provide high-level guidelines for managers who seek to address uncertainties in all levels of decision making in operations. Our study is motivated by a large consumer electronics company which is in the process of designing a new sourcing strategy. The company sought better understanding on how demand uncertainty can be managed when there are different types of demand, depending on the product category and market segment. Such challenges are not unique: because common planning systems make only use of point demand forecast, and deviation at best, the impact of the shape of demand distribution is largely neglected. According to Van Nieuwenhuyse et al. [32], companies lack capability to analyze demand uncertainty and use the results as decision support. For example, they note that SAP's Advanced Planning and Optimization module “disregards uncertainty”. However, the same authors have developed an advanced software module that accounts for stochastic demand and they report promising results from two cases in different manufacturing industries. Other promising applications have been reported in this area: Talluri et al. [42] present a simple enhancement for lead time demand estimation that could lead to large saving in inventory costs at a pharmaceutical company. Nagali et al. [31] describe the Procurement Risk Management approach at Hewlett-Packard, where instead of a point forecast, a scenario-based approach to demand forecasting has been applied successfully with improved component availability and significant cost savings. Sodhi [40] presents exploratory work on managing Sales and Operations Planning process (S&OP) at a consumer electronics manufacturer. He demonstrates how the value of flexibility and risk of shortages or excess inventories can be analyzed with a stochastic demand model. Finally, according to survey of 180 executives by Jain et al. [20], “Non-normal demand distributions that make traditional forecast modeling difficult” was pointed out as one of the biggest challenges of demand management across companies. Jain et al. concluded that companies with best-in-class demand management capabilities reap multiple benefits in form of, e.g., improved invetory turns and higher order fulfillment rates. The rest of the paper is structured as follows: Section 2 relates our work to earlier approaches in uncertainty modeling and operations management. Section 3 covers the example demand distributions and Section 4 describes the models and corresponding numerical results. Subsequently, Section 5 elaborates the value of distributional information in these models. Finally, Section 6 discusses the implications for managers and Section 7 presents conclusions.

In this paper, we have stressed the importance of uncertainty modeling in risk management models. This was illustrated with examples from inventory replenishment, tactical procurement and strategic capacity planning, which demonstrated how the results of models vary significantly when assumptions of the demand distribution change. The examples were constructed in co-operation with a case company, which found the presented analysis insightful: it helped increase understanding of uncertainties and their implications for various business decisions, before moving ahead with subsequent modeling and implementation activities. Specifically, we have shown that models are sensitive to the shape of the demand distribution, not only to single parameters such as expected demand or demand variation: skewness, minimum or maximum limits, or bimodality of demand can translate into significant differences in inventory levels, expected profits, or costs in different models. We have also shown that the model design has an impact on what is important in uncertainty modeling: for example, it was noted that in a facility location model, the amount of facilities is only dependent on the expected value of demand, whereas the size of each facility is dependent on the demand distribution shape. Further, we assessed the value of distributional information with a minmax regret analysis and concluded that the relative importance of knowledge about the distribution shape varies depending both on the model and its parameters. The analysis helps the decision maker to concentrate on specific features in demand uncertainty, when willing to obtain more information about the demand. It also allows assessing the trade-off between obtaining information and the cost of the required action. We believe that the utilization of qualitative distribution knowledge has major potential for applications, especially when most software make use of mean and variance only. Many useful methods and tools have already been developed to support the incorporation of qualitative knowledge into decision making models. For existing model-assisted decision processes, the distribution based sensitivity analysis helps in model validation and leads to more robust and risk-adjusted models.