Managing an Available-to-Promise Assembly System with Dynamic Pseudo Order Forecast Susan H. Xu Department of Supply Chain and Information Systems Smeal College of Business Penn State University (Joint work with Long Gao, UC Riverside) Presentation in Department of DS&ME Faculty of Business Administration Chinese University of Hong Kong June 13, 2011

Outline 1. Motivation and problem statement 2. Literature 3. An ATP-A model a. A pseudo order model with dynamic forecast b. Dynamic programming formulation 4. Characterizations of the optimal policy a. Class prioritization b. Capacity-Inventory-Demand (CID) matching c. Resource Imbalance Based (RIB) rationing 5. Numerical results 6. Concluding Remarks and Contributions

What is a pseudo order? Pseudo orders are tentative customer orders in a B2B environment Sales personnel often maintain information of attributes of pseudo orders, including revenue, the likelihood of order cancellation, order quantity, confirmation timing, etc. Attributes of pseudo orders evolve over time and sales personnel revise pseudo order forecasts frequently pseudo orders tend to be lumpy, non-stationary and volatile In this paper, we consider an available-to-promise assembly (ATP-A) system whose demands constitute of pseudo orders

What is an Available-to-Promise (ATP) system? ATP is a business function that matches incoming orders to available resources to achieve high profitability Due to long procurement lead times, ATP resources during the execution period are planned in advance based on long-term demand forecasts ATP specifies acceptance and production scheduling decisions relative to a set of orders with different profitability Through BOM, ATP matches accepted orders to available system resources, and delivers these orders within a quoted lead time

ATP example: Toshiba Toshiba uses an electronic ATP system to process orders from different classes of its business customers Orders for several thousand models are collected and processed by a single central order processing system Book orders up to 10 weeks in advance of delivery Sales Division keeps track of and updates pseudo order information and critical resources are frequently reserved for high priority future orders Similar ATP systems and business practices are also used by Dell, Intel and Maxtor for order promising and fulfillment (Ball et al. 2004)

ATP examples: Dell Dell’s two-stage order promising practice Customer differentiation: home, small, medium and large businesses, education, government, etc. Provide initial soft confirmation via Generate hard confirmation after checking resource availabilities Critical resources are frequently reserved for high- value, future pseudo orders.

Objectives However, ATP business practices typically are ad hoc The academic literature implicitly assumes pseudo orders are firm orders, or their attributes are static Objectives: develop models and tools to integrate dynamic pseudo order information into ATP systems study the policy structure for the ATP-A system that contains both perishable (e.g. capacity) and non-perishable (e.g., inventory) resources Investigate numerically when and how to use noisy pseudo order information and the robustness of the optimal policy

ATP-A system: modeling constructs Demand: J classes of pseudo orders available at the beginning of the ATP execution horizon, with revenues satisfying r1>r2>…>rJ In each period t, ATP-A receives firm orders Nt(i.e., realized pseudo orders confirmed in period t) from J classes and makes order acceptance decisions Attributes of future pseudo orders are updated dynamically in each period ATP resources: Two types of resources, production capacity and component inventory, are shared among all classes Resource levels of both types in each period are exogenously given: planned capacity Kt and planned inventory St become available in period t, 1≤ t ≤T BOM requirement: One manufactured unit: uses one unit of capacity and needs a single period to produce One inventory unit The manufactured unit and the inventory unit are assembled into an end product Assembly time is negligible An accepted order must be filled before the delivery lead time L (a hard constraint), same for all classes

Outline 1. Motivation and problem statement 2. Literature 3. An ATP-A model a. A pseudo order model with dynamic forecast b. Dynamic programming formulation 4. Characterizations of the optimal policy a. Class prioritization b. Capacity-Inventory-Demand (CID) matching c. Resource Imbalance Based (RIB) rationing 5. Numerical results 6. Concluding Remarks and Contributions

Literature Imperfect Advance Demand Information (ADI) in production-inventory systems: DeCroix and Mookerjee 1997, Tan et al. 2007, Gayon et al. (2009), Benjaafar et al. (2011), among others The ATP Literature: Ball et al. (2004): A survey paper on ATP research and practices Most studies employ optimization techniques to study various aspects of ATP decisions, including delivery lead time quotations (Taylor and Plenert 1999, Hopp and Sturgis 2001) resource allocation (Ervolina and Dietrich 2001) production scheduling (Moses et al. 2002) requirements planning (Balakrishnan and Geunes 2000), order promising (Kilger and Schneeweiss 2000, de Kok 2000, Robinson and Carlson 2007, Chen et al. 2008)

Outline 1. Motivation and problem statement 2. Literature 3. An ATP-A model a. A pseudo order model with dynamic forecast b. Dynamic programming formulation 4. Characterizations of the optimal policy a. Class prioritization b. Capacity-Inventory-Demand (CID) matching c. Resource Imbalance Based (RIB) rationing 5. Numerical results 6. Concluding Remarks and Contributions

An Example of Dynamic Pseudo Order Forecast (two classes)

A Markov chain model for dynamic pseudo order forecast

Dynamic Programming Formulation State of the System : (I t,Q t,N t,E t ): I t is the net inventory, i.e., inventory on hand minus inventory backlogs at the beginning of period t, before planned inventory S t is received Q t is the net capacity, i.e., zero minus capacity backlogs, at the beginning of period t, before the planned capacity K t is received ( Q t cannot be positive) N t is the realized demand vector in period t E t is the future pseudo order forecasted in period t Decision vector : x t is the accepted demand vector subject to demand and resource availability constraints

DP Formulation: Optimality Equations The action set A t satisfies The net inventory and net capacity are updated as

Outline 1. Motivation and problem statement 2. Literature 3. An ATP-A model a. A pseudo order model with dynamic forecast b. Dynamic programming formulation 4. Characterizations of the optimal policy a. Class prioritization b. Capacity-Inventory-Demand (CID) matching c. Resource Imbalance Based (RIB) rationing 5. Numerical results 6. Concluding Remarks and Contributions

Structural Properties of the optimal policy We show that in the ATP-A system, the optimal acceptance policy has three key drivers: Class Prioritization: confirmed orders should be accepted in a decreasing order of their profitability Resource Imbalance-Based (RIB) Rationing: the two-resource rationing control can be achieved by the inventory rationing control alone, and the inventory rationing threshold depends only on the net resource imbalance level rather than individual resource levels Capacity-Inventory-Demand (CID) Matching: availability of perishable and nonperishable resources should be kept balanced and also matched with demand as closely as possible.

Class Prioritization Due to Class Prioritization, we can replace decision vector x t in DP by the totally accepted demand x, assuming a higher-reward class will be accepted before a lower-reward class

Resource Imbalance-Based Rationing Theorem 2 The optimal acceptance policy is a multilevel base- demand acceptance policy, with the base-demand acceptance level of the first j classes satisfying For each j, cumulative demands of the first j classes are accepted until one of the following constraints is met: a) the base-demand acceptance level for the first j class is reached b) all realized demands of the first j classes are all accepted c) either the available inventory or available capacity during lead time L, is exhausted.

Resource Imbalance-Based Rationing Theorem 3 (RIB Rationing) The optimal order acceptance policy is a multilevel inventory rationing policy, with inventory rationing levels satisfying For each j, demands from the first j classes are accepted until one of the following constraints is met: a) the rationing level for the first j classes is reached b) The first j classes of confirmed demands are all accepted c) either the available inventory or capacity during lead time L is exhausted is exhausted

Resource Imbalance-Based Rationing Remarks: At the level of the optimal rationing pair, the marginal value of a unit pair of resources equals the marginal profit of class j demand RIB rationing captures not only the notion of resource reservation, but also the notion of resource balancing The rationing level decreases in the resource imbalance level (capacity overage) Due to the positive delivery lead time, the optimal inventory rationing level can be either positive or negative. As such, RIB rationing can reserve resources for both current and future higher-valued orders

Capacity-Inventory-Demand Matching Theorem 4. V t is a generalized submodular function of (I t,Q t ) Intuitively, Theorem 4 means that the marginal value of each resource diminishes as both resource levels increase pairwise Notably, V t is neither supermodular nor submodular in (I t,Q t ), i.e., the marginal value of one resource is not monotone as another resource level increases Marginal value of capacity is low when inventory is either scarce (because additional capacity cannot be utilized due to lack of inventory) or excess (because additional capacity is not needed due to lack of demand) To achieve high resource utilization and profitability, resources must be properly balanced and closely aligned with demand We refer to this property as CID matching.

Numerical Results: CID Matching This example illustrates the concept of CID matching, i.e., each value function achieves the maximum value when planned capacity K is slightly above planned inventory S

Marginal Value of Resources Marginal value of capacity diminishes as both resource levels increase pairwise Marginal value of capacity is not monotone as inventory increases

Numerical result: Value of dynamic pseudo order forecast An accurate short-term forecast significantly improves ATP performance over an accurate long-term forecast, when the planned resource is moderate and customer heterogeneity is high (over 6%)

Impact of Dynamic Pseudo Order Forecast

Numerical result: Value of dynamic pseudo order forecast An accurate short-term forecast significantly improves ATP performance over an accurate long-term forecast, when the planned resource is moderate and customer heterogeneity is high (over 6%) The “optimal policy” under a biased short-term forecast with small to moderate forecasting errors (<25~30%) is robust, and outperforms the optimal policy under an accurate long-term forecast The optimal policy under an accurate long-term forecast should be used when short-term forecast errors are significant Firms need effective sales force monitoring systems and forecast mechanisms. Compared with underestimating, overestimating potential sales, as is often the case for sales personnel, causes more harm to firms.

Contributions We develop a Markov chain modeling framework to capture stochastic attributes of ever-changing real-time demand information, which appears to be a new research endeavor To a larger extent, we demonstrate how real-time, dynamic data sources can be used to support execution-level decision making, while most supply chain decision models have been based on stable demand forecasts We integrate the dynamic short-term forecast in an ATP-A environment and gain insights on how two types of resources should be managed We derive strong analytical results for the optimal policy and show that class prioritization, CID matching and RIB rationing are the three key principles driving the optimal policy in the ATP-A system Our numerical results shed lights on when and how the dynamic pseudo order forecast generates values and should be incorporated into ATP decisions Our insights can be applied to other problem context such as revenue management