Managing an Available-to-Promise Assembly System with Dynamic Pseudo Order Forecast Susan H. Xu Department of Supply Chain and Information Systems Smeal

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 BusinessPenn State University

(Joint work with Long Gao, UC Riverside)Presentation in

Department of DS&ME Faculty of Business AdministrationChinese University of Hong Kong

June 13, 2011

Outline

1. Motivation and problem statement

2. Literature

3. An ATP-A modela. A pseudo order model with dynamic forecast

b. Dynamic programming formulation

4. Characterizations of the optimal policya.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)

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


2. Literature








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 practicesMost 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


2. Literature








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: (It,Qt,Nt,Et):

It is the net inventory, i.e., inventory on hand minus inventory backlogs at the beginning of period t, before planned inventory St is received

Qt is the net capacity, i.e., zero minus capacity backlogs, at the beginning of period t, before the planned capacity Kt is received (Qt cannot be positive)

Nt is the realized demand vector in period t

Et is the future pseudo order forecasted in period t

Decision vector: xt is the accepted demand vector subject to demand and resource availability constraints

DP Formulation: Optimality Equations

The action set At satisfies

The net inventory and net capacity are updated as

Outline


2. Literature








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 xt 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.


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


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 balancingThe 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. Vt is a generalized submodular function of (It,Qt)

Intuitively, Theorem 4 means that the marginal value of each resource diminishes as both resource levels increase pairwiseNotably, Vt is neither supermodular nor submodular in (It,Qt), 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 demandWe 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

Documents

Managing an Available-to-Promise Assembly System with Dynamic Pseudo Order Forecast Susan H. Xu Department of Supply Chain and Information Systems Smeal