Commonality and postponement in multistage assembly systems

Abstract

Postponement of the point of differentiation and the use of common components for different products (commonality) are important methodologies for managing product variety and maintaining competitiveness in the age of mass customization and supply chain competition. This paper focuses on the dynamics between the processing time and the component procurement leadtime and its impact on commonality and postponement decisions. We formulate a multi-period and multistage assembly network model with multiple products and stochastic demands, and propose a scheme to express the desired base-stock level at each stocking point as a function of the corresponding achieved fill rate. By requiring high component availability, as commonly practiced in industry, stages can be “de-coupled” and closed-form results for the base-stock levels and inventory costs can then be derived. We can then demonstrate analytically whether introducing commonality at a particular stage or delaying the point of differentiation by one more stage can be justified. We found that a key factor for commonality and postponement decisions is the interactions between processing and procurement leadtimes. This leadtime factor is unique to multistage systems. Although a number of simplifying assumptions are made in our model, our analysis indicates that some important observations regarding the pooling effect and leadtime dynamics should still be true for more general systems.

Introduction

Component commonality generally refers to an approach in manufacturing in which two or more different components for different end products (of perhaps the same product family) are replaced by a common component that can perform the functions of those it replaces. Using common components continuously along the line, the point of product differentiation can also be postponed. Commonality and postponement are not new concepts. Alderson (1950) was the first to analyze the concept of postponement in marketing literature while Dogramaci (1979) provided a early study of component commonality from a risk pooling perspective. Both concepts are now attracting renewed attention as companies are compelled to provide and manage an increasing product variety and to compete in supply chain excellence in a global market. In this paper, we study component commonality and manufacturing postponement in multistage and multi-product assembly systems.

Component commonality reduces the total number of distinct components and can bring about benefits in a variety of functional areas throughout a firm. The major benefits of commonality are risk-pooling and leadtime uncertainty reduction. These lead to a safety stock reduction and have been studied extensively by many researchers, including, but not limited to, Baker et al. (1986), Collier (1982), Guerrero (1985), Gerchak et al. (1988), Eynan and Rosenblatt (1996), and Grotzinger et al. (1993). Commonality also has the following additional benefits: improving the economy of scale through larger order sizes; simplifying planning, scheduling and control; and streamlining and speeding up product development processes. Discussion of these benefits can be found in Collier, 1981, Collier, 1982, Thomas (1981), Walleigh (1989), Berry et al. (1992), Vakharia et al. (1996), Hopson et al. (1989), Baldwin and Clark (1997), and Sheu and Wacker (1997).

There are also costs for using a common component, including higher unit component costs due to excessive performance, higher workload variability (imbalance in workload) and more variable work-in-process inventory levels (Collier, 1982; Bott and Ritzman, 1983; Tsubone et al., 1994; Vakharia et al., 1996; Guerrero, 1985). These costs and benefits will determine the suitability of a commonality strategy and should be quantified.

Commonality has been a subject of study for over two decades. Dogramaci (1979) authored one of the early publications on commonality. From a risk-pooling perspective, he noted that the use of common components across multiple end items reduces forecasting errors. Collier (1981) proposed a commonality measure, the degree of commonality index (DCI), to study the effect of commonality on setup and holding costs. Collier (1982) analyzed the effect of commonality on the aggregate safety stock requirement and found it to be an inverse function of DCI. Thomas (1981) and Wacker and Treleven (1986) also analyzed the impact of the commonality index.

Baker (1985) considered the impact of correlated component demands on safety stock requirements. He pointed out that the traditional (safety stock) zσ-policy might not be sufficient to provide the desired service level. Baker et al. (1986) analyzed a problem with two end items with independent and uniformly distributed demands. They drew the following conclusions: (1) the total inventory (in number of units) decreases with commonality; (2) the inventory level of the common component is smaller than the combined inventory levels of the components it replaces; and (3) the inventory levels of non-common components increase with commonality. This work was later extended to a model with multiple end products and fairly general demand patterns in Gerchak et al. (1988). They considered the cost minimization subject to a service level constraint and found that while property (1) (see above) is still true, (2) and (3) may not necessarily hold. Bagchi and Gutierrez's model maximizes the service level for a fixed total number of units in stock (cf. Bagchi and Gutierrez, 1992). For exponential and geometric demand distributions, they found that the marginal cost reduction increases with commonality.

Eynan and Rosenblatt (1996) demonstrated that commonality might not always be a preferred strategy for some component cost structures and presented conditions under which commonality should not be used. Eynan (1996) studied a commonality model with correlated demands and showed that the impact of commonality is stronger with negative correlation. Vakharia et al. (1996) investigated the impact of increased parts commonality on the operating characteristics of a manufacturing firm using an MRP system. Through simulation, they showed that while the average shop load decreases, the loading variability increases.

Most authors used aggregate service levels in their models with the exception of Baker (1985). Recently, Mirchandani and Mishra (1999a) studied the commonality problem in a two-stage assembly system with a product-specific service level (PSL) requirement. They showed that since ASL may provide a higher than necessary service level, the use of PSL leads to additional inventory savings.

A number of authors have focused their research on computational issues in commonality models. For example, Hillier (1998) developed bounds on the multi-period cost for Gerchak and Henig's profit maximization model (cf. Gerchak and Henig, 1986). Jönsson and Silver (1989), Jönsson et al. (1993), Tayur (1995) and Mirchandani and Mishra (1999b) developed computational approaches to solve large-scale commonality problems.

In a manufacturing–distribution system, a considerable portion of the risk and uncertainty costs is due to differentiation in form, place, and time. Postponement of the point of differentiation is an important means to reducing or eliminating this risk and uncertainty. This has long been recognized and studied in marketing and logistics literature. Many authors have provided extensive analysis of the benefits of postponement and various postponement strategies from marketing, logistics, and supply chain perspectives. These include, but are not limited to, Alderson (1950), Bucklin (1965), Zinn and Bowersox (1988), Child et al. (1991), Maskell (1991), Stern and El-Ansary (1992), Cooper (1993), Lee and Billington (1994), Feitsinger and Lee (1997), and Pagh and Cooper (1998). In addition to many of the same benefits as those described above from commonality, postponement can also shorten the configuration and customization leadtime, improve forecasting accuracy by shortening the forecasting time horizon, and enhance a firm's flexibility and responsiveness in an uncertain and changing market. While early studies were primarily qualitative, some recent works have focused on the quantitative modeling of the benefits and criteria of various postponement strategies, for example, Lee, 1993, Lee, 1996, Howard (1994), Lee and Billington (1994), Lee and Feitzinger (1995), Garg and Tang (1997), and Garg and Lee (1997). Lee (1996) presented a model that captures the effect of postponement on inventory reduction. Lee and Tang (1997) extended Lee's work in a number of ways. The authors allowed holding inventories of semi-finished goods at different points of the process instead of only finished goods inventory and incorporated additional factors such as design and processing costs and production leadtimes. They also presented three different postponement approaches, namely standardization, modular design, and process restructuring.

The above literature review reveals that the current research on commonality has mainly focused on its pooling effect on the safety stock at a single location (single-stage). Although, multistage production system dynamics will interact with a commonality strategy and may lead to different outcomes, this important aspect is largely unexplored in the literature. In postponement, Lee and Tang's work is closely related to ours. The main difference is that we focus on the standardization approach and consider component procurement leadtimes along an assembly line. Thus our model considers component inventory cost explicitly and captures the dynamics of component procurement leadtimes and production leadtimes. We will examine how interactions among assembly leadtimes, procurement leadtimes, and the end-product service level requirement affect a postponement decision. Our objective is to derive analytical results that can clearly demonstrate the effect of the leadtime interactions. To achieve this objective, we make a number of assumptions to simplify the model. It will be argued that these assumptions do not affect the basic leadtime dynamics and can thus be justified for complicated multistage assembly systems.

We organize the paper in seven sections. In 2 The model, 3 Base-stock levels, we present the model formulation and some analytical results mainly for the commonality problem, although with minor changes, these results can also be used for the postponement decision. In Section 4, we focus on a de-coupled assembly system and derive an analytical approximation of the cost function associated with a commonality decision. We also discuss the properties of the cost function and provide some managerial insights into how to formulate a component commonality strategy for multistage systems. In Section 5, we formulate a model for postponement in de-coupled systems and demonstrate that the criterion to delay the point of differentiation by one more stage is the same as that of using a common component in that stage. In Section 6, we provide further analysis of the properties of the cost function under some specific scenarios for both commonality and postponement models. We conclude the paper in Section 7 and point out some future research directions.