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Description
1. Introduction
Flexibility is essential for businesses in order to deal with variability, uncertainty, and changes in the business environment. Manufacturing flexibility can be achieved in many ways including labor force, machinery, product mix, product design, or new products. Increasingly, companies are also turning to customer segmentation and tactical inventory decisions as a source of flexibility.
Differentiated service levels based on delivery time allow customers with an immediate need (e.g., businesses) to receive expedited product, while flexible customers receive incentives for their patience. An example of a company using differentiation is Amazon.com, where consumers can choose expedited shipping or free shipping. In the latter Amazon.com receives increased flexibility, since the stated leadtime exceeds the actual processing and transportation time. Customer segmentation by time, whether in manufacturing or the airline industry, provides a mechanism for balancing the supply and demand requirements of the system (e.g., shifting leisure travel from Friday to Saturday), which allows more efficient use of existing resources. A key example of a manufacturing company that employs flexibility in managing customer demand is Dell Inc. Customers are segmented according to type (e.g., business versus personal), and prices of products change regularly (Agrawal and Kambil, 2000).
The primary goal of this research is to provide tools for managing production and inventory tactically when customers differ in their willingness to pay and their willingness to wait. The key questions we address are how much to produce and how to allocate scarce resources (either current inventory or future limited production capacity) dynamically among different customer classes. We incorporate a firm's tactical inventory decisions, which we define to mean inventory or capacity allocations in one time period to serve customer demand in another time period. Specifically, we allow the firm to reserve inventory to satisfy future demand (sometimes called "discretionary sales"), and to plan backlogging, where the firm can accept orders in a period to be delivered in the future.
For example, many manufacturing companies face the following problem: some customers are willing to pay high prices to receive faster fulfillment, while other customers are willing to accept a lower priority for fulfillment, but they demand low prices. The manufacturer has limited production capacity, and in order to maximize profit, he needs to allocate the capacity effectively. With an advanced strategy, the manufacturer can separate the customers into multiple classes according to priority levels and then manage the production and the inventory appropriately; we refer to this as a differentiated strategy.
In this paper we study the Priority Differentiation Strategy (PDS), where we assume the first class pays a premium to have higher priority in the current period over production and inventory resources compared to the second class. We assume that the manufacturer can or is willing to prioritize demand classes. That is, the manufacturer makes a decision on higher priority demand before he accepts or rejects the lower priority demand requests. This situation might occur in practice when requests are submitted electronically and are handled in batches, or it could result from any working environment where a manufacturer may temporarily ignore requests from second-class customers. Studying the general model also allows us to analyze several situations that are special cases or extensions of it. For example, in some circumstances the manufacturer is not able or not allowed to differentiate the customers and will deal with them as a single class.
We assume demand in each period is a general function of price, is continuous and differentiable, and is lost if rejected; we do not make restrictive assumptions regarding the stochastic demand arrivals and the production process. We focus on a periodic-review environment where prices are predetermined but not known by customers until the current period. We initially assume backordered demand is fulfilled in the next period and extend our results to allow backorders until the end of the time horizon.
2. Literature review
One stream of literature related to our work is inventory theory, especially when there are multiple classes of customers. Two seminal papers in this area are Veinott (1965) and Topkis (1968). Veinott shows some conditions under which a base stock policy is optimal for the production decision when cost minimization is the goal. When parameters are time varying and the classes have different priorities, the demand from a higher class should be satisfied before demand from a lower class, and further restrictions are necessary on the costs. A related topic is considered by Topkis who extends the work of Veinott so as to be able to decide a set of critical levels that determine when to satisfy a particular class of demand. Topkis outlines some assumptions under which the optimal policy has a set of critical numbers (e.g., one assumption is that penalty costs must be cheaper now than in the future). In both Veinott (1965) and Topkis (1968), the classes of demand are essentially the same except for priority. In our case, there may be inherent differences between the classes of demand (e.g., willingness to wait or pay), and we may intentionally backlog customers or reserve inventory for future customers, which further distinguishes how the different classes may be served. In addition, we assume production capacity is limited, we do not make any assumptions on costs over time, and we allow revenue to depend upon customer class.
More recent research in inventory that is relevant includes Sobel and Zhang (2001). In this work, the authors study an inventory problem with fixed plus linear production costs and two demand classes. The deterministic demand class must be satisfied immediately, and the stochastic demand can be backlogged if there is not enough inventory. The main result is that a modified (s, S) policy is optimal. In our case, our production costs are simpler (linear only), but demand for both classes is stochastic and we allow tactical inventory.
Frank et al. (2003) add to the work, again considering one deterministic and one stochastic demand class. They allow the firm to specify how much of the stochastic demand to satisfy; this is somewhat similar to using discretionary sales. Their main result is that a state-dependent optimal policy exists but is quite complex, so they propose a heuristic policy of the form (s, k, S), where the rationing policy k specifies the amount of on-hand inventory to reserve for deterministic demand before ordering; thus, k also determines the inventory available to satisfy stochastic demand. Katircioglu and Atkins (1996) also consider production and allocation problems with multiple classes of customers. In this work, customer classes require different service levels, and they propose a heuristic that solves the problem myopically and is easy to implement. For our problem, the optimal policy has a simple structure and includes explicit decisions for reserving and backordering (other differences are as outlined above).
One stream of research that considers multiple classes of customers with stochastic demand in manufacturing focuses on rationing (see for instance, Moon and Kang (1998) or Dekker et al. (2002) as well as Topkis (1968) reviewed above). The term "rationing" is generally used to refer to the allocation of a resource such as capacity or inventory between competing customer classes. The results in this research area often describe threshold or critical levels that indicate the resource to be allocated to each class. This critical-level policy is optimal for some cases and is used as a heuristic in others. These papers generally focus on dynamic control of a single machine, and they do not consider production problems that span a number of periods with non-stationary parameters. In our case we find threshold values of this type (see the nesting policy for PDS), and we also incorporate resource allocations across time periods.
In most of the described results in the rationing area, a key assumption is that demand is Poisson (see for example, Balakrishnan et al. (1996) and Melchiors et al. (2000)). In some, there is also an assumption that the production time is exponential (Ha, 1997). The most relevant work in this stream is Ha (2000), who assumes demand is Poisson and the processing time is Erlang. The key contribution is that the optimal policy has critical levels with monotonic properties. This policy is most similar to the one we find for PDS in this paper, although in our case we have limited production capacity and tactical inventory. We also consider leadtime differences explicitly and allow planned backlogs.
An important paper that allows tactical inventory is Scarf (2000), who introduced discretionary sales into a problem with fixed production setup costs and one customer class. In his case, a base stock type of policy is optimal for production, but unlike the production decision, the optimal discretionary sales decision should be decided after demand is revealed in a given period in order to achieve the maximum profit. The use of discretionary sales is also analyzed in Chan et al. (2006), which considers a single-class stochastic inventory model with multi-period pricing and production decisions under limited capacity when demand is a general stochastic function.
In the current paper, we build on our work in Chan et al. (2006), where we found that a modified base stock policy with a production and reserving decision pair was optimal, in which the optimal values do not depend on the demand that arrives if price is decided in advance. A fundamental difference in the current research is that we add multiple classes of customers who differ in their willingness to wait (and pay), and we allow delayed fulfillment. The current work also builds on Liu and Simchi-Levi (2003), who extended Chan et al. (2005) to allow delayed fulfillment until the end of the horizon.
The rest of this paper is organized as follows. In Section 3, we introduce and analyze the PDS and non-differentiation strategies. We perform computational analysis to compare expected profits under the two strategies in Section 4 to explore the effectiveness of market segmentation in manufacturing. Conclusions are contained in Section 5.
3. Models and results
We focus on a single product sold at a single manufacturer over a multi-period time horizon, where the manufacturer has limited production capacity in each period. The manufacturer serves two customer classes, whose demand is ordered by class (i.e., sorted by priority). This means that in any period, first-class demand is fully known by the manufacturer before he has to make a decision regarding second-class demand. The customers of these two classes differ in their priority level and willingness to pay. The first-class customers are willing to pay a premium over the price of the second-class customers in order to have priority access in the current period to both on-hand inventory and backlogging availability. Thus, by paying the premium, first-class customers are satisfied first with the inventory and backlogging resources available to the manufacturer in the current period, and the demand of the second-class customers is addressed with the remaining resources.
The main model that we will consider throughout this paper is the PDS, where we assume that the manufacturer has the ability to differentiate the customer classes. We seek... |
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