Coordinated selection of procurement bids in finite capacity environments

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Abstract

Pressure to increase agility and reduce costs is pushing enterprises to dynamically select among offers from a broader range of suppliers. This process is facilitated by the adoption of web services standards. An important requirement in this context is the ability to move away from unidimensional price-based e-procurement models and develop richer solutions that are capable of capturing other important attributes in the selection of supplier bids. Research on the evaluation and selection of supplier bids (“winner determination”) has traditionally ignored the temporal and finite capacity constraints under which manufacturers and service providers often operate. We consider the problem faced by a firm that procures multiple key components or services from a number of possible suppliers. Bids submitted by suppliers include both a price and a delivery date. The firm has to select a combination of supplier bids that will maximize its overall profit. Profit is determined by the revenue generated by the products (or services) sold by the firm, the costs of the components (or services) it acquires as well as late delivery penalties it incurs if it fails to deliver its products/services in time to its own customers. We provide a formal model of this important class of problems, discuss its complexity and introduce rules that can be used to efficiently prune the resulting search space. We proceed to show that our model can be characterized as a pseudo-early/tardy scheduling problem and use this observation to build an efficient heuristic search procedure. Computational results show that our heuristic procedure typically yields solutions that are within a few percent from the optimum. They further indicate that taking into account the manufacturer/service provider’s capacity can significantly improve its bottom line.

Introduction

Today’s global economy is characterized by fast changing market demands, short product lifecycles and increasing pressure to offer high degrees of customization, while keeping costs and lead times to a minimum. In this context, the competitiveness of both manufacturing and service companies will increasingly be tied to their ability to dynamically select among multiple possible supply chain partners in response to changing market conditions. In this paper, we consider an environment where a firm needs to meet customer delivery commitments while procuring a combination of key components or services from multiple possible suppliers. At any point in time, components or services offered by different suppliers may vary both in terms of prices and delivery dates. Such a situation arises in a number of different contexts. This includes manufacturers with long-term relationships with more than one supplier (possibly independently managed plants owned by the same firm) as well as manufacturers or service providers dynamically selecting prospective suppliers in response to changing market demands. These latter scenarios arise in the context of capacity subcontracting in manufacturing and logistics [1], as well as in a wide range of other sectors (e.g., call center capacity, dynamic procurement of programming services (Programmingbids.com [19]), translation services (Language123.com [12]), and a growing number of other services [13]). These dynamic practices are increasingly facilitated by the emergence of web services standards, such as ebXML [6], W3C SOAP [26], OASIS UDDI [15]and W3C WSDL [27].

Prior research on bid selection (“winner determination”) has generally ignored temporal and capacity constraints under which companies operate (e.g., due dates by which different orders need to be delivered to customers as well as the limited capacity available to assemble components/services obtained from suppliers). The work presented herein shows that taking such constraints into account can help companies make more judicious decisions when it comes to selecting among multiple supply alternatives.

Specifically, we present techniques aimed at exploiting temporal and capacity constraints to help a firm select among supply alternatives that differ in price and delivery date. We refer to this problem as the Finite Capacity Multi-Component Procurement (FCMCP) problem. This article provides a formal definition of the FCMCP problem, discusses its complexity and introduces several rules that can be used to prune its search space. It presents an efficient pseudo-early/tardy heuristic search procedure that takes advantage of these pruning rules. Computational results show that accounting for the firm’s finite capacity can significantly improve its bottom line, confirming the important role played by finite capacity considerations in procurement problems. Results are also presented that compare the performance of our heuristic search procedures both in terms of solution quality and computational requirements under different supply profiles (or “bid profiles”). These results suggest that our pseudo-early/tardy procedure is generally capable of generating solutions that are within just a few percent from the optimum and that it scales nicely as problem size increases.

The balance of this paper is organized as follows. Section 2 provides a brief review of the literature. In Section 3, we introduce a formal model of the FCMCP problem. Section 4 identifies three rules that can help a firm (manufacturer or service provider) eliminate non-competitive procurement bids or bid combinations. Section 5 introduces a heuristic search procedure that exploits a property of pruned FCMCP problems introduced in Section 4 to solve the resulting problem as a pseudo-early/tardy scheduling problem. Section 6 presents a post-processing procedure that can further improve the quality of a solution. An extensive set of computational results are presented and discussed in Section 7. Section 8 provides some concluding remarks and discusses future extensions of this research.

Section snippets

Literature overview

A number of different studies have examined tradeoffs associated with different sourcing and procurement strategies, going back to work comparing Japanese and US sourcing and procurement models in the automotive industry in the late 80s [28]. More recent work includes that of Pyke and Johnson [20] who argue that different types of sourcing strategies are better suited for different situations: critical, high-value added components or components with complex interfaces are often better handled

The finite capacity multi-component procurement problem

The finite capacity multi-component procurement (FCMCP) problem involves a manufacturer or service provider (later referred to as the “manufacturer”) that has to satisfy a set of customer commitments or orders Oi, i  {1,  , m}, where m is the total number of orders (see Fig. 1). Table 1 provides a summary of the notations used in this article. Each order i needs to be completed by a due date ddi, and requires one or more components or services (later referred to as “components” or “supplies”),

Pruning the search space

In this section, we introduce several rules that can be used to prune the bid search space. The first pruning rule eliminates unnecessarily expensive bids with late delivery dates, while the second one eliminates expensive bids with unnecessarily early delivery dates. Following the application of these two rules, a third pruning rule is used to eliminate expensive bid combinations with unnecessarily early delivery dates. We proceed to show that, following the application of these three rules,

A pseudo-early/tardy heuristic

The Monotonic Property tells us that, following the application of the pruning rules, the procurement costs of non-dominated bid combinations strictly decrease as release dates increase. Fig. 4 plots the total procurement cost and tardiness cost of an order for different possible start times. While tardiness costs increase linearly with start times that miss the order’s due date, procurement costs vary according to a decreasing step-wise function. Specifically, the circles in Fig. 4 represent

Right-shifting procedure

Since the total cost function of each order is the sum of a linearly increasing tardiness cost function and a step-wise non-increasing earliness cost function, the total cost function has multiple local minima, as shown in Fig. 6. Meanwhile, the above pseudo-early/tardy heuristic dispatches orders as soon as the machine becomes available. Hence, the solution produced by the pseudo-early/tardy heuristic can sometimes be further improved by right-shifting orders to lower local minima without

Computational evaluation

A number of experiments have been run to evaluate the impact of our pruning rules, the performance of our heuristic search procedures, and the benefits of our FCMCP model over one-dimensional bid selection models that ignore the manufacturer’s finite capacity. These experiments are further discussed below.

Concluding remarks

The Web is facilitating the emergence of more flexible and expressive supply chain trading practices. In this article, we focused on a situation where a firm uses the Web to obtain and evaluate alternative procurement options for several of the components or services it needs to fulfill multiple customer delivery commitments. This problem is representative of the one faced by manufacturers with long-term relationships with more than one supplier as well as by manufacturers or service providers

Acknowledgement

The research reported in this paper has been funded by the National Science Foundation under ITR Grant 0205435.

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