Thomas R. Ervolina

Two strongly polynomial cut cancelling algorithms for minimum cost network flow

Abstract We present two new strongly polynomial algorithms for the minimum cost network flow problem (MCNF). They are dual algorithms based on cancelling positive augmenting cuts, which are the duals of negative augmenting cycles. The first cancels maximum mean cuts, which are cuts whose increase in the dual objective function per arc is maximum. The second, Dual Cancel and Tighten, employs a more flexible cut selection rule that allows it to be more efficient. These algorithms are duals to the Minimum Mean Cycle Cancelling and (Primal) Cancel and Tighten algorithms of Goldberg and Tarjan. These algorithms do not use explicit scaling to achieve polynomiality.

Computing maximum mean cuts

Abstract Most primal minimum cost network flow (MCNF) algorithms can be seen as variants on cancelling negative augmenting cycles. The analogous view of dual MCNF algorithms is that they cancel positive augmenting cuts. In a companion paper we show that if a dual algorithm chooses to cancel cuts which have the greatest rate of increase in dual objective value per arc, which are called maximum mean cuts, a strongly polynomial algorithm results. However, this result depends on being able to compute maximum mean cuts in polynomial time. In this paper we present an efficient parametric algorithm that computes maximum mean cuts by doing O (min{ n, log (nU) (l+ loglog (nU)− loglog n) }) min cut calculations (these bounds are due to Radzik (1992)) where U is the largest absolute arc capacity.

Managing product availability in an assemble-to-order supply chain with multiple customer segments

In this article, we propose a novel availability management process called Available-to-Sell (ATS) that incorporates demand shaping and profitable demand response to drive better supply chain efficiency. The proposed process aims at finding marketable product alternatives in a quest to maintain a financially viable and profitable product portfolio, and to avoid costly inventory overages and shortages. The process is directly supported by a mathematical optimization model that enables on demand up-selling, alternative-selling and down-selling to better integrate the supply chain horizontally, connecting the interaction of customers, business partners and sales teams to procurement and manufacturing capabilities of a firm. We outline the business requirements for incorporating such a process into supply chain operations, and highlight the advantages of ATS through simulations with realistic production data in a computer manufacturing environment. The models featured in this paper have contributed to substantial business improvements in industry-size supply chains, including over

Canceling most helpful total cuts for minimum cost network flow

100M of inventory reduction in IBM’s server computer supply chain.

Supply and Demand Synchronization in Assemble-to-Order Supply Chains

We present a polynomial algorithm for the minimum cost network flow problem (MCNF). It is a dual algorithm that is based on canceling positive augmenting cuts, which are the duals of negative augmenting cycles. We focus on canceling most helpful total cuts, which are cuts together with augmentation amounts that lead to the maximum possible increase in the dual objective function. We show how to compute a most helpful total cut and give a rigorous dual conformal decomposition theorem. Canceling most helpful cuts is, in spirit, dual to an algorithm of Weintraub as modified by Barahona and Tardos. We also show how our algorithm specializes to the case of shortest s–t path with nonnegative distances, show that this specialization is not finite for real data, and show that our bound on the number of cancellations is essentially tight.

Simulating order fulfillment with product substitutions in an assemble-to-order supply chain

In this chapter, we describe a methodology for effectively synchronizing supply and demand through the integrated use of supply and demand flexibilities. While most prior literature focuses on the concept of Available-To-Promise (ATP) to determine product availability, we propose a new methodology called Available-To-Sell (ATS) that incorporates firm-driven product substitutions into capitalize on up-sell and alternative-sell opportunities in the production planning phase. ATS aims at finding marketable product alternatives that replace demand on supply-constrained products while minimizing expected stock-out costs for unfilled product demand and holding costs for leftover inventory. It enables a firm to maintain a financially viable and profitable product portfolio, taking effective actions to avoid excess component inventory, and articulating marketable product alternatives. We formulate a mathematical programming model to analyze the performance of ATS, and show how to exploit the structural properties of the model to develop an efficient solution procedure utilizing column generation techniques. The model can easily be embedded into a firm’s supply chain operations to improve day-to-day flexibility.

Framework for manufacturing logistics decision support

In todays competitive and dynamic business environment, companies need to continually evaluate the effectiveness of their supply chain and look for ways to transform business processes to achieve superior customer service and higher profitability. In this paper we propose a novel availability management process called available-to-sell (ATS) that incorporates demand shaping and profitable demand response to drive better operational efficiency through improved synchronization of supply and demand. We develop an order fulfillment simulation model to assess how the proposed availability management system affects supply chain performance, and apply the model in a server computer manufacturing environment. The simulation plays an important role in making strategic business decisions that impact customer service, revenue and profitability