Sridhar R. Tayur

Value of Information in Capacitated Supply Chains

We incorporate information flow between a supplier and a retailer in a two-echelon model that captures the capacitated setting of a typical supply chain. We consider three situations: (1) a traditional model where there is no information to the supplier prior to a demand to him except for past data; (2) the supplier knows the (s, S) policy used by the retailer as well as the end-item demand distribution; and (3) the supplier has full information about the state of the retailer. Order up-to policies continue to be optimal for models with information flow for the finite horizon, the infinite horizon discounted and the infinite horizon average cost cases. Study of these three models enables us to understand the relationships between capacity, inventory, and information at the supplier level, as well as how they are affected by the retailers (S - s) values and end-item demand distribution. We estimate the savings at the supplier due to information flow and study when information is most beneficial.

A Capacitated Production-Inventory Model with Periodic Demand

For a single product, single-stage capacitated production-inventory model with stochastic, periodic (cyclic) demand, we find the optimal policy and characterize some of its properties. We study the finite-horizon, the discounted infinite-horizon and the infinite-horizon average cases. A simulation based optimization method is provided to compute the optimal parameters. Based on a numerical study, several insights into the model are also provided.

Due Date Management Policies

To gain an edge over competitors in an increasingly global and competitive marketplace, companies today need to differentiate themselves not only in cost, but in the overall “value” of the products and the services they offer. As customers demand more and more variety of products, better, cheaper, and faster, an essential value feature for customer acquisition and retention is the ability to quote short and reliable lead times. Reliability is important for customers especially in a business-to-business setting, because it allows them to plan their own operations with more reliability and confidence [67].

On Bipartite and Multipartite Clique Problems

In this paper, we introduce the maximum edge biclique problem in bipartite graphs and the edge/node weighted multipartite clique problem in multipartite graphs. Our motivation for studying these problems came from abstractions of real manufacturing problems in the computer industry and from formal concept analysis. We show that the weighted version and four variants of the unweighted version of the biclique problem are NP-complete. For random bipartite graphs, we show that the size of the maximum balanced biclique is considerably smaller than the size of the maximum edge cardinality biclique, thus highlighting the difference between the two problems. For multipartite graphs, we consider three versions each for the edge and node weighted problems which differ in the structure of the multipartite clique (MPC) required. We show that all the edge weighted versions are NP-complete in general. We also provide a special case in which edge weighted versions are polynomially solvable.

Computing the Optimal Policy for Capacitated Inventory Models

We consider an infinite-horizon inventory model with finite production capacity and stochastic demands. Federgruen and Zipkin [2][3] showed that a base-stock policy is optimal; however, they did not provide an algorithm for the computation of the optimal policy or the cost. We provide, for the average cost criteria, an algorithm to compute the critical number and the associated cost. Our approach uses results from the theory of storage processes and multi-stage uncapacitated systems

Quantitative Analysis for Internet-Enabled Supply Chains

A supply chain, from an operations perspective, has three components: sourcing or procurement, manufacturing and distribution, and inventory disposal. In each component, the Internet is significantly affecting how supply chains are being managed, leading to new challenges while ultimately promising to provide value. The likely future is collaborative supply-chain management that promises to make, for the first time, the dream of virtual integration a reality. Quantitative modeling provides companies decision support as well as insights for better management of supply chains. But there are still a number of challenges that require further OR/MS analysis.

The Stability of a Capacitated, Multi-Echelon Production-Inventory System Under a Base-Stock Policy

Most models of multilevel production and distribution systems assume unlimited production capacity at each site. When capacity limits are introduced, an ineffective policy may lead to increasingly large order backlogs: The stability of the system becomes an issue. In this paper, we examine the stability of a multi-echelon system in which each node has limited production capacity and operates under a base-stock policy. We show that if the mean demand per period is smaller than the capacity at every node, then inventories and backlogs are stable, having a unique stationary distribution to which they converge from all initial states. Under i.i.d. demands we show that the system is a Harris ergodic Markov chain and is thus wide-sense regenerative. Under a slightly stronger condition, inventories return to their target levels infinitely often, with probability one. We discuss cost implications of these results, and give extensions to systems with random lead times and periodic demands.

A comparison of alternative kanban control mechanisms. I: Background and structural results

The design of inventory control policies for serial systems is a topic currently being explored by a number of researchers. Our goal -in two papers - is to synthesize and extend some of these efforts. We consider, simultaneously, four sources of variability in production lines - processing time variability, machine breakdowns, rework and yield loss - and show some similarities and differences in their effects on the performance of the line. In this paper we introduce an enhanced model that accommodates raw material and demand uncertainity and demonstrate that many of the sample path results obtained previously can be extended. The main objectives of this paper are: (1) to demonstrate that Constant-Work-in-Process (CONWIP) and the traditional kanban control are just two extremes in a finite family of implementable pull controls; (2) to show that while machine breakdowns, rework and random processing times have a similar effect in terms of the optimal decisions, yield losses in the line may have to be manag...

Optimal Policies and Simulation-Based Optimization for Capacitated Production Inventory Systems

The motivation for this stream of research has come from problems faced by diverse set of companies, such as IBM, AMD, Allegheny Ludlum, GE, Proctor and Gamble, Westinghouse, Intel, American Standard, McDonald’s, and Caterpillar. Smaller local (to Pittsburgh) companies such as Sintermet, Blazer Diamond, ASKO and Northside Packing have also provided several interesting issues to pursue. At the heart of many of the problems is the interaction between demand variability and non-stationarity, available production capacity, holding costs of inventory (at different locations), lead times and desired service levels. The central goal of this research stream is to understand the interactions in simple single and multiple stage settings and to provide insights and implementable solutions for managing inventories in a cost-effective manner for complex systems. The goal of this chapter is to introduce in a systematic manner some recent advances in ‘Discrete-time, Capacitated Production-Inventory Systems facing Stochastic Demands’ and we limit ourselves to single product setting. The material here is collected from papers that have appeared in the literature: [31, 22, 23, 48, 49].

A simple approximation for a multistage capacitated production-inventory system

We develop a simple approximation for multistage production‐inventory systems with limited production capacity and variable demands. Each production stage follows a base‐stock policy for echelon inventory, constrained by production capacity and the availability of upstream inventory. Our objective is to find base‐stock levels that approximately minimize holding and backorder costs. The key step in our procedure approximates the distribution of echelon inventory by a sum of exponentials; the parameters of the exponentials are chosen to match asymptotically exact expressions. The computational requirements of the method are minimal. In a test bed of 72 problems, each with five production stages, the average relative error for our approximate optimization procedure is 1.9%.