Karthik Sourirajan

A genetic algorithm for a single product network design model with lead time and safety stock considerations

We consider a two-stage supply chain with a production facility that replenishes a single product at retailers. The objective is to locate distribution centers in the network such that the sum of facility location, pipeline inventory, and safety stock costs is minimized. We explicitly model the relationship between the flows in the network, lead times, and safety stock levels. We use genetic algorithms to solve the model and compare their performance to that of a Lagrangian heuristic developed in earlier work. A novel chromosome representation that combines binary vectors with random keys provides solutions of similar quality to those from the Lagrangian heuristic. The model is then extended to incorporate arbitrary demand variance at the retailers. This modification destroys the structure upon which the Lagrangian heuristic is based, but is easily incorporated into the genetic algorithm. The genetic algorithm yields significantly better solutions than a greedy heuristic for this modification and has reasonable computational requirements.

A single-product network design model with lead time and safety stock considerations

Most existing network design and facility location models have focused on the trade-off between the fixed costs of locating facilities and variable transportation costs between facilities and customers. However, operational performance measures such as service levels and lead times are what motivates customers to bring business to a company and should be considered in the design of a distribution network. While some previous work has considered lead times and safety stocks separately, they are closely related in practice, since safety stocks are often set relative to the distribution of demand over the lead time. In this paper we consider a two-stage supply chain with a production facility that replenishes a single product at retailers. The objective is to locate Distribution Centers (DCs) in the network such that the sum of the location and inventory (pipeline and safety stock) costs is minimized. The replenishment lead time at the DCs depends on the volume of flow through the DC. We require the DCs to carry enough safety stock to maintain the prescribed service levels at the retailers they serve. The explicit modeling of the relationship between the flows in the network, lead times and safety stocks allows us to capture the trade-off between them. We develop a Lagrangian heuristic to obtain near-optimal solutions with reasonable computational requirements for large problem instances.

Joint Pricing and Production Decisions in an Assemble-to-Order System

This paper studies coordinated pricing and production decisions in an assemble-to-order system. We first show that unlike in make-to-stock systems, a state-dependent base-stock list-price policy is optimal. The optimal state-dependent base-stock levels and list prices may increase or decrease as demand backlogs increase, whereas demand backlogs always improve the optimal expected profit. Because the problem easily becomes intractable under general system settings, we next develop a simple heuristic policy. The heuristic policy decouples inventory replenishment, pricing, and component allocation decisions in a coordinated way. We provide a sufficient condition that ensures the optimality of the heuristic policy, and present a numerical study to demonstrate its performance when the condition is not met. The numerical study also shows how the performance of the heuristic policy is affected by various market and operational conditions, and by the structure of the assemble-to-order system. By focusing on the simple W-model, we show how the heuristic pricing decisions are made in response to changes in inventory levels and various cost parameters.

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

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.

Inventory allocation and transportation scheduling for logistics of network-centric military operations

This paper describes a prototype inventory-placement and transportation-scheduling solution developed in support of the emerging military doctrine of Network-Centric Operations (NCO). NCO refers to an unprecedented ability to share information among cooperating forces, enabled by modern communications and computing technology. The objective of the Network-Centric concept is to collect, disseminate, and react to real-time information in order to improve the performance of the U.S. Army as a fighting force. One problem that arises in the logistics domain involves the maintenance of combat vehicles. We seek to determine the improvement, if any, made possible by exploiting accurate information on the status of available repair parts inventory, the current locations of mobile supply points, and the demand for parts. We describe logistics algorithms for maximizing the operational availability of combat vehicles by producing, flexible, optimized inventory and delivery plans that decrease replenishment times and prioritize parts allocations and repairs. Our algorithms are designed to leverage real-time information available from modern communications and inventory tracking technology by employing state-of-the-art mathematical optimization models. Our simulations indicate that Network-Centric Logistics (NCL) can significantly improve combat vehicle availability in comparison with current practice.

Carbon management in assembly manufacturing logistics

In this paper, we present the IBM Carbon Analyzer Tool, a software solution that models and quantifies carbon emissions and explores ways to reduce emissions through advanced analytics. The tool is designed to manage carbon emissions associated with the support logistics for an assembly manufacturing operation. The tool has four analytical modules. A shipment analysis module calculates carbon emissions from transportation activities and analyzes opportunities for reducing emissions by changing fuel types of vehicles and using larger vehicles that permit consolidated shipments. A sourcing analysis module compares sourcing alternatives, including changes to supplier locations, routing of shipments, frequency of orders, and transportation modes. A scenario analysis module explores various consolidation policies to minimize transportation, inventory, and carbon costs, subject to inventory availability requirements. A sensitivity analysis module quantifies the effects of changes to uncontrollable and uncertain inputs, such as manufacturing demand for components, carbon prices, and supplier reliability. The tool makes use of a Javae™- based graphical user interface and an IBM® DB2t (Database 2e) platform to manage input and output data. A pilot implementation of the solution, using actual customer data, showed that emissions and transportation costs can be reduced simultaneously by optimizing vehicle use, fuel types, and shipment consolidation. Achieving a 20%-30% reduction in emission was possible with minimal cost increase.

Empirical methods for two-echelon inventory management with service level constraints based on simulation-regression

We present a simulation-regression based method for obtaining inventory policies for a two-echelon distribution system with service level constraints. Our motivation comes from a wholesale distributor in the consumer products industry with thousands of products that have different cost, demand, and lead time characteristics. We need to obtain good inventory policies quickly so that supply chain managers can run and analyze multiple scenarios effectively in reasonable amount of time. While simulation-based optimization approaches can be used, the time required to solve the inventory problem for a large number of products is prohibitive. On the other hand, available quick approximations are not guaranteed to provide satisfactory solutions. Our approach involves sampling the universe of products with different problem parameters, obtaining their optimal inventory policies via simulation-based optimization and then using regression methods to characterize the inventory policy for similar products. We show that our method obtains near-optimal policies and is quite robust.