Rachel Q. Zhang

Inventory Management with Asset-Based Financing

Most of the traditional models in production and inventory control ignore the financial states of an organization and can lead to infeasible practices in real systems. This paper is the first attempt to incorporate asset-based financing into production decisions. Instead of setting a known, exogenously determined budgetary constraint as most existing models suggest, we model the available cash in each period as a function of assets and liabilities that may be updated periodically according to the dynamics of the production activities. Furthermore, our models allow different interest rates on cash balance and outstanding loans, which is an enhancement over most traditional models in that inventory financed by a loan may be more expensive than that by out-of-pocket cash. We demonstrate the importance of joint consideration of production and financing decisions in a start-up setting in which the ability to grow the firm is mainly constrained by its limited capital and dependence on bank financing. We then explain the motivation for asset-based financing by examining the decision making at a bank and a set of retailers in a newsvendor setting.

Pushing Quality Improvement Along Supply Chains

In this paper, we consider a buyer who designs a product and owns the brand, yet outsources the production to a supplier. Both the buyer and the supplier incur quality-related costs, e.g., costs of customer goodwill and future market share loss by the buyer and warranty-related costs shared by both the buyer and the supplier whenever a nonconforming item is sold to a customer. Therefore, both parties have an incentive to invest in quality-improvement efforts. This paper explores the roles of different parties in a supply chain in quality improvement. We show that the buyers involvement can have a significant impact on the profits of both parties and of the supply chain as a whole, and he cannot cede the responsibility of quality improvement to the supplier in many cases. We also investigate how quality-improvement decisions interact with operational decisions such as the buyers order quantity and the suppliers production lot size.

Optimal Policies for Inventory Systems with Priority Demand Classes

We consider a periodic review inventory system with two priority demand classes, one deterministic and the other stochastic. The deterministic demand must be met immediately in each period. However, the units of stochastic demand that are not satisfied during the period when demand occurs are treated as lost sales. At each decision epoch, one has to decide not only whether an order should be placed and how much to order, but also how much demand to fill from the stochastic source. The firm has the option to ration inventory to the stochastic source (i.e., not satisfy all customer demand even though there is inventory in the system).We first characterize the structure of the optimal policy. We show that, in general, the optimal order quantity and rationing policy are state dependent and do not have a simple structure. We then propose a simple policy, called ( s, k, S) policy, wheres andS (ordering policy) determine when and how much to order, whilek (rationing policy) specifies how much of the stochastic demand to satisfy. We report the results of a numerical study, which shows that this simple policy works extremely well and is very easy to compute.

Inventory Decisions in Dell's Supply Chain

The Tauber Manufacturing Institute (TMI) is a partnership between the engineering and business schools at the University of Michigan. In the summer of 1999, a TMI team spent 14 weeks at Dell Inc. in Austin, Texas, and developed an inventory model to identify inventory drivers and quantify target levels for inventory in the final stage of Dells supply chain, the revolvers or supplier logistics centers (SLC). With the information and analysis provided by this model, Dells regional materials organizations could tactically manage revolver inventory while Dells worldwide commodity management could partner with suppliers in improvement projects to identify inventory drivers and to reduce inventory. Dell also initiated a pilot program for procurement of XDX (a disguised name for one of the major components of personal computers (PCs)) in the United States to institutionalize the model and promote partnership with suppliers. Based on the model predictions, Dell launched e-commerce and manufacturing initiatives with its suppliers to lower supply-chain-inventory costs by reducing revolver inventory by 40 percent. This reduction would raise the corresponding inventory turns by 67 percent. Net Present Value (NPV) calculations for XDX alone suggest

Inventory Policies for Systems with Stochastic and Deterministic Demand

43 million in potential savings. To ensure project longevity, Dell formed the supply-chain-optimization team and charged it with incorporating the model into a strategic redesign of Dells business practices and supervising improvement projects the model identified.

Easily Implementable Inventory Control Policies

We consider a periodic review inventory system with demand arriving simultaneously from a deterministic source and a random source. The deterministic demand has to be satisfied immediately and the stochastic demand can be backordered. Assuming that the stochastic demand is never backlogged if there is stock in the system, we prove that a modified ( s, S) policy is optimal under general conditions if there is a setup cost. If there is a smoothing cost instead of the setup cost, we observe that the problem corresponds to a standard model with one source of demand.

Buffer Capacity for Accommodating Machine Downtime in Serial Production Lines

This work was initiated and supported by a manufacturer of mail processing equipment, which stocks 30,000 distinct parts in a distribution center to support field maintenance of their equipment. To find an effective stocking policy for this system we formulate a constrained optimization model with the objective of minimizing overall inventory investment at the distribution center subject to constraints on customer service and order frequency. Because size, integrality, and nonconvexity make this problem intractable to exact analysis, we develop three heuristic algorithms based on simplified representations of the inventory and service expressions. These lead to what we call easily implementable inventory policies, in which the control parameters for a newly introduced part can be computed in closed form without reoptimizing the rest of the system. Numerical comparisons against a lower bound on the cost function show that even our simplest heuristic works well when a high service level is required. However...

An easily implementable hierarchical heuristic for a two-echelon spare parts distribution system

This paper investigates the smallest level of buffering (LB), necessary to ensure the desired production rate in serial lines with unreliable machines. The reliability of machines is assumed to obey either exponential, or Erlang, or Rayleigh models. The LB is measured in units of the average downtime, T down . The dependence of LB on the reliability model, the number of machines, M , the average uptime, T up , and the efficiency, e = T up /( T up + T down ) is analysed. It is shown that reliability models with larger coefficient of variation require larger LB, and an empirical law that connects LB of the exponential model with those for other reliability models is established. It is shown that LB is an increasing function of M , but with an exponentially decreasing rate, saturating at around M = 10. Also, it is shown that LB does not depend explicitly on T up and is a decreasing function of e . Based on these results, rules-of-thumb are provided for selecting buffer capacity, which guarantee sufficiently high line efficiency.

RISK-NEUTRAL OPTION PRICING METHODS FOR ADJUSTING CONSTRAINED CASH FLOWS

This paper addresses a two-echelon spare parts stocking and distribution system consisting of a central Distribution Center (DC) and regional facilities. Because the primary purpose for holding inventory is to provide timely repairs of customer′s equipment, we set as our objective to minimize total inventory investment subject to constraints on the delay due to parts outages. We decompose the resulting problem by level and by facility. By simplifying the expressions for the delay constraints and applying previously developed heuristics for the single-level problem [1], we are able to derive closed-form expressions for the inventory control parameters. We then develop a search algorithm (on DC fill rate) to approximate the parameters (Lagrange multipliers) in the closed-form expressions. Numerical comparisons against an analytic lower bound and, for small problems, exact solutions show the approximation to be quite accurate. We also found that it outperforms methods currently in use by the firm that motivated this work. Finally, because it yields closed-form expressions for inventory control parameters and the parameters are only updated periodically, the policy is “easily implementable” once suitable Lagrange multipliers have been computed.

OPTIMAL CONTROL OF A FLEXIBLE SERVER

ABSTRACT Standard procedures for evaluating future cash flows are to find an appropriate discount rate consistent with the cash flows risk and then to derive a present value. While discounted cash flows seem appropriate for many instances, finding appropriate discount rates is often difficult, or discount rates may not exist when the risk is actually a function of a decision that requires the cash-flow valuation. We consider two approaches that have been suggested to alleviate this problem: the capital asset pricing model (CAPM) and the risk-neutral pricing arguments from option theory. We discuss the assumptions inherent in these models and show the results on the well-known news vendor model. Our option pricing results correspond to Singhals [17] results using CAPM and a different valuation procedure for the option pricing model. We, however, derive a simpler expression that clearly illustrates differences from the standard form ignoring risk.