Modeling inventory and responsiveness costs in a supply chain

Evaluation of supply chain performance is often complicated by the various interrelationships that exist within the network of suppliers. Currently many supply chain metrics cannot be analytically determined. Instead, metrics are derived from monitoring historical data, which is commonly referred to as Supply Chain Analytics. With these analytics it is possible to answer questions such as: What is the inventory cost distribution across the chain? What is the actual inventory turnover ratio? What is the cost of demand changes to individual suppliers? However, this approach requires a significant amount of historical data which must be continuously extracted from the associated Enterprise Resources Planning (ERP) system. In this dissertation models are developed for evaluating two Supply Chain metrics, as an alternative to the use of Supply Chain Analytics. First, inventory costs are estimated by supplier in a deterministic (Q , R, δ )2 supply chain. In this arrangement each part has two sequential reorder (R) inventory locations: (i) on the output side of the seller and (ii) on the input side of the buyer. In most cases the inventory policies are not synchronized and as a result the inventory behavior is not easily characterized and tends to exhibit long cycles. This is primarily due to the difference in production rates ( δ), production batch sizes, and the selection of supply order quantities (Q) for logistics convenience. The (Q , R, δ )2 model that is developed is an extension of the joint economic lot size (JELS) model first proposed by Banerjee (1986). JELS is derived as a compromise between the seller\u27s and the buyer\u27s economic lot sizes and therefore attempts to synchronize the supply policy. The (Q , R, δ )2 model is an approximation since it approximates the average inventory behavior across a range of supply cycles. Several supply relationships are considered by capturing the inventory behavior for each supplier in that relationship. For several case studies the joint inventory cost for a supply pair tends to be a stepped convex function. Second, a measure is derived for responsiveness of a supply chain as a function of the expected annual cost of making inventory and production capacity adjustments to account for a series of significant demand change events. Modern supply chains are expected to use changes in production capacity (as opposed to inventory) to react to significant demand changes. Significant demand changes are defined as shifts in market conditions that cannot be buffered by finished product inventory alone and require adjustments in the supply policy. These changes could involve a ± 25% change in the uniform demand level. The research question is what these costs are and how they are being shared within the network of suppliers. The developed measure is applicable in a multi-product supply chain and considers both demand correlations and resource commonality. Finally, the behavior of the two developed metrics is studied as a function of key supply chain parameters (e.g., reorder levels, batch sizes, and demand rate changes). A deterministic simulation model and program was developed for this purpose

The demand for money, financial innovation, and the welfare cost of inflation: an analysis with household data

We use microeconomic data on households to estimate the parameters of the demand for currency derived from a generalized Baumol-Tobin model. Our data set contains information on average currency, deposits, and other interest-bearing assets; the number of trips to the bank; the size of withdrawals; and ownership and use of ATM cards. We model the demand for currency accounting for adoption of new transaction technologies and the decision to hold interest-bearing assets. The interest rate and expenditure flow elasticities of the demand for currency are close to the theoretical values implied by standard inventory models. However, we find significant differences between individuals with an ATM card and those without. The estimates of the demand for currency allow us to calculate a measure of the welfare cost of inflation analogous to Bailey's triangle, but based on a rigorous microeconometric framework. The welfare cost of inflation varies considerably within the population but never turns out to be very large (about 0.1 percent of consumption or less). Our results are robust to various changes in the econometric specification. In addition to the main results based on the average stock of currency, the model receives further support from the analysis of the number of trips to and average withdrawals from the bank and the ATM

The demand for money, financial innovation, and the welfare cost of inflation: an analysis with household data

We use microeconomic data on households to estimate the parameters of the demand for currency derived from a generalized Baumol-Tobin model. Our data set contains information on average currency, deposits, and other interest-bearing assets; the number of trips to the bank; the size of withdrawals; and ownership and use of ATM cards. We model the demand for currency accounting for adoption of new transaction technologies and the decision to hold interest-bearing assets. The interest rate and expenditure flow elasticities of the demand for currency are close to the theoretical values implied by standard inventory models. However, we find significant differences between individuals with an ATM card and those without. The estimates of the demand for currency allow us to calculate a measure of the welfare cost of inflation analogous to Bailey's triangle, but based on a rigorous microeconometric framework. The welfare cost of inflation varies considerably within the population but never turns out to be very large (about 0.1 percent of consumption or less). Our results are robust to various changes in the econometric specification. In addition to the main results based on the average stock of currency, the model receives further support from the analysis of the number of trips to and average withdrawals from the bank and the ATM

Inventory model with different demand rate and different holding cost

This paper deals with the development of an inventory model for time varying demand and constant demand; and time dependent holding cost and constant holding cost for case 1 and case 2 respectively. Previous models incorporating that the holding cost is constant for the entire inventory cycle. Mathematical model has been developed for determining the optimal order quantity, the optimal cycle time and optimal total inventory cost for both cases. Differential calculus is used for finding optimal solution. Numerical examples are given for both cases to validate the proposed model. Sensitivity analysis is carried out to analyze the effect of changes in the optimal solution with respect to change in various parameters

On Setup Cost Reduction in the Economic Lot-Sizing Model Without Speculative Motives

An important special case of the economic lot-sizing problem is the one in which there are no speculative motives to hold inventory, i.e., the marginal cost of producing one unit in some period plus the cost of holding it until some future period is at least the marginal production cost in the latter period. It is already known that this special case can be solved in linear time. In this paper we study the effects of reducing all setup costs by the same amount. It turns out that the optimal solution changes in a very structured way. This fact will be used to develop faster algorithms for several problems that can be reformulated as parametric lot-sizing problems. One result, worth a sepparate mention, is an algorithm for the so-called dyna-mic lot-.sizing proble-m with learning effects in setups. This algorithm has a complexity that is of the same order as the fastest algorithm known so far, but it is valid for a more general class of models than usually considered. OR/MS subject classification: Analysis of algorithms, computational complexity: parametric economic lot-sizing problem; Dynamic programming /optimal control, applications: parametric economic lot-sizing problem; Inventory/)production, planning horizon: setup cost reduction in economic lot-sizing molel

The Demand for Money, Financial Innovation, and the Welfare Cost of Inflation: An Analysis with Households' Data

How far can shoe-leather go in explaining the welfare cost of inflation? Using a unique set of microeconomic data on households, we estimate the parameters of the demand for money derived from a generalized Baumol-Tobin model. Our data set contains information on average holdings of cash, on deposits and other interest bearing accounts, on the number of trips to the bank, on the size of withdrawals and on the ownership and use of ATM cards. We model the adoption of new transaction technologies and use these estimates to correct for the selectivity bias induced by some households choosing to hold no interest bearing assets and some to use an ATM card. The interest rate and expenditure flow elasticities of the demand for cash are close to the theoretical values implied by standard inventory models. However, we find significant differences between the individuals with an ATM card and those without. The estimates of the demand for cash allow us to calculate a measure of the welfare cost of inflation analogous to Bailey's triangle, but based on a rigorous microeconometric framework. The welfare cost of inflation varies considerably within the population, but never turns out to be very large (about 0.1 percent of consumption or less). Our results are robust to various changes in the specification. In addition to the main results based on the average stock of cash held, we provide some evidence based on the number of trips to the bank and on the average withdrawals that confirm our basic findings.demand for money, financial innovation, welfare cost of inflation