Note--Effects of Centralization on Expected Costs in a Multi-Location Newsboy Problem

This paper concerns a multilocation newsboy problem with normal demand at each location and identical linear holding and penalty cost functions at each location. Consolidation of demand from several facilities is considered, and an expression is derived for the resulting expected holding and penalty costs as a function of the demand parameters for each location (means, variances, and correlation coefficients). The expression is used to demonstrate that (i) the expected holding and penalty costs in a decentralized system exceed those in a centralized system; (ii) the magnitude of the saving depends on the correlation of demands; and (iii) if demands are identical and uncorrelated, the costs increase as the square root of the number of consolidated demands.facilities/equipment planning, inventory/production: operating characteristics, inventory/production: stochastic models

A Dynamic Analysis of a Class of Deteriorating Systems

This paper considers a model for the maintenance of a deteriorating system with a discrete state space. At discrete points in time a sequence of maintenance decisions is to be made. These decisions are either to leave the system in its present state, or by performing maintenance to place it in a "higher state." Between maintenance visits the behavior of the system is described by a stationary Markov matrix. For a maintenance cost c\cdotz (where z is the number of states by which the system is improved) and a convex one-period operating cost L(\cdot) a class of transition matrices is found which lead to simple maintenance policies. It is also shown that the restrictions on the transition matrix are not only sufficient but "almost necessary" if the result is to hold for all possible choices of L(\cdot).

Capital Rationing and Organizational Slack in Capital Budgeting

This paper reconciles three stylized facts about capital budgeting in firms and shows that they are tied to the presence of asymmetric information among the several members of the firm, each with his or her own objectives and decisions. The facts of interest are: 1. The existence of organizational slack. 2. The "rationing" of resources within organizations. 3. The stated "cut off rate" for accepting capital projects in firms is often greater than the market rate of interest. Organizational slack is defined as the excess of resources allocated over the minimum necessary to accomplish the tasks assigned. Resource rationing is defined as the under-allocation of resources; i.e., an increase in the amount allocated would generate revenues in excess of its costs. Rationing and slack are both manifestations of ex post inefficiencies. An LP model is used to show that these inefficiencies can occur in ex ante efficient organizational designs when asymmetric information is present. The optimal allocation policy involves a hurdle rate criterion in which the hurdle rate is strictly in excess of the cost of capital, thus inducing rationing in some states of the world. Typically, resources are optimally allocated such that slack exists in other states. The optimal allocation policy trades off these two inefficiencies.capital budgeting, capital rationing, organizational slack, agency theory

Quantitative concepts for management: decision making without algorithms/ Gould

xxiv, 744 hal.: ill.; 23 cm

Three Asset Cash Balance and Dynamic Portfolio Problems

This paper describes the form of the optimal operating policy for a three asset cash balance problem in which (1) holding and penalty costs are proportional to the level of the cash balance, (2) the costs incurred in transferring funds between cash and earning assets are proportional to the amount of funds transferred, and (3) inflows and outflows of cash are to some extent random. There are assumed to be two earning assets, called "bonds" and "stock," that can be used to change the level of cash. "Stock" assets are the major source of the firm's earnings, and they are assumed to have higher expected returns per period than bonds but also to have higher transactions costs. The major concern, then, is with how "bonds" should be used as a buffer against random fluctuations in the cash account.

Quantitative concepts for management: decision making without algorithms/ Gould

xxiv, 744 hal.: ill.; 23 cm

Backup Agreements in Fashion Buying---The Value of Upstream Flexibility

We focus on backup agreements between a catalog company and manufacturers---a scheme to provide upstream sourcing flexibility for fashion merchandise. A backup agreement states that if the catalog company commits to a number of units for the season, the manufacturer holds back a constant fraction of the commitment and delivers the remaining units before the start of the fashion season. After observing early demand, the catalog company can order up to this backup quantity for the original purchase cost and receive quick delivery but will pay a penalty cost for any of the backup units it does not buy. In representative contracts with five companies, the fraction held as backup varies from 20% to 33% and the penalty ranges from 0 to 20% of cost. We model this inventory problem and derive the optimal solution. We provide results from a retrospective parallel test of the model against buyer decisions in 1993 based on a data set from the women's fashion department at a catalog company (Catco). The results indicate that backup arrangements can have a substantial impact on expected profits and may result in an increase in the committed quantity. Also, these arrangements may maintain the manufacturer's expected profit for a wide range of parameters.inventory, lead time, Bayesian updating, fashion buying, backup agreements

Determining Safety Stock in the Presence of Stochastic Lead Time and Demand

We consider the problem of setting safety stock when both the demand in a period and the lead time are random variables. There are two cases to consider. In the first case the parameters of the demand and lead time distributions are known; in the second case they are unknown and must be estimated. For the case of known parameters a standard procedure is presented in the literature. In this paper, examples are used to show that this procedure can yield results that are far from the desired result. A correct procedure is presented. When the parameters are unknown, it is assumed that a simple exponential smoothing model is used to generate estimates of demand in each period and that a discrete distribution of the lead time can be developed from historical data. A correct procedure for setting safety stocks that is based on these two inputs is given for two popular demand models. The approach is easily generalized to other models of demand. Safety stock calculation is simplified when certain normality assumptions are valid. Simulation results in the Appendix indicate when these assumptions about normality are reasonable.inventory/production: stochastic models, inventory/production: simulation, inventory/production: parameter estimation