George Nenes

Inventory management of multiple items with irregular demand: A case study

We present the case of a Greek commercial enterprise facing the problem of managing the inventories of thousands of different items, supplied by more than 20 European and Asian manufacturers and sold to a large number of different-type customers. A key feature of the problem is that the demand for the vast majority of items is intermittent and lumpy, thus not allowing the use of the usual normal or Poisson distributions. The paper describes the solutions given to several practical problems in the course of developing an easy-to-use yet effective and all-encompassing inventory control system. Emphasis is placed on the accurate modeling of demand by means of a gamma distribution with a probability mass at zero or a package Poisson distribution for very-slow-moving items. Using those models and simple quantitative tools we develop an efficient procedure for approximate but quite accurate determination of the base stock levels that achieve the desired fill rates in the proposed periodic review system. We briefly describe the computerized implementation of the new system and the very encouraging results.

The economically designed two-sided Bayesian X¯ control chart

Abstract This paper studies a model for the economic design of an adaptive X ¯ chart for short production runs that are subject to the occurrence of assignable causes, which may either increase or decrease the mean of the quality characteristic. At each sampling instance, the probabilities that the process operates under the effect of an assignable cause are updated using Bayes’ theorem. All three chart parameters, i.e., the time until the next sampling instance, the sample size and the control limit are adaptive and depend on these probabilities. We derive properties that facilitate the cost computation and eventually the optimization of the proposed scheme. Then, we evaluate the effectiveness of this chart by comparing its cost against the expected cost of (a) a fixed-parameter Shewhart chart optimized for short runs and (b) a variable-parameter Shewhart chart, optimized for an infinite process. The numerical results indicate that the potential savings from using the Bayesian scheme are significant.

An economically designed, integrated quality and maintenance model using an adaptive Shewhart chart

This paper proposes a model for the economic design of a variable-parameter (Vp) Shewhart control chart used to monitor the mean in a process, where, apart from quality shifts, failures may also occur. Quality shifts result in poorer quality outcome, higher operational cost and higher failure rate. Thus, removal of such quality shifts, besides improving the quality of the outcome and reducing the quality cost, is also a preventive maintenance (PM) action since it reduces the probability of a failure and improves the equipment reliability. The proposed model allows the determination of the scheme parameters that minimize the total expected quality and maintenance cost of the procedure. The monitoring mechanism of the process employs an adaptive Vp-Shewhart control chart. To evaluate the effectiveness of the proposed model, its optimal expected cost is compared against the optimum cost of a fixed-parameter (Fp) chart.

A multi-period model for managing used product returns

During the last decades there has been a consistent need for companies to manufacture ‘green’ products in order to contribute to environmental protection. The utilisation of used products (literally, the extension of their useful life cycle) is an excellent, indirect way for companies to conform to this requirement and, at the same time, increase their profit. In this paper a mixed integer linear programming mathematical model is proposed, which can be used for the optimisation of procurement, remanufacturing, stocking and salvaging decisions. The model is flexible enough to incorporate multiple suppliers, several quality levels of returned products and multiple periods of time. The applicability of the model is demonstrated through the optimisation of alternative scenarios, the optimal solutions of which reveal the potential profitability of used products exploitation.

Optimal procurement and sampling decisions under stochastic yield of returns in reverse supply chains

We study the problem of optimizing the sampling and procurement decisions in a remanufacturing system under stochastic yield of returns in a single-period setting. Returned products are characterized by uncertainty regarding their ability to be successfully remanufactured. This uncertainty is formulated as a variable probability of each returned unit in a batch to be remanufacturable (returns yield). We study the impact of returns yield on the optimal procurement policy and the benefits of sampling inspection of returns prior to the procurement decision. It is shown that sampling inspection improves the procurement decisions since it allows the Bayesian updating of the prior information regarding the returns yield. We derive analytical expressions for the determination of the economically optimal procurement quantity and structural properties that facilitate the optimization procedure and provide useful insights. The determination of the economically optimal sample size is also discussed and the benefits of sampling are illustrated through numerical examples.

An economic comparison of CUSUM and Shewhart charts

This paper compares the economic performance of CUSUM and Shewhart schemes for monitoring the process mean. We develop new simple models for the economic design of Shewhart schemes and more accurate ways to evaluate the economic performance of CUSUM schemes. The results of the comparative analysis show that the economic advantage of using a CUSUM scheme rather than the simpler Shewhart chart is substantial only when a single measurement is available at each sampling instance, i.e., only when the sample size is always n = 1, or when the sample size is constrained to low values.

The economically designed CUSUM chart for monitoring short production runs

This paper proposes a model for the design of a CUSUM chart for monitoring the process mean in short production runs. The model allows the determination of the scheme parameters that minimize the relevant expected cost of the procedure as well as the calculation of several measures of statistical performance. To evaluate the economic effectiveness of the proposed scheme, we compare its optimal expected cost against the expected cost corresponding to implementation of a CUSUM chart optimized for continuous operation (infinite horizon). The numerical results indicate that the potential savings from using the CUSUM scheme designed specifically for short runs are substantial in cases of unreliable processes with high costs of sampling, searching, and removing assignable causes. The results also show that because of the short duration of the run, in many cases it is optimal not to monitor the process at all; the use of the infinite-horizon CUSUM chart in those cases typically leads to significant cost penalties.

A general model for the economic-statistical design of adaptive control charts for processes subject to multiple assignable causes

Fully adaptive control charts are efficient statistical process control means to monitor a quality characteristic affecting the outcome of a manufacturing process. Usually, the performance of these adaptive charts is investigated in processes characterised by the possibility of the occurrence of a single assignable cause. However, this assumption is frequently far from reality, because a process shift to the out-of-control condition can be the consequence of several assignable causes, which can occur at the same time or independently. In this paper, we investigate the economic-statistical design of a variable-parameter (Vp) Shewhart control chart monitoring the process mean in the presence of multiple assignable causes. We develop a Markov chain that models the occurrence of several assignable causes leading to progressive process deterioration and calling for different corrective actions. A benchmark of examples has been generated to compare the performance of the Vp control chart with other adaptive control charts and the fixed-parameter control chart. The obtained results reveal the economic superiority of the Vp control chart.

Evaluation of CUSUM Charts for Finite-Horizon Processes

This article analyses and evaluates the properties of a CUSUM chart designed for monitoring the process mean in short production runs. Several statistical measures of performance that are appropriate when the process operates for a finite-time horizon are proposed. The methodology developed in this article can be used to evaluate the performance of the CUSUM scheme for any given set of chart parameters from both an economic and a statistical point of view, and thus, allows comparisons with various other charts.

Joint optimization of manufacturing/remanufacturing lot sizes under imperfect information on returns quality.

The increased quality volatility that characterizes returned used products in reverse supply chains, has led both academic research and industrial practice to support the establishment of, preferably fast and inexpensive, procedures for the quality assessment of returns. To this end, an initial classification of returns is typically performed based on some easily acquirable usage information, which is inherently - yet not always perfectly - related to their quality. Despite the criticality of the returns classification process and its impact on the reverse supply chain operation and profitability, little work has been done on the determination of the optimal threshold values, used to classify returns into different quality categories, taking into account the inevitable quality assessment inaccuracies. Motivated by multiple related reports from industrial applications, in the present paper the problem of optimizing the returns classification process under partial quality information in a hybrid manufacturing/remanufacturing facility is studied. More specifically, analytical models for the joint optimization of the new and returned products lot-sizing decisions are developed, based on usage information of returns which is only indirectly related to their remanufacturability. Our analysis provides useful insights on the value of information regarding the quality of returns under an indicator-based initial classification process. Numerical evidence on the economic superiority of the proposed models under alternative quality patterns of returns is also provided.