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Using Multivariate Statistics

Numerical Methods for Scientists and Engineers

In many applications involving make-to-order or time-sensitive (e.g., perishable, seasonal) products, finished orders are often delivered to customers immediately or shortly after the production. Consequently, there is little or no finished product inventory in the supply chain such that production and outbound distribution are very intimately linked and must be scheduled jointly to achieve a desired on-time delivery performance at minimum total cost. Research on integrated scheduling models of production and outbound distribution is relatively recent but is growing very rapidly. In this paper, we provide a survey of such existing models. We present a unified model representation scheme, classify existing models into several different classes, and for each class of the models give an overview of the optimality properties, computational tractability, and solution algorithms for the various problems studied in the literature. We clarify the tractability of some open problems left in the literature and some new problems by providing intractability proofs or polynomial-time exact algorithms. We also identify several problem areas and issues for future research.

Integrated Production and Outbound Distribution Scheduling: Review and Extensions

Although the supply chain management literature is extensive, the benefits and challenges of coordinated decision making within supply chainscheduling models have not been studied. We consider a variety of scheduling, batching, and delivery problems that arise in an arborescent supply chain where a supplier makes deliveries to several manufacturers, who also make deliveries to customers. The objective is to minimize the overall scheduling and delivery cost, using several classical scheduling objectives. This is achieved by scheduling the jobs and forming them into batches, each of which is delivered to the next downstream stage as a single shipment. For each problem, we either derive an efficient dynamic programming algorithm that minimizes the total cost of the supplier or that of the manufacturer, or we demonstrate that this problem is intractable. The total system cost minimization problem of a supplier and manufacturer who make cooperative decisions is also considered. We demonstrate that cooperation between a supplier and a manufacturer may reduce the total system cost by at least 20%, or 25%, or by up to 100%, depending upon the scheduling objective. Finally, we identify incentives and mechanisms for this cooperation, thereby demonstrating that our work has practical implications for improving the efficiency of supply chains.

https://www.jstor.org/stable/pdfplus/4132420.pdf

Supply chain scheduling: Batching and delivery

Motivated by applications in the computer and food catering service industries, we study an integrated scheduling model of production and distribution operations. In this model, a set of jobs (i.e., customer orders) are first processed in a processing facility (e.g., manufacturing plant or service center) and then delivered to the customers directly without intermediate inventory. The problem is to find a joint schedule of production and distribution such that an objective function that takes into account both customer service level and total distribution cost is optimized. Customer service level is measured by a function of the times when the jobs are delivered to the customers. The distribution cost of a delivery shipment consists of a fixed charge and a variable cost proportional to the total distance of the route taken by the shipment. We study two classes of problems under this integrated scheduling model. In the first class of problems, customer service is measured by the average time when the jobs are delivered to the customers; in the second class, customer service is measured by the maximum time when the jobs are delivered to the customers. Two machine configurations in the processing facility--single machine and parallel machine--are considered. For each of the problems studied, we provide an efficient exact algorithm, or a proof of intractability accompanied by a heuristic algorithm with worst-case and asymptotic performance analysis. Computational experiments demonstrate that the heuristics developed are capable of generating near-optimal solutions. We also investigate the possible benefit of using the proposed integrated model relative to a sequential model where production and distribution operations are scheduled sequentially and separately. Computational tests show that in many cases a significant benefit can be achieved by integration.

Integrated Scheduling of Production and Distribution Operations

In most classical scheduling models, it is assumed that a job is dispatched to a customer immediately after its processing completes. In many practical situations, however, a set of delivery dates may be fixed before any jobs are processed. This is particularly relevant where delivery is an expensive or complicated operation, for example, as with heavy machinery. A similar situation arises where customers find deliveries disruptive and thus require them to be made within a limited time interval that repeats periodically. A third possibility is that a periodic business function, for example, the supplier's billing cycle, effectively defines a delivery date, and includes all jobs that have been completed since the previous billing cycle. These situations are not adequately represented by classical scheduling models. We consider a variety of deterministic scheduling problems in which a job is dispatched to a customer at the earliest fixed delivery date that is no earlier than the completion time of its processing. Problems where the number of delivery dates is constant, and others where it is specified as part of data input, are studied. For almost all problems considered, we either provide an efficient algorithm or establish that such an algorithm is unlikely to exist. By doing so, we permit comparisons between the solvability of these fixed delivery date problems and of the corresponding classical scheduling problems.

Scheduling with Fixed Delivery Dates

This paper combines factor analysis and multinomial logistic regression (MLR) in understanding the relationship between extracted factors of quality of life pertaining to education and variables of five key areas of the levels of development in the context of the South African 2009 General Household Survey. MLR was used to analyse the identified educational factors from factor analysis. It was also used to determine the extent to which these factors impact on educational level outcomes across South Africa. The overall classification accuracy rate displayed was 73.0% which is greater than the proportion by chance accuracy criteria of 57.0%. This means that the model improves on the proportion by chance accuracy rate of 25.0% or more so that the criterion for classification accuracy is satisfied and the model is adequate. Evidence is that being historically disadvantaged, absence of parental care, violence in schools and the perception that fees were too high generally have a negative influence on education...

Application of multinomial logistic regression to educational factors of the 2009 General Household Survey in South Africa

This paper presents a transportation branch and bound algorithm for solving the generalized assignment problem. This is a branch and bound technique in which the sub-problems are solved by the available efficient transportation techniques rather than the usual simplex based approaches. A technique for selecting branching variables that minimize the number of sub-problems is also presented.

/pdf/a-transportation-branch-and-bound-algorithm-for-solving-the-3qodbb56dt.pdf

A transportation branch and bound algorithm for solving the generalized assignment problem

In this paper we fit a time-heterogeneous generalised Pareto distribution (GPD) to the flood heights in the lower Limpopo River basin of Mozambique (LLRB). The maximum likelihood method is used for parameter estimation of the nonstationary GPD. We take an in-depth review of the merits of peaks-over-threshold and block maxima. We also show the relationship between generalised extreme value (GEV) distribution and GPD in a mathematical proof and discuss the link between the mathematical proof and the findings. Nonstationary time-dependent GPD models with a trend in the scale parameter are considered in this study. The results show overwhelming evidence in support of the existence of a linear trend in the scale parameter of the GPD models at all the three sites in the LLRB. The timeheterogeneous GPD models developed in this study were found to be statistically worthwhile and provide an improvement in fit over the time-homogeneous GPD models based on the goodness-of-fit tests. This study shows the importance of extending the time-homogeneous GPD models to incorporate climate change factors such as trend in the LLRB. The models developed in this study are expected to be more reliable than their stationary counterparts for planning and decision making processes in Mozambique.

http://www.intlpress.com/site/pub/files/_fulltext/journals/sii/2017/0010/0001/SII-2017-0010-0001-a012.pdf

Modelling extreme flood heights in the lower Limpopo River basin of Mozambique using a time-heterogeneous generalised Pareto distribution

In this article we fit a time-dependent generalised extreme value (GEV) distribution to annual maximum flood heights at three sites: Chokwe, Sicacate and Combomune in the lower Limpopo River basin of Mozambique. A GEV distribution is fitted to six annual maximum time series models at each site, namely: annual daily maximum (AM1), annual 2-day maximum (AM2), annual 5-day maximum (AM5), annual 7-day maximum (AM7), annual 10-day maximum (AM10) and annual 30-day maximum (AM30). Non-stationary time-dependent GEV models with a linear trend in location and scale parameters are considered in this study. The results show lack of sufficient evidence to indicate a linear trend in the location parameter at all three sites. On the other hand, the findings in this study reveal strong evidence of the existence of a linear trend in the scale parameter at Combomune and Sicacate, whilst the scale parameter had no significant linear trend at Chokwe. Further investigation in this study also reveals that the location parameter at Sicacate can be modelled by a nonlinear quadratic trend; however, the complexity of the overall model is not worthwhile in fit over a time-homogeneous model. This study shows the importance of extending the time-homogeneous GEV model to incorporate climate change factors such as trend in the lower Limpopo River basin, particularly in this era of global warming and a changing climate.

/pdf/modelling-non-stationary-annual-maximum-flood-heights-in-the-3nnd1tvwxn.pdf

Maseka Lesaoana

Papers

Scheduling with Fixed Delivery Dates

Application of multinomial logistic regression to educational factors of the 2009 General Household Survey in South Africa

A transportation branch and bound algorithm for solving the generalized assignment problem

Modelling extreme flood heights in the lower Limpopo River basin of Mozambique using a time-heterogeneous generalised Pareto distribution

Modelling non-stationary annual maximum flood heights in the lower Limpopo River basin of Mozambique