A Make-to-Order (MTO) set-up is one in which production starts only on receiving confirmed orders, and there is no inventory. An enterprise is a group of production sites that may be geographically separated. This paper considers enterprises that operate on the MTO principles. Upon receiving orders for products, the orders are assigned to the different production sites that are geographically distributed. In order to have an efficient production plan, the decision support system must address challenges at the enterprise level, as well as at the individual production site level. In this paper our interest is in an optimal distribution of orders across sites while exploiting individual capacities at those sites. The enterprise level decisions are referred to as routing decisions, while the site level decisions are called scheduling decisions. The planning horizon for these decisions is typically short, that is, a day or a week and hence the proposed solution approach falls under short term capacity planning. A central router is assumed to receive orders on behalf of the enterprise, and is then expected to divide the order workload amongst the sites, in order to minimize the overall costs (production as well as transportation). At each site, an optimal schedule is determined to minimize the maximal completion time, as well as maximize remaining capacity on each machine, after satisfying the workload assigned to it. A framework for cost efficient routing and scheduling while ensuring job deadlines is proposed which allows iterative interaction of routing and scheduling modules. The feedback on capacity based on deadline violations at each site is used to iteratively optimize routing of jobs while ensuring job deadlines, along with the objective of cost efficient capacity planning. We present two iterative frameworks one using Mixed Integer Program (MIP) and the second using MIP and discrete event simulation model. The proposed frameworks have been implemented and computational results are presented to compare their performances.

We propose an online scheduling algorithm for posting crowdsourcing tasks which maximizes a novel metric called task viewership. This metric is computed using stochastic model based on coverage process and it measures the likelihood that a task is viewed by multiple crowd workers, which is correlated to the likelihood that it will be selected and completed.

We consider k-coverage of a line by a two-dimensional, non homogeneous Poisson-Boolean model. This has applications in sensor networks. We extend the analysis of [1] to the case for k > 1. The extension requires us to define a vector Markov process that tracks the k segments that have the longest residual coverage at a point. This process is used to determine the probability of a segment of the line being completely covered by k or more sensors. We illustrate the extension by considering the case of k = 2.

We analyze the statistical properties of the k-coverage of a point-target moving in a straight line in a nonuniform dynamic sensor field. Sensor locations form a spatial point process. The environmental variation is captured by making the sensor locations form a non homogeneous spatial Poisson process with a fixed, spatially varying density function. The sensing areas of the sensors are circles of i.i.d. radii. The availability of each node is modeled by an independent, {0, 1}- valued, continuous time Markov chain. This gives a Markov-non homogeneous Poisson-Boolean model for which we perform a coverage analysis. We first obtain k-coverage of the target at an arbitrary time instant. We then obtain k-coverage statistics of the target during the time interval [0, T]. We also provide an asymptotically tight, closed form approximation for the duration for which the target is not k-covered in [0, T]. Numerical results illustrate the analysis. The environmental variation can also be captured by modeling the density function as a spatial random process resulting in the point process being a two-dimensional Cox process. For this model, we discuss issues in the coverage analysis.

We analyze the statistical properties of the coverage of a one-dimensional path induced by a two-dimensional nonhomogeneous random sensor network. Sensor locations form a nonhomogeneous Poisson process and sensing area for the sensors are circles of random independent and identically distributed radii. We first characterize the coverage of a straight-line path by the nonhomogeneous one-dimensional Boolean model. We then obtain an equivalent M t /G t /∞, queue whose busy period statistics is the same as the coverage statistics of the line. We obtain k -coverage statistics for an arbitrary point and a segment on the x -axis. We provide upper and lower bounds on the probability of complete k -coverage of a segment. We illustrate all our results for the case of the sensor deployment having a “Laplacian” intensity function.

We analyze the statistical properties of the coverage of a one-dimensional path induced by a two dimensional non homogeneous random sensor network. Sensor locations form a non homogeneous Poisson process and coverage area of each sensor is a circle of random i.i.d. radius. We first describe the one-dimensional coverage process on the line and describe an equivalent time-inhomogeneous Mt/Gt/infin queue whose busy period statistics will be equal to the coverage statistics of the line. We also obtain properties like conditional forward and backward hole-lengths. Additional results for the case of fixed coverage radius are obtained. We also obtain some numerical results for a deployment that has a 'Laplacian' intensity function.