This paper addresses the problem of scheduling activities in projects with stochastic activity durations. The aim is to determine for each activity a gate-a time before it the activity cannot begin. Setting these gates is analogous to setting inventory levels in the news vendor problem. The resources required for each activity are scheduled to arrive according to its gate. Since activities' durations are stochastic, the start and finish time of each activity is uncertain. This fact may lead to one of two outcomes: (1) an activity is ready to start its processing as all its predecessors have finished, but it cannot start because the resources required for it were scheduled to arrive at a later time.(2) The resources required for the activity have arrived and are ready to be used but the activity is not ready to start because of precedence constraints. In the first case we will incur a "holding" cost while in the second case, we will incur a "shortage" cost. Our objective is to set gates so as to minimize the sum of the expected holding and shortage costs. We employ the Cross-Entropy method to solve the problem. The paper describes the implementation of the method, compares its results to various heuristic methods and provides some insights towards actual applications.
This paper proposes a new methodology to schedule activities in projects with stochastic activity durations. The main idea is to determine for each activity an interval in which the activity is allowed to start its processing. Deviations from these intervals result in penalty costs. We employ the Cross-Entropy methodology to set the intervals so as to minimize the sum of the expected penalty costs. The paper describes the implementation of the method, compares its results to other heuristic methods and provides some insights towards actual applications.
The objective of inventory management models is to determine effective policies for managing the trade-off between customer satisfaction and the cost of service. These models have become increasingly sophisticated, incorporating many complicating factors that are relevant in practice such as demand uncertainty, finite supplier capacity, and yield losses. Curiously absent from these models are the financial constraints imposed by working capital requirements (WCR). In practice, many firms are self-financing; their ability to replenish their own inventories is directly affected not only by their current inventory levels, but also by their receivables and payables. In this paper, we analyze the materials management practices of a self-financing firm whose replenishment decisions are constrained by cash flows, which are updated periodically following purchases and sales in each period. In particular, we investigate the interaction between the financial and operational parameters as well as the impact of WCR constraints on the long-run average cost.
This paper addresses the problem of scheduling activities in projects with stochastic activity durations. The aim is to determine for each activity a gate-a time before it the activity cannot begin. Setting these gates is analogous to setting inventory levels in the news vendor problem. The resources required for each activity are scheduled to arrive according to its gate. Since activities' durations are stochastic, the start and finish time of each activity is uncertain. This fact may lead to one of two outcomes: (1) an activity is ready to start its processing as all its predecessors have finished, but it cannot start because the resources required for it were scheduled to arrive at a later time.(2) The resources required for the activity have arrived and are ready to be used but the activity is not ready to start because of precedence constraints. In the first case we will incur a "holding" cost while in the second case, we will incur a "shortage" cost. Our objective is to set gates so as to minimize the sum of the expected holding and shortage costs. We employ the Cross-Entropy method to solve the problem. The paper describes the implementation of the method, compares its results to various heuristic methods and provides some insights towards actual applications.
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