In this paper, we apply the stochastic dynamic programming to approximate the mean project completion time in dynamic Markov PERT networks. It is assumed that the activity durations are independent random variables with exponential distributions, but some social and economical problems influence the mean of activity durations. It is also assumed that the social problems evolve in accordance wit...

Radiotherapy treatment is often delivered in a fractionated manner over a period of time. Emerging delivery devices are able to determine the actual dose that has been delivered at each stage facilitating the use of adaptive treatment plans that compensate for errors in delivery. We formulate a model of the day-to-day planning problem as a stochastic program and exhibit the gains that can be ac...

Demand information can easily be shared in advance with the use of the latest technologies in the supply chain. Advance demand information can be used to compensate demand uncertainty and decrease inventory costs. In order to benefit from advance demand information, it should be effectively integrated into the system. In this paper, we examine a production-inventory system with multiple classes...

Hydro-electric power utilities convert the potential energy of water to electricity through the operation of generation turbines. Each turbine unit has an operating range and incurs a fixed start-up cost. The problem of determining which turbines should be operating at any point during the day whilst ensuring that the demand for electricity is satisfied is known as the unit commitment problem. ...

In this paper, we use stochastic dynamic programming to model the choice of a municipality which has to design an optimal waste management program under uncertainty about the price of recyclables in the secondary market. The municipality can, by undertaking an irreversible investment, adopt a ‡exible program which integrates the existing land…ll strategy with recycling, keeping the option to sw...

We employ a stochastic dynamic programming approach to study decision making by an individual wishing to have an arranged marriage. First, we show that this individual never opts out of a voluntarily agreed uponmarriage. Second, we demonstrate that our marrying individual uses a reservation utility to determine which marriage proposal to accept. Third, we compute the expected length of time dur...

Mathematical programming has been applied to various problems. For many actual problems, the assumption that the parameters involved are deterministic known data is often unjustified. In such cases, these data contain uncertainty and are thus represented as random variables, since they represent information about the future. Decision-making under uncertainty involves potential risk. Stochastic ...

We study a quality control problem in a two-stage system. We assume that at each stage units are processed in batches, and the rates are random variables with known distributions. Final products are supplied to customers under warranties or service contracts, with penalty costs associated with defective units. Our focus is on coordinating the inspection procedures at the two stages. Using a sto...

We consider the problem of determining (for a short lifecycle) retail product initial and replenishment order quantities that minimize the cost of lost sales, back orders, and obsolete inventory. We model this problem as a two-stage stochastic dynamic program, propose a heuristic, establish conditions under which the heuristic finds an optimal solution, and report results of the application of ...

In this paper, we demonstrate the use of stochastic dynamic programming to solve over-constrained scheduling problems. In particular, we propose a decision method for efficiently calculating, prior to start of execution, the optimal decision for every possible situation encountered in sequential, predictable, overconstrained scheduling domains. We present our resuits using an example problem fr...