Theodosis D. Dimitrakos

Single vehicle routing problems with a predefined customer sequence, compartmentalized load and stochastic demands

We consider the problem of finding the optimal routing of a single vehicle that delivers K different products to N customers according to a particular customer order. The demands of the customers for each product are assumed to be random variables with known distributions. Each product type is stored in its dedicated compartment in the vehicle. Using a suitable dynamic programming algorithm we find the policy that satisfies the demands of the customers with the minimum total expected cost. We also prove that this policy has a specific threshold-type structure. Furthermore, we investigate a corresponding infinite-time horizon problem in which the service of the customers does not stop when the last customer has been serviced but it continues indefinitely with the same customer order. It is assumed that the demands of the customers at different tours have the same distributions. It is shown that the discounted-cost optimal policy and the average-cost optimal policy have the same threshold-type structure as the optimal policy in the original problem. The theoretical results are illustrated by numerical examples.

An improved algorithm for the computation of the optimal repair/replacement policy under general repairs

We consider a system which deteriorates with age and may experience a failure at any time instant. On failure, the system may be replaced or repaired. The repair can partially reset the failure intensity of the unit. Under a suitable cost structure it has been proved in the literature that the average-cost optimal policy is of control-limit type, i.e. it conducts a replacement if and only if, on the nth failure, the real age of the system is greater than or equal to a critical value. We develop an efficient special-purpose policy iteration algorithm that generates a sequence of improving control-limit policies. The value determination step of the algorithm is based on the embedding technique. There is strong numerical evidence that the algorithm converges to the optimal policy.

A single vehicle routing problem with pickups and deliveries, continuous random demands and predefined customer order

This paper extends the results of a particular capacitated vehicle routing problem with pickups and deliveries (see Pandelis et al., 2013b) to the case in which the demands for a material that is delivered to N customers and the demands for a material that is collected from the customers are continuous random variables instead of discrete ones. The customers are served according to a particular order. The optimal policy that serves all customers has a specific threshold-type structure and it is computed by a suitable efficient dynamic programming algorithm that operates over all policies having this structure. The structural result is illustrated by a numerical example.

Single Vehicle Routing Problem with a Predefined Customer Sequence, Stochastic Demands and Partial Satisfaction of Demands

We consider the problem of finding the optimal routing of a single vehicle that starts its route from a depot and delivers a product to N customers that are served according to a particular sequence. The vehicle during its route can return to the depot for restocking. The demands of the customers are random variables with known distributions. The actual demand of each customer is revealed as soon as the vehicle visits the customer’s site. It is permissible to satisfy fully or to satisfy partially or not to satisfy the demand of a customer. The cost structure includes travel costs between consecutive customers, travel costs between the customers and the depot and penalty costs if a customer’s demand is not satisfied or if it is satisfied partially. A dynamic programming algorithm is developed for the determination of the optimal routing policy. It is shown that the optimal routing policy has a specific threshold-type structure.

Stochastic single vehicle routing problem with ordered customers and partial fulfilment of demands

We consider the problem of finding the optimal routing of a single vehicle that starts its route from a depot and delivers a product to N customers that are served according to a particular order. ...

A semi-Markov decision model for the optimal control of a simple immigration-birth-death process through the introduction of a predator

ABSTRACT This article is concerned with the problem of controlling a simple immigration-birth-death process, which represents a pest population, by the introduction of a predator in the habitat of the pests. The optimization criterion is the minimization of the expected long-run average cost per unit time. It is possible to construct an appropriate semi-Markov decision model with a finite set of states if and only if the difference between the per capita birth rate and the per capita death rate of the pests is smaller than half of the rate at which the predator is introduced in the habitat.