Determining optimal frequency and vehicle capacity for public transit routes: A generalized newsvendor model

The level of service on public transit routes is very much affected by the frequency and vehicle capacity. The combined values of these variables contribute to the costs associated with route operations as well as the costs associated with passenger comfort, such as waiting and overcrowding. The new approach to the problem that we introduce combines both passenger and operator costs within a generalized newsvendor model. From the passenger perspective, waiting and overcrowding costs are used; from the operator’s perspective, the costs are related to vehicle size, empty seats, and lost sales. Maximal passenger average waiting time as well as maximal vehicle capacity are considered as constraints that are imposed by the regulator to assure a minimal public transit service level or in order to comply with other regulatory considerations. The advantages of the newsvendor model are that (a) costs are treated as shortages (overcrowding) and surpluses (empty seats); (b) the model presents simultaneous optimal results for both frequency and vehicle size; (c) an efficient and fast algorithm is developed; and (d) the model assumes stochastic demand, and is not restricted to a specific distribution. We demonstrate the usefulness of the model through a case study and sensitivity analysis

Optimal manufacturer's cost sharing ratio, shipping policy and production rate – A two-echelon supply chain

We analyze an integrated inventory supply chain and seek the optimal production lot, optimal production rate, and optimal (integer) number of shipments per production lot. An increasing need for higher operational efficiency, as well as growing competition among multiple products for a limited storage capacity, is driving retailers to require more frequent shipping. This imposes pressure on suppliers to share the shipping cost with retailers. The sharing ratio of the shipment cost has not previously been considered within the context of an integrated supply chain. Therefore, we contribute to the literature by investigating this entirely new parameter, assuming that the shipment cost is shared between a manufacturer and a retailer. We also consider a distributed supply chain in which each party optimizes its own cost. We analyze the problem of finding the optimal sharing ratio of the shipment cost for such a supply chain and show that there exists a specific choice of shipment cost-sharing ratio (set by the manufacturer) that results in total costs similar to those obtained in the integrated inventory model. We develop deterministic models that provides basic insights into the investigated problem. Through mathematical analysis of a nested-designs model, we provide intermediate results (which are of interest in their own right) as well as optimal analytical solutions. We show, through numerical examples, that in the scenario where each party optimizes its own cost, the manufacturer's shipment cost is a central control variable in the sense that it affects the costs of both parties

Direct marketing of an event under hazards of customer saturation and forgetting

We address the problem of optimising the intensity of online advertising. In contrast to the classical literature, we tackle the advertising interaction between the firm and the potential customer, for the sale of a onetime event, in a very limited time horizon. The problem is intrinsically dynamic due to two conflicting situations: the first arises when the customer is subjected to intense advertising pressure, which may lead to customer saturation and even irritation, while the second is the tendency for customers to forget if they are not reminded systematically through advertising. In order to determine an optimal event-advertising policy and develop an efficient enumerative shooting algorithm to solve the problem, we suggest a hazard rate-based approach to modeling the conflicting factors. Our analysis shows that the initial level of customer interest in the event has a non-trivial effect on the dynamics of the optimal advertising policy. In particular, this advertising policy consists of monotonic increase overtime prior to the event in the case of high initial interest and a concave, peak-wise form in the case of low initial interest

The cost-benefit approach to an optimal charging scheme for an embryo storage service

Cryostorage of human embryos produced during the course of in vitro fertilization (IVF) treatment is an important issue for hospitals, governments and individuals who are facing fertility challenges. Embryo cryostorage is giving rise to increasing economic, ethical and legal concerns due to the increasing holding and operational costs of storage, the rise in the number of unused embryos, and the absence of economic incentives for hospitals to provide free cryostorage services. These issues may reduce the availability of storage services and encourage individuals to seek embryo donations from abroad with attendant medical risks and the possibility of illegal transactions. Given that both public and private healthcare institutions are increasingly motivated by economic factors, increasing the economic incentive to offer cryostorage has the potential to increase the provision of storage facilities. This paper proposes a nonlinear programming model to enable a hospital or other service provider to determine the optimal price it should charge for storage. The suggested pricing policy comprises three components; however, our analysis shows that an optimal solution can only include a maximum of two of these components. Finally, the paper introduces a numerical example as well as a real-data comparison among several providers to demonstrate the applicability and value of the proposed model