We consider a distribution logistics scenario where a shipping operator, managing a limited amount of resources, receives a stream of collection requests, issued by a set of customers along a booking time-horizon, that are referred to a future operational period. The shipping operator must then decide about accepting or rejecting each incoming request at the time it is issued, accounting for revenues, but also considering resource consumptions. In this context, the decision process is based on dynamically finding the best trade-off between the immediate return of accepting the request and the convenience of preserving capacity to possibly exploit more valuable future requests. We give a dynamic formulation of the problem aimed at maximizing the operator revenues, accounting also for the operational distribution costs. Due to the "curse of dimensionality", the dynamic program cannot be solved optimally. For this reason, we propose a mixed-integer linear programming approximation, whose exact or approximate solutions provide the relevant information to apply some commonplace revenue management policies in the real-time decision-making. Adopting a capacitated vehicle routing problem as an underlying distribution application, we analyze the computational behaviour of the proposed techniques on a set of academic test problems.
We propose a multi-criteria Composite Index Method (CIM) to compare the performance of alternative approaches to solving an optimization problem. The CIM is convenient in those situations when neither approach dominates the other when tested on different sizes of problem instances. The CIM takes problem instance size and multiple performance criteria into consideration within a weighting scheme to produce a single number that measures the relative improvement of one alternative over the other. Different weights are given to each dimension based on their relative importance as determined by the…
This paper considers a Markov decision model for profit maximization of a cloud computing service provider catering to customers submitting jobs with firm real-time random deadlines. Customers are charged on a per-job basis, receiving a full refund if deadlines are missed. The service provider leases computing resources from an infrastructure provider in a two-tier scheme: long-term leasing of basic infrastructure, consisting of heterogeneous parallel service nodes, each modeled as a multi-server queue, and short-term leasing of external servers. Given the intractability of computing an optima…
We present a compact mixed integer program (MIP) for the backhaul profit maximization problem in which a freight carrier seeks to generate profit from an empty delivery vehicle's backhaul trip from its last scheduled delivery to its depot by allowing it to deviate from the least expensive (or fastest) route to accept delivery requests between various points on the route as allowed by its capacity and required return time. The MIP is inspired by a novel representation of multicommodity flow that significantly reduces the size of the constraint matrix and the linear programming upper bound on op…
We develop an optimization model and corresponding algorithm for the management of a demand-side platform (DSP), whereby the DSP aims to maximize its own profit while acquiring valuable impressions for its advertiser clients. We formulate the problem of profit maximization for a DSP interacting with ad exchanges in a real-time bidding environment in a cost-per-click/cost-per-action pricing model. Our proposed formulation leads to a nonconvex optimization problem due to the joint optimization over both impression allocation and bid price decisions. We use Lagrangian relaxation to develop a trac…
We develop a model for pricing, lead-time quotation and delay compensation in a Markovian make-to-order production or service system with strategic customers who exhibit risk aversion. Based on a concave utility function of their net benefit, customers make individual decisions to join the system or balk without observing the state of the queue. The decisions of arriving customers result in a symmetric join/balk game. Regarding the firm's strategy, the provider announces a fixed entrance fee, a lead-time quotation and a compensation rate for the part of a customer delay which exceeds the quote…
We propose a novel approach to modeling advertising dynamics for a firm operating over distributed market domain based on controlled partial differential equations of diffusion type. Using our model, we consider a general type of finite-horizon profit maximization problem in a monopoly setting. By reformulating this profit maximization problem as an optimal control problem in infinite dimensions, we derive sufficient conditions for the existence of its optimal solutions under general profit functions, as well as state and control constraints, and provide general characterization of the optimal…
In this article, we study a fractional control problem that models the maximization of the profits obtained by exploiting a certain resource whose dynamics are governed by the fractional logistic equation. Due to the singularity of this problem, we develop different resolution techniques, both for the classical case and for the fractional case. In the last section we perform several numerical simulations to make a comparison between both cases.
In this paper we study a revenue maximization problem for optical routing nodes. We model the routing node as a single server polling model with the aim to assign visit periods (service windows) to the different stations (ports) such that the mean profit per cycle is maximized. Under reasonable assumptions regarding retrial and dropping probabilities of packets the optimization problem becomes a separable concave resource allocation problem, which can be solved using existing algorithms.
The fast growth of communication technology within the concept of smart grids can provide data and control signals from/to all consumers in an online fashion. This could foster more participation for end-user customers. These types of customers do not necessarily have powerful prediction tools or capability of storing a large amount of historical data. Besides, the relevant information is not always known a priori, while decisions need to be made fast within a very limited time. These limitations and also the novel structure of decision making, which comes from the necessities to make the deci…
A fundamental problem in revenue management is to optimally choose the attributes of products, such that the total profit or revenue or market share is maximized. Usually, these attributes can affect both a product's market share (probability to be chosen) and its profit margin. For example, if a smart phone has a better battery, then it is more costly to be produced, but is more likely to be purchased by a customer. The decision maker then needs to choose an optimal vector of attributes for each product that balances this trade-off. In spite of the importance of such problems, there is not ye…
The growth of e-commerce has created increasing complexity in logistics services. To remain competitive, logistics and e-commerce companies are exploring new modes as supplements to traditional home delivery, one of which is the self-service parcel locker. This paper studies a parcel locker location problem where a company plans to introduce the locker service by locating locker facilities to attract customers. The objective is to maximize the profit, accounting for the revenue and the cost of facilities. To estimate the revenue, we use the threshold Luce model (TLM) to predict customers' like…
Research on container loading problems has been proved effective in increasing the filling rate of containers in different practical situations. However, the broader logistic context might pressure the loading process, leading to sub-optimal solutions. Some facilities like cross-docks have reduced storage space which might force early loading activities. We propose a container loading problem which accounts for this limited storage by explicitly considering the schedule of arrival for the boxes and the departure time of the trucks. Also, we design a framework which handles the geometric and te…
We consider a profit maximization problem in an urban mobility on-demand service, of which the operator owns a fleet, provides both exclusive and shared trip services, and dynamically determines prices of offers. With knowledge of the traveler preference and the distribution of future trip requests, the operator wants to find the pricing strategy that optimizes the total operating profit of multiple trips during a specific period, namely, a day in this paper. This problem is first formulated and analyzed within the dynamic programming framework, where a general approach combining parametric ro…
This paper studies optimal pricing and rebalancing policies for Autonomous Mobility-on-Demand (AMoD) systems. We take a macroscopic planning perspective to tackle a profit maximization problem while ensuring that the system is load-balanced. We begin by describing the system using a dynamic fluid model to show the existence and stability of an equilibrium (i.e., load balance) through pricing policies. We then develop an optimization framework that allows us to find optimal policies in terms of pricing and rebalancing. We first maximize profit by only using pricing policies, then incorporate re…
We use a control framework to analyze the digital vendor's profit maximization problem. The vendor captures market share by focusing costly effort on post-launch product maintenance, which influences user perception of the product and drives a revenue stream associated with product use. Our theoretical results show necessary and sufficient conditions for product maintenance to decline over a product's life-cycle, thus showing conditions when Lehman's 7th law of software evolution holds. We also numerically illustrate control paths under different market conditions.
