MARKETING FINANCIAL PRODUCTS WITHIN THE ACTIVITY OF INVESTMENT BANKS

A production system which produces a large number of items in many steps can be modelled as a continuous flow problem. The resulting hyperbolic partial differential equation (PDE) typically is nonlinear and nonlocal, modeling a factory whose cycle time depends nonlinearly on the work in progress. One of the few ways to influence the output of such a factory is by adjusting the start rate in a time dependent manner.We study two prototypical control problems for this case: i) demand tracking where we determine the start rate that generates an output rate which optimally tracks a given time dependent demand rate and ii) backlog tracking which optimally tracks the cumulative demand. The method is based on the formal adjoint method for constrained optimization, incorporating the hyperbolic PDE as a constraint of a nonlinear optimization problem. We show numerical results on optimal start rate profiles for steps in the demand rate and for periodically varying demand rates and discuss the influence of the nonlinearity of the cycle time on the limits of the reactivity of the production system. Differences between perishable and non-perishable demand (demand vs. backlog tracking) are highlighted

Parallel statistical model checking for safety verification in smart grids

By using small computing devices deployed at user premises, Autonomous Demand Response (ADR) adapts users electricity consumption to given time-dependent electricity tariffs. This allows end-users to save on their electricity bill and Distribution System Operators to optimise (through suitable time-dependent tariffs) management of the electric grid by avoiding demand peaks. Unfortunately, even with ADR, users power consumption may deviate from the expected (minimum cost) one, e.g., because ADR devices fail to correctly forecast energy needs at user premises. As a result, the aggregated power demand may present undesirable peaks. In this paper we address such a problem by presenting methods and a software tool (APD-Analyser) implementing them, enabling Distribution System Operators to effectively verify that a given time-dependent electricity tariff achieves the desired goals even when end-users deviate from their expected behaviour. We show feasibility of the proposed approach through a realistic scenario from a medium voltage Danish distribution network

Resource Allocation with Reverse Pricing for Communication Networks

Reverse pricing has been recognized as an effective tool to handle demand uncertainty in the travel industry (e.g., airlines and hotels). To investigate its viability for communication networks, we study the practical limitations of (operator-driven) time-dependent pricing that has been recently introduced, taking into account demand uncertainty. Compared to (operator-driven) time-dependent pricing, we show that the proposed pricing scheme can achieve "triple-win" solutions: an increase in the total average revenue of the operator; higher average resource utilization efficiency; and an increment in the total average payoff of the users. Our findings provide a new outlook on resource allocation, and design guidelines for adopting the reverse pricing scheme.Comment: to appear in IEEE International Conference on Communications (ICC) 2016, Kuala Lumpur, Malaysia (6 pages, 3 figures

Controllable deterioration rate for time-dependent demand and time-varying holding cost

In this paper, we develop an inventory model for non-instantaneous deteriorating items under the consideration of the facts: deterioration rate can be controlled by using the preservation technology (PT) during deteriorating period, and holding cost and demand rate both are linear function of time, which was treated as constant in most of the deteriorating inventory models. So in this paper, we developed a deterministic inventory model for non-instantaneous deteriorating items in which both demand rate and holding cost are a linear function of time, deterioration rate is constant, backlogging rate is variable and depend on the length of the next replenishment, shortages are allowed and partially backlogged. The model is solved analytically by minimizing the total cost of the inventory system. The model can be applied to optimizing the total inventory cost of non-instantaneous deteriorating items inventory for the business enterprises, where the preservation technology is used to control the deterioration rate, and demand & holding cost both are a linear function of time

An Inventory Model for Deteriorating Commodity under Stock Dependent Selling Rate

Economic order quantity (EOQ) is one of the most important inventory policy that have to be decided in managing an inventory system. The problem addressed in this paper concerns with the decision of the optimal replenishment time for ordering an EOQ to a supplier. This Model is captured the affect of stock dependent selling rate and varying price. We developed an inventory model under varying of demand-deterioration-price of commodity when the relationship of supplier-grocery-consumer at stochastic environment. The replenishment assumed instantaneous with zero lead time. The commodity will decay of quality according to the original condition with randomize characteristics. First, the model is addressed to solve a problem phenomenon how long is the optimum length of cycle time. Then, an EOQ of commodity to be ordered by will be determined by model. To solve this problem, the first step is developed a mathematical model based on reference’s model, and then solve the model analytically. Finally, an inventory model for deteriorating commodity under stock dependent selling rate and considering selling price was derived by this research. Keywords: deterioration commodity, expected profit, optimal replenishment time stock dependent selling rate

An EOQ model for time-dependent deteriorating items with alternating demand rates allowing shortages by considering time value of money

The present paper deals with an economic order quantity (EOQ) model of an inventory problem with alternating demand rate: (i) For a certain period, the demand rate is a non linear function of the instantaneous inventory level. (ii) For the rest of the cycle, the demand rate is time dependent. The time at which demand rate changes, may be deterministic or uncertain. The deterioration rate of the item is time dependent. The holding cost and shortage cost are taken as a linear function of time. The total cost function per unit time is obtained. Finally, the model is solved using a gradient based non-linear optimization technique (LINGO) and is illustrated by a numerical example

Deterministic generation of an on-demand Fock state

We theoretically study the deterministic generation of photon Fock states on-demand using a protocol based on a Jaynes Cummings quantum random walk which includes damping. We then show how each of the steps of this protocol can be implemented in a low temperature solid-state quantum system with a Nitrogen-Vacancy centre in a nano-diamond coupled to a nearby high-Q optical cavity. By controlling the coupling duration between the NV and the cavity via the application of a time dependent Stark shift, and by increasing the decay rate of the NV via stimulated emission depletion (STED) a Fock state with high photon number can be generated on-demand. Our setup can be integrated on a chip and can be accurately controlled.Comment: 13 pages, 9 figure

High Multiplicity Scheduling with Switching Costs for few Products

We study a variant of the single machine capacitated lot-sizing problem with sequence-dependent setup costs and product-dependent inventory costs. We are given a single machine and a set of products associated with a constant demand rate, maximum loading rate and holding costs per time unit. Switching production from one product to another incurs sequencing costs based on the two products. In this work, we show that by considering the high multiplicity setting and switching costs, even trivial cases of the corresponding "normal" counterparts become non-trivial in terms of size and complexity. We present solutions for one and two products.Comment: 10 pages (4 appendix), to be published in Operations Research Proceedings 201