Spin squeezing and quantum correlations

We discuss the notion of spin squeezing considering two mutually exclusive classes of spin-s states, namely, oriented and non-oriented states. Our analysis shows that the oriented states are not squeezed while non-oriented states exhibit squeezing. We also present a new scheme for construction of spin-s states using 2s spinors oriented along different axes. Taking the case of s=1, we show that the ‘non-oriented’ nature and hence squeezing arise from the intrinsic quantum correlations that exist among the spinors in the coupled state.     

Enhanced Adjacent Extreme-point Search and Tabu Search for the Minimum Concave-cost Uncapacitated Transshipment Problem

Practicable methods for optimising concave-cost, uncapacitated transshipment networks are non exact. In this paper, one such effective method, that of adjacent extreme point search, is further developed to enhance its overall computational efficiency. The enhanced search algorithm is then imbedded in a tabu search scheme which proved capable of finding better solutions, by a wide margin in some instances. Another tabu search scheme, somewhat inferior in terms of solution quality but computationally more efficient, is also developed to provide an alternative solution vehicle for larger networks. Results of extensive computational testing are included.     

A variable neighbourhood search algorithm for the open vehicle routing problem

In the open vehicle routing problem (OVRP), the objective is to minimise the number of vehicles and then minimise the total distance (or time) travelled. Each route starts at the depot and ends at a customer, visiting a number of customers, each once, en route, without returning to the depot. The demand of each customer must be completely fulfilled by a single vehicle. The total demand serviced by each vehicle must not exceed vehicle capacity. Additionally, in one variant of the problem, the travel time of each vehicle should not exceed an upper limit.     

Theory of sheath in a collisional multi-component plasma

The aim of this brief report is to study the behaviour of sheath structure in a multi-component plasma with dust-neutral collisions. The plasma consists of electrons, ions, micron size negatively charged dust particles and neutrals. The sheath-edge potential and sheath width are calculated for collisionally dominated sheath. Comparison of collisionless and collisionally dominated sheath are made.     

Efficient Solution of the Single-item,Capacitated Lot-sizing Problem with Start-up and Reservation Costs

A capacitated dynamic lot-sizing model, where the costs incurred are a start-up cost for switching the production facility on and another reservation cost for keeping the facility on, whether or not it is producing, is considered. The resulting scheduling problem is NP-hard. An efficient shortest path model of the uncapacitated version of the problem is developed. This model is then included, via a redefinition of variables, into a tight capacitated model; tight in the sense that sharp lower bounds can be produced from it. The lower bound problems are solved efficiently by recovering the shortest path structure through column generation, and effective upper bounds are generated by solving a small capacitated trans-shipment problem. The results of computational tests to verify the computational efficiency of the resulting solution scheme are presented.     

Analysis of a shielded TE011 mode composite dielectric resonator for stable frequency reference

Analysis of a TE₀₁₁ mode composite sapphire-rutile dielectric resonator has been carried out to study the temperature variation of resonance frequency, close to the Cs atomic clock hyperfine frequency of 9.192 GHz. The complementary behavior of dielectric permittivity with temperature of the composite has been exploited to obtain the desired turning point in the resonant frequency. The frequency of the composite structure is found to be independent of the shield diameter beyond four times the puck diameter.     

A branch-and-bound algorithm for single-machine scheduling with batch delivery minimizing flow times and delivery costs

This paper addresses scheduling a set of jobs on a single machine for delivery in batches to customers or to other machines for further processing. The problem is a natural extension of minimizing the sum of flow times by considering the possibility of delivering jobs in batches and introducing batch delivery costs. The scheduling objective adopted is that of minimizing the sum of flow times and delivery costs. The extended problem arises in the context of coordination between machine scheduling and a distribution system in a supply chain network. Structural properties of the problem are investigated and used to devise a branch-and-bound solution scheme. Computational experiments show significant improvements over an existing dynamic programming algorithm.     

Single-machine batch scheduling minimizing weighted flow times and delivery costs

This paper addresses scheduling a set of jobs on a single machine for delivery in batches to one customer or to another machine for further processing. The problem is a natural extension of that of minimising the sum of weighted flow times, considering the possibility of delivering jobs in batches and introducing batch delivery costs. The scheduling objective adopted is that of minimising the sum of weighted flow times and delivery costs. The extended problem arises in the context of coordination between machine scheduling and a distribution system in a supply chain network. Structural properties of the problem are investigated and used to devise a branch-and-bound solution method. For the special case, when the maximum number of batches is fixed, the branch-and-bound scheme provided shows significant improvements over an existing dynamic-programming algorithm.     

Multi-level production scheduling for a class of flexible machining and assembly systems

A class of machining and assembly systems characterised by a flat assembly component structure, the existence of families of similar items, non-negligible setups and fast material flow between work-centres is considered. A hierarchical production scheduling framework is proposed for this class of systems. The decision problems at each level of the hierarchy are identified and formulated. The formulations constitute a sufficiently accurate reflection of reality, while at the same time leading to tractable mathematical models that can be handled by carefully chosen and adapted optimisation techniques. The models can, when combined with suitable knowledge bases form the core of an effective multi-pass, hierarchical decision support system. Possible srategies for coordinating the various decision problems at the different levels of the hierarchy are also discussed.This work was supported by the ACME Directorate of the Science and Engineering Research Council of the United Kingdom, Grant No. GR/D 51476, and was carried out in collaboration with Lucas Aerospace (Engines Division), Shaftmoor Lane, Birmingham, U.K.On leave from Warsaw University of Technology, Institute of Automatic Control, Nowowiejska 15/19, 00-665 Warszawa, Poland.