The Yang-Mills functional and Laplace's equation on quantum Heisenberg manifolds

In this paper, we discuss the Yang-Mills functional and a certain family of its critical points on quantum Heisenberg manifolds using noncommutative geometrical methods developed by A. Connes and M. Rieffel. In our main result, we construct a certain family of connections on a projective module over a quantum Heisenberg manifold that gives rise to critical points of the Yang-Mills functional. Moreover, we show that there is a relationship between this particular family of critical points of the Yang-Mills functional and Laplace's equation on multiplication-type, skew-symmetric elements of quantum Heisenberg manifolds; recall that Laplacian is the leading term for the coupled set of equations making up the Yang-Mills equation.     

Non-commutative Markov chains and multi-analytic operators

We study a model of repeated interaction between quantum systems which can be thought of as a non-commutative Markov chain. It is shown that there exists an outgoing Cuntz scattering system associated to this model which induces an input-output formalism with a transfer function corresponding to a multi-analytic operator, in the sense of multivariate operator theory. Finally we show that observability for this system is closely related to the scattering theory of non-commutative Markov chains.     

New Route to Polymeric Nanoparticles by Click Chemistry Using Bifunctional Cross-Linkers

A new route to functional polymeric nanoparticles (PNPs) of different chemical nature in the 3 to 20 nm size range is reported by combining both radical addition fragmentation chain transfer (RAFT) polymerization and “click” chemistry (CC) techniques. RAFT polymerization was employed for the synthesis of well-defined statistical copolymers with pending –Cl groups along the macromolecular chain. After transformation of the –Cl groups to –N₃ groups by treatment with sodium azide, an appropriate bifunctional cross-linker is employed to obtain PNPs under CC conditions promoting intramolecular cycloaddition (cross-linking). Following this new route, polystyrene, poly(alkyl (meth)acrylate), polymethacrylic acid, poly(sodium styrenesulfonate) and poly(N-isopropyl) NPs have been synthesized and in-deep characterized.     

Supply chain interactions due to store-brand introductions: The impact of retail competition

Store-brand products are of increasing importance in retailing, often causing channel conflict as they compete with national brands. Focusing on the interactions that arise in single-manufacturer single-retailer settings, previous research suggests that one main driver of store-brand profitability to the retailer is that it leads to a reduction of the national-brand wholesale price. Under retail competition, the Robinson Patman Act then introduces an interesting trade-off: A retailer that introduces a store brand incurs the associated costs and risks, while sharing this benefit with its competition. We show that the resulting interactions can cause retailers to play “chicken”, either of them preferring a store-brand introduction by the competitor. Such interactions do not arise in channels with a single retailer, as has been the object of most previous research, and we show that some of the key insights derived from single-retailer models fail to hold when retailers compete. We conduct a numeric study, and our findings suggest that retailers are more likely to randomize their store-brand introduction strategies when customers have strong store preferences, and when the retailers’ store-brand products are similar to the national-brand product in terms of customer valuations and production cost.     

An optimal production-inventory model for deteriorating items with multiple-market demand

The global markets of today offer more selling opportunities to the deteriorating items’ manufacturers, but also pose new challenges in production and inventory planning. From a production management standpoint, opportunities to exploit the difference in the timing of the selling season between geographically dispersed markets for deteriorating items are important to improving a firm’s profitability. In this paper, we examined the above issue with an insightful production-inventory model of a deteriorating items manufacturer selling goods to multiple-markets with different selling seasons. We also provided a solution procedure to find the optimal replenishment schedule for raw materials and the optimal production plan for finished products. A numerical example was then used to illustrate the model and the solution procedure. Finally, sensitivity analysis of the optimal solution with respect to major parameters was carried out.     

Repeated newsvendor game with transshipments under dual allocations

We study a repeated newsvendor game with transshipments. In every period n retailers face a stochastic demand for an identical product and independently place their inventory orders before demand realization. After observing the actual demand, each retailer decides how much of her leftover inventory or unsatisfied demand she wants to share with the other retailers. Residual inventories are then transshipped in order to meet residual demands, and dual allocations are used to distribute residual profit. Unsold inventories are salvaged at the end of the period. While in a single-shot game retailers in an equilibrium withhold their residuals, we show that it is a subgame-perfect Nash equilibrium for the retailers to share all of the residuals when the discount factor is large enough and the game is repeated infinitely many times. We also study asymptotic behavior of the retailers’ order quantities and discount factors when n is large. Finally, we provide conditions under which a system-optimal solution can be achieved in a game with n retailers, and develop a contract for achieving a system-optimal outcome when these conditions are not satisfied.     

Manufacturer cooperation in supplier development under risk

Supplier development involves efforts undertaken by manufacturing firms to improve their suppliers’ capabilities and performance. These improvement efforts can be targeted at a variety of areas such as quality management, product development, and cost reduction. Since supplier development requires investments on the part of the manufacturer, it is important to optimally allocate investment dollars among multiple suppliers to minimize risk while maintaining an acceptable level of return. This paper presents a set of optimization models that address this issue. We consider two scenarios: single-manufacturer and multiple suppliers (SMMS) and two-manufacturer and multiple suppliers (TMMS). In the SMMS case, we suggest optimal investments in various suppliers by effectively considering risk and return. The TMMS case investigates whether manufacturers with differing capabilities could gain risk reduction benefits from cooperating with each other in supplier development. Through illustrative applications, we identify conditions in which both cooperation and non-cooperation are beneficial for manufacturers. Under conditions of cooperation, we propose optimal investments for manufacturers to achieve high levels of risk reduction benefits.     

On contracts for VMI program with continuous review (r, Q) policy

Based on continuous review (r, Q) policy, this paper deals with contracts for vendor managed inventory (VMI) program in a system comprising a single vendor and a single retailer. Two business scenarios that are popular in VMI program are “vendor with ownership” and “retailer with ownership”. Taking the system performance in centralized control as benchmark, we define a contract “perfect” if the contract can enable the system to be coordinated and can guarantee the program to be trusted. A revenue sharing contract is designed for vendor with ownership, and a franchising contract is designed for retailer with ownership. Without consideration of order policy and related costs at the vendor site, it is shown that one contract can perform satisfactorily and the other one is a perfect contract. With consideration of order policy and related costs at the vendor site, it is shown that one contract can perform satisfactorily and the performance of the other one depends on system parameters.     

Incorporating quantity discounts and their inventory impacts into the centralized purchasing decision

Multi-site organizations must balance conflicting forces to determine the appropriate degree of purchasing centralization for their respective supplies. The ability to garner quantity discounts represents one of the primary reasons that organizations centralize procurement. This paper provides methodologies to calculate optimal order quantities and compute total purchasing and inventory costs when products have quantity discount pricing. Procedures for both all-units and incremental quantity discount schedules are provided for four different strategic purchasing configurations (scenarios): complete decentralization, centralized pricing with decentralized purchasing, centralized purchasing with local distribution, and centralized purchasing and warehousing. For ordering decisions under local distribution, procedures to determine optimal order quantities and costs are presented in a precise form that could be easily implemented into spreadsheets by practicing managers. For the more complicated multi-echelon scenarios, we introduce a single-cycle policy with a tailored aggregation refinement step that performs very well under experimentation when compared to a conservative bound.