Contracting with asymmetric demand information in supply chains

We solve a buyback contract design problem for a supplier who is working with a retailer who possesses private information about the demand distribution. We model the retailer’s private information as a space of either discrete or continuous demand states so that only the retailer knows its demand state and the demand for the product is stochastically increasing in the state. We focus on contracts that are viable in practice, where the buyback price being strictly less than the wholesale price, which is itself strictly less than the retail price. We derive the optimal (for the supplier) buyback contract that allows for arbitrary allocation of profits to the retailer (subject to the retailer’s reservation profit requirements) and show that in the limit this contract leads to the first-best solution with the supplier keeping the entire channel’s profit (after the retailer’s reservation profit).     

Towards minimum loss job routing to parallel heterogeneous multiserver queues via index policies

This paper considers a Markovian model for the optimal dynamic routing of homogeneous traffic to parallel heterogeneous queues, each having its own finite input buffer and server pool, where buffer and server-pool sizes, as well as service rates, may differ across queues. The main goal is to identify a heuristic index-based routing policy with low complexity that consistently attains a nearly minimum average loss rate (or, equivalently, maximum throughput rate). A second goal is to compare alternative policies, with respect to computational demands and empirical performance. A novel routing policy that can be efficiently computed is developed based on a second-order extension to Whittle’s restless bandit (RB) index, since the latter is constant for this model. New results are also given for the more computationally demanding index policy obtained via policy improvement (PI), including that it reduces to shortest queue routing under symmetric buffer and server-pool sizes. A numerical study shows that the proposed RB index policy is nearly optimal across the instances considered, and substantially outperforms several previously proposed index policies.     

Constrained denumerable state non-stationary MDPs with expected total reward criterion

1.IntroductionandModelTheearlierliteratureaboutconstrainedMarkovdecisionprocesses(MDPs,forshort)canbefoundinDerman'sbook[1].Later,therehavebeenmanyachievementsinthisarea.Forexample,averagerewardMDPswithaconstrainthasbeendiscussedbyBeutleandRosslz],HordijkandKallenberg[3]jAltmanandSchwartz[4],etal.Inthecaseoffinitestatespace,discountedrewardcriterionMDPswithaconstrainthasbeentreatedbyKallenberg['landTanaka[6],etal.Whenstatespaceisdenumerable,suchproblemswerediscussedbySennott[71andAlt…     

A new strong optimality criterion for nonstationary Markov decision processes

This paper deals with a new optimality criterion consisting of the usual three average criteria and the canonical triplet (totally so-called strong average-canonical optimality criterion) and introduces the concept of a strong average-canonical policy for nonstationary Markov decision processes, which is an extension of the canonical policies of Herna′ndez-Lerma and Lasserre [16] (pages: 77) for the stationary Markov controlled processes. For the case of possibly non-uniformly bounded rewards and denumerable state space, we first construct, under some conditions, a solution to the optimality equations (OEs), and then prove that the Markov policies obtained from the OEs are not only optimal for the three average criteria but also optimal for all finite horizon criteria with a sequence of additional functions as their terminal rewards (i.e. strong average-canonical optimal). Also, some properties of optimal policies and optimal average value convergence are discussed. Moreover, the error bound in average reward between a rolling horizon policy and a strong average-canonical optimal policy is provided, and then a rolling horizon algorithm for computing strong average ε(>0)-optimal Markov policies is given.     

A Simple and Effective Component Procurement Policy for Stochastic Assembly Systems

We examine the component procurement problem in a single-item, make-to-stock assembly system. The suppliers are uncapacitated and have independent but non-identically distributed stochastic delivery lead times. Assembly is instantaneous, product demand follows a Poisson process and unsatisfied demand is backordered. The objective is to minimize the sum of steady-state holding and backorder costs over a pre-specified class of replenishment policies. To keep the analysis tractable, we impose a synchronization assumption that no mixing occurs between sets of component orders. Combining existing results from queueing theory with original results concerning distributions that are closed under maximization and translation, we derive a simple approximate solution to the problem when lead time variances are identical. In simulations, our derived policy is within 2% of optimal and significantly outperforms policies that ignore either component dependence or lead time stochasticity. It is also quite robust with respect to various model assumptions, except the synchronization one.     

能力验证及其评价

The definitions, purposes and uses of proficiency testing and interlaboratory comparison were expounded in detail. Main types of proficiency testing were illustrated. Special emphases were made on the organization, practice and evaluation of the planning of proficiency testing. Related policies about proficiency testing given by the China National Accreditation Board for Laboratories （CNAL） were also briefly introduced.     

Optimal pricing in a duopoly: A noncooperative differential games solution

This paper deals with a differential games model of an oligopoly ofn profit-maximizing firms competing for the same stock of customers. For the sale dynamics, it is assumed that the customers of each firm are driven away gradually by increasing product prices. Since the state variable is absent from the Hamiltonian maximizing conditions as well as from the adjoint equations, open-loop Nash solutions can be obtained. By using phase diagram analysis, for two players the behavior of the optimal pricing strategies can be characterized qualitatively. The main importance of the paper lies in the solution technique, rather than in the economic significance of the proposed model. Under the proposed assumptions, the two-point boundary-value problem resulting from the maximum principle is reduced to a terminal-value problem. It turns out that, for special salvage values of the market shares and if the planning horizon is not too short, nonmonotonic Nash-optimal price trajectories occur.Thanks are due to S. Jørgensen, A. Mehlmann, and R. Willing for helpful suggestions.     

Marginal productivity index policies for scheduling a multiclass delay-/loss-sensitive queue

This paper addresses the problem of scheduling a Markovian multiclass queue with a finite dedicated buffer for each class, where class-dependent linear holding and rejection cost rates model differing levels of tolerance to delay and loss. The goal is to design well-grounded and tractable scheduling policies that nearly minimize expected total discounted or long-run average cost. New dynamic index policies are introduced, awarding higher priority to classes with larger index values, where a class’ index measures the marginal productivity of work at its current state. The results are obtained by deploying the work-cost analysis approach to marginal productivity indices (MPIs) for restless bandits developed by the author, which is extended to the bias criterion. The MPI furnishes new insights: for a loss-sensitive class, it is a decreasing function of the number of empty buffer spaces, independent of the buffer size; for a delay-sensitive class, it is a decreasing function of the queue length. Such opposite orderings show that preventive work is more valuable than reactive work for the latter classes, whereas the opposite holds for the former. The results of a computational study on two-class instances are reported, shedding light on how the MPI policy’s relative performance varies with each parameter. Parameter ranges are thus identified where the MPI policy is near optimal, and substantially outperforms conventional benchmark policies. 2000 Mathematics Subject Classification 90B22 · 90B36 · 90B18 · 60K25 · 60K30 · 68M20     

非齐次马氏决策过程的齐次化

该文考虑的是可数状态空间有限行动空间非齐次马氏决策过程的期望总报酬准则．与以往不同的是，我们是通过扩大状态空间的方法，将非齐次的马氏决策过程转化成齐次的马氏决策过程，于是非常简洁地得到了按传统的方法所得的主要结果．