Inventory based allocation policies for flexible servers in?serial systems

Motivated by an industry example, we study a two-station serial system in which we allocate flexible servers in order to maximize throughput. We investigate two cases which are different in the way that servers work together when at the same station; namely collaboratively or non-collaboratively. For the collaborative case we prove the optimal policy to be such that the servers work together at a single station at any point in time. In addition to the policy being state-dependent, it also follows a switching-curve structure. In the non-collaborative case, on the other hand, it may be optimal to allocate servers to different stations. Some numerical examples and results regarding policy assignments, switching curves, and system throughput are presented.     

Income redistribution policies and decision support systems — Problems and potentials

Recent trends in Western industrial countries towards a re-examination of the means and goals of the welfare state have increased the demand for studies of the redistributive effects of government policies. The purpose of this paper is to discuss some problems and potentials of decision support systems in this field, with emphasis on the problems of value judgements and evaluation criteria and with reference to the author's experiences from the development of an interactive computer model of the Swedish tax and transfer system. The basic structure of the model and some examples of its application are briefly described.     

Channel coordination with manufacturer��s return policies within a newsvendor framework

The saliency of returns in today’s business world is unquestionable, in such items as toys, Christmas decorations, books, seasonal/fashion items and the like. This is largely due to the high economic benefits prevalent in some industries today and to the increasing opportunities for resale in secondary and global markets. This paper attempts to model the profitability of returns policy in presence of a secondary market, to a profit-maximizing manufacturer in a newsvendor framework. The returns policy applies both for the unsold merchandise left at the end of the selling season and the items returned by the unsatisfied customers within the specified time period. With a returns policy, the manufacturer shares the risks of demand uncertainty, in turn assuaged by the availability of secondary market. The manufacturer’s decision is to arrive at an optimal wholesale price and the returns policy, based on the retailer’s reaction on that offer. The retailer in turn optimizes the retail price and the order quantity to meet a price-dependent uncertain demand. This set of optimal policies has then been contrasted to that obtained from maximizing the combined profit of the manufacturer and of the retailer. The key question in the comparison has been clearly answered. The total combined profit that coordinates the policies of both channels exceeds that of the sum of the profits obtained independently.     

A selection algorithm for ∊-optimal policies in undiscounted maekovian decision problems

In many real-world problems it is interesting to know the whole set of optimal or e-optimal policies of a finite-state, finite-action undiscounted Markovian Decision Problem. For finding all optimal or e-optimal policies of such a given problem we present in many real-world problems it is interesting to know the whole set of optimal or e-optimal policies of a finite-state, finite-action undiscounted Markovian Decision Problem. For finding all optimal or e-optimal policies of such a given problem we present sideration of subproblems which will be solved by Howard'S policy iteration.     

Multi-mode resource-constrained project scheduling problem with material ordering under bonus–penalty policies

This study emphasizes that project scheduling and material ordering (time and quantity of an order) must be considered simultaneously to minimize the total cost, as setting the material ordering decisions after the project scheduling phase leads to non-optimal solutions. Hence, this paper mathematically formulates the model for the multi-mode resource-constrained project scheduling with material ordering (MRCPSMO) problem. In order to be more realistic, bonus and penalty policies are included for the project. The objective function of the model consists of four elements: the material holding cost, the material ordering cost, the bonus paid by the client and the cost of delay in the project completion. Since MRCPSMO is NP-hard, the paper proposes three hybrid meta-heuristic algorithms called PSO-GA, GA-GA and SA-GA to obtain near-optimal solutions. In addition, the design of experiments and Taguchi method is used to tune the algorithms’ parameters. The proposed algorithms consist of two components: an outside search, in which the algorithm searches for the best schedule and mode assignment, and the inside search, which determines the time and quantity of orders of the nonrenewable resources. First, a comparison is made for each individual component with the exact or best solutions available in the literature. Then, a set of standard PROGEN test problems is solved by the proposed hybrid algorithms under fixed CPU time. The results reveal that the PSO-GA algorithm outperforms both GA-GA and SA-GA algorithms and provides good solutions in a reasonable time.     

Optimal repair–replacement policies for a system with two types of failures

In this paper, the optimal replacement problem is investigated for a system with two types of failures. One type of failure is repairable, which is conducted by a repairman when it occurs, and the other is unrepairable, which leads to a replacement of the system at once. The repair of the system is not “as good as new”. The consecutive operating times of the system after repair form a decreasing geometric process, while the repair times after failure are assumed to be independent and identically distributed. Replacement policy N is adopted, where N is the number of repairable failures. The system will be replaced at the Nth repairable failure or at the unrepairable failure, whichever occurs first. Two replacement models are considered, one is based on the limiting availability and the other based on the long-run average cost rate of the system. We give the explicit expressions for the limiting availability and the long-run average cost rate of the system under policy N, respectively. By maximizing the limiting availability A(N) and minimizing the long-run average cost rate C(N), we theoretically obtain the optimal replacement policies N^∗ in both cases. Finally, some numerical simulations are presented to verify the theoretical results.     

Optimal business policies for a supplier–transporter–buyer channel with a price-sensitive demand

As the third party logistics partners (carriers) taking a more and more significant role in supply chain practices and customer service performance improvement, there is an emerging need for the studies on optimal channel coordination policies for business processes involving not only supplier and buyer (retailer), but also transportation partners. In this paper, we explicitly add a transportation partner with concave cost functions into the analysis for supplier–buyer channel coordination policies, and analyse the impact of coordination and pricing policies on supply chain profitability. The market demand is assumed to be a decreasing convex function of buyer's selling price (x), D(x)=d/x². Under this assumption, we quantify the improvement on total supply chain profitability when moving from a non-cooperative environment to a fully cooperative environment, and show that the joint annual profit of three partners in a cooperative environment can be at least twice of what may be achieved by three independently operated companies in a leader–follower business game. While in a real-world business environment, a perfect collaboration is hard to achieve, this result can be used to provide a quick estimation on the upper bound on the budget for profit sharing or discount offers among the supply chain partners.     

On the properties of ε(≥0) optimal policies in discounted unbounded return model

This paper investigates the properties of (0) optimal policies in the model of [2]. It is shown that, if * = ( ₀ ^* , ₁ ^* ,..., _n ^* , _n ^+1/* , ...) is a-discounted optimal policy, then ( ₀ ^* , ₁ ^* , ..., _n ^* ) for alln0 is also a-discounted optimal policy. Under some condition we prove that stochastic stationary policy _n ^* corresponding to the decision rule _n ^* is also optimal for the same discounting factor. We have also shown that for each-optimal stochastic stationary policy ₀ ^* , ₀ ^* can be decomposed into several decision rules to which the corresponding stationary policies are also-optimal separately; and conversely, a proper convex combination of these decision rules is identified with the former ₀ ^* . We have further proved that for any (,)-optimal policy, say *=( ₀ ^* , ₁ ^* , ..., _n ^* , _n ^+1/* , ...), _n–1 ^* ) is ((1– ⁿ )^–1 e, ) optimal forn>0. At the end of this paper we mention that the results about convex combinations and decompositions of optimal policies of § 4 in [1] can be extended to our case.Project supported by the Science Fund of the Chinese Academy of Sciences.     

Who contributes to public goods? With an application to local economic policies in the Netherlands

We present three models for the extent to which actors reduce their contributions to the production of a public good because of expected contributions by other actors. The first model is a simple game theoretic model, the second a spatial autocorrelation model, and the third is a hybrid of the first two models. Estimation of the three models from incomplete data is discussed. The three models are applied to data on economic policies of municipalities in the Netherlands. In particular, it is probed whether municipalities take a free ride on the measures of their neighbors.     

Sequential location—allocation of public facilities in one- and two-dimensional space: Comparison of several policies

The present paper examines the sequential location—allocation problems of public facilities in one- and two-dimensional space under several policies. It is shown that the efficiency loss due to the adoption of a myopic policy is not so large, contrary to common belief, provided that the efficiency can be measured by the total transportation cost of users and by the total capacity of facilities. If the total serving area is sufficiently narrow, then the spatial allocations of optimal solutions in two-dimensional problems can be closely approximated by those in one-dimensional problems.     

Generalised ‘join the shortest queue’ policies for the dynamic routing of jobs to multi-class queues

Jobs or customers arrive and require service that may be provided at one of several different stations. The associated routing problems concern how customers may be assigned to stations in an optimal manner. Much of the classical literature concerns a single class of customers seeking service from a collection of homogeneous stations. We argue that many contemporary application areas call for the analysis of routing problems in which many classes of customer seek service provided at a collection of diverse stations. This paper is the first to consider routing policies in such complex environments which take appropriate account of the degree of congestion at each service station. A simple and intuitive class of policies emerges from a policy improvement approach. In a numerical study, the policies were close to optimal in all cases.     

Asymptotically optimal interruptible service policies for?scheduling jobs in a diffusion regime with?nondegenerate slowdown

A?parallel server system is considered, with I customer classes and many servers, operating in a heavy traffic diffusion regime where the queueing delay and service time are of the same order of magnitude. Denoting by $\widehat{X}^{n}$ and $\widehat{Q}^{n}$ , respectively, the diffusion scale deviation of the headcount process from the quantity corresponding to the underlying fluid model and the diffusion scale queue-length, we consider minimizing r.v.??s of the form $c^{n}_{X}=\int_{0}^{u}C(\widehat{X}^{n}(t))\,dt$ and $c^{n}_{Q}=\int_{0}^{u}C(\widehat{Q}^{n}(t))\,dt$ over policies that allow for service interruption. Here, C:? ^I ???₊ is continuous, and u>0. Denoting by ?? the so-called workload vector, it is assumed that $C^{*}(w):=\min\{C(q):q\in\mathbb{R}_{+}^{\mathbf{I}},\theta\cdot q=w\}$ is attained along a continuous curve as w varies in ?₊. We show that any weak limit point of $c^{n}_{X}$ stochastically dominates the r.v. $\int_{0}^{u}C^{*}(W(t))\,dt$ for a suitable reflected Brownian motion W and construct a sequence of policies that asymptotically achieve this lower bound. For $c^{n}_{Q}$ , an analogous result is proved when, in addition, C ^? is convex. The construction of the policies takes full advantage of the fact that in this regime the number of servers is of the same order as the typical queue-length.     

The optimal order and payment policies for deteriorating items in discount cash flows analysis under the alternatives of conditionally permissible delay in payments and cash discount

This study investigates a deteriorating inventory problem in which the supplier simultaneously offers the retailer either a conditionally permissible delay in payments or a cash discount. In the case of a conditionally permissible delay, if the retailer orders more than a predetermined quantity, then he/she has a grace period to make the full payment. Otherwise, he/she must pay the payment for goods of certain proportion first while receiving the goods and has a grace period to pay off the rest. As to a cash discount, if the retailer pays for the entire amount of the order within a certain short period, then he/she will receive a cash discount from the supplier. In additions, from a financial standpoint, all cash outflows related to the inventory control that occur at different points of time have different values. Hence, it is necessary to take account of the factor of time value of monetary when drafting the replenishment policy. In a word, this paper uses an alternate approach-discount cash flow (DCF) analysis to establish an inventory problem for deteriorating items in which the supplier provides the retailer either a conditionally permissible delay or a cash discount. We then study the necessary and sufficient conditions for finding the optimal solution. Furthermore, we establish several theoretical results to obtain the solution that provides the smallest present value of all future cash flows. Finally, several numerical examples are given to illustrate the results and obtain some managerial insights.