Location-allocation on a line with demand-dependent costs

This paper extends the location-allocation formulation by making the cost charged to users by a facility a function of the total number of users patronizing the facility. Users select their facility based on facility charges and transportation costs. We explore equilibria where each customer selects the least expensive facility (cost and transportation) and where the facility is at a point that minimizes travel costs for its customers. The problem in its general form is quite complex. An interesting special case is studied: facilities and customers are located on a finite line segment and demand is distributed on the line by a given density function.     

Determining dominant wind directions

In this paper we address the problem of selecting a set of wind directions that could represent the wind regime at a location. This problem is cast in the form of a non-convex mathematical program. Important properties of the problem are discussed and a convergent solution algorithm is designed. The algorithm could yield local optimal solutions. A case study which involves the construction of a transition probability matrix for the wind at a location is presented.     

A dynamic lot sizing model with exponential machine breakdowns

This paper addresses the dynamic lot sizing model with the assumption that the equipment is subject to stochastic breakdowns. We consider two different situations. First we assume that after a machine breakdown the setup is totally lost and new setup cost is incurred. Second we consider the situation in which the cost of resuming the production run after a failure might be substantially lower than the production setup cost. We show that under the first assumption the cost penalty for ignoring machine failures will be noticeably higher than in the classical lot sizing case with static demand. For the second case, two lot sizes per period are required, an ordinary lot size and a specific second (or resumption) lot size. If during the production of a future period demand the production quantity exceeds the second lot size, the production run will be resumed after a breakdown and terminated if the amount produced is less than this lot size. Considering the results of the static lot sizing case, one would expect a different policy. To find an optimum lot sizing decision for both cases a stochastic dynamic programming model is suggested.     

Fuzzy facility location-allocation problem under the Hurwicz criterion

Facility location-allocation (FLA) problem has been widely studied by operational researchers due to its many practical applications. Many researchers have studied the FLA problem in a deterministic environment. However, the models they proposed cannot accommodate satisfactorily various customer demands in the real world. Thus, we consider the FLA problem with uncertainties. In this paper, a new model named α-cost model under the Hurwicz criterion is presented with fuzzy demands. In order to solve this model, the simplex algorithm, fuzzy simulations and a genetic algorithm are integrated to produce a hybrid intelligent algorithm. Finally, some numerical examples are presented to illustrate the effectiveness of the proposed algorithm.     

Location of single-server immobile facilities subject to a loss constraint

Waiting may be unacceptable, even a short time, at a facility providing a serviceinvolving medical or other emergencies. Hence, it is appropriate to locate suchfacilities so that the rate at which users are lost is limited. Eachfacility will here be modelled as anM/E _r /m/N queueing systemsubject to a loss restriction constraint and the single-server case(m=1) will be treated in detail. Introduction of the Erlangdistribution for service times allows a better fit of the model to actual valuesof both mean and variance than do currently available models that use anexponential distribution. Location of facilities will be such that the averagetravel time to a facility is minimized. It is shown how a deterministicconstraint, equivalent to the loss constraint, can be generated resulting in aninteger linear program, and values of a parameterρ _c which facilitates this linearization aretabulated for various values of r, N and service leveldemanded. Numerical experiments are performed including an application looselyrelated to the location of neonatal clinics in the Municipality of Rio deJaneiro. Finally, there is a discussion of how further improved modelling of theservice time distribution might be effected.     

带惩罚的动态设施选址问题的近似算法

本文研究带惩罚的动态设施选址问题,在该问题中假设不同时段内设施的开放费用、用户的需求及连接费用可以不相同,而且允许用户的需求不被满足,但是要有惩罚.对此问题我们给出了第-个近似比为1.8526的原始对偶(组合)算法.     

Dynamic uncapacitated lot sizing with random demand under a fillrate constraint

This paper deals with the single-item dynamic uncapacitated lot sizing problem with random demand. We propose a model based on the “static uncertainty” strategy of Bookbinder and Tan (1988). In contrast to these authors, we use exact expressions for the inventory costs and we apply a fillrate constraint. We present an exact solution method and modify several well-known dynamic lot sizing heuristics such that they can be applied for the case of dynamic stochastic demands. A numerical experiment shows that there are significant differences in the performance of the heuristics whereat the ranking of the heuristics is different from that reported for the case of deterministic demand.     

Location and size of day nurseries— a multiple goal approach

This paper uses a mathematical model to determine the location and size of day nurseries within a town. The solution consists of finding a compromise among three conflicting objectives. Mixed integer multiple goal programming is used to solve the problem. Actual data is analysed.     

Minimizing Weighted Number of Early and Tardy Jobs with a Common Due Window Involving Location Penalty

This paper studies a single machine scheduling problem to minimize the weighted number of early and tardy jobs with a common due window. There are n non-preemptive and simultaneously available jobs. Each job will incur an early (tardy) penalty if it is early (tardy) with respect to the common due window under a given schedule. The window size is a given parameter but the window location is a decision variable. The objective of the problem is to find a schedule that minimizes the weighted number of early and tardy jobs and the location penalty. We show that the problem is NP-complete in the ordinary sense and develop a dynamic programming based pseudo-polynomial algorithm. We conduct computational experiments, the results of which show that the performance of the dynamic algorithm is very good in terms of memory requirement and CPU time. We also provide polynomial time algorithms for two special cases.     

Location of depots in a sugar-beet distribution system

In the following case study the problem of the location of depots in a sugar-beet distribution system for a certain sugar enterprise in Poland is considered. The sugar-beet is delivered from farms to sugar-mills either directly or through some depots. Lower and upper limits on the depot throughputs are imposed. The depot investment and operating costs are estimated by a piecewiselinear function. Given a set of possible depot locations, costs associated with the depots and the unit transportation costs, we seek a minimum cost location-transportation plan determining the number, location and sizes of the depots to be opened and the amounts of the sugar-beet flows. Two solution procedures are developed: (1) The application of MPSX and MIP systems for the problem of the reduced size; (2) The heuristic method. Based upon the computational results both approaches can be treated as alternative solution techniques to the presented problem.     

Location game on disjoint line segments

Two players are endowed with resources for setting up N locations on K line segments of identical length, with N > K ≥ 1. The players alternately choose these locations (possibly in batches of more than one in each round) in order to secure the area closer to their locations than that of their rival’s. The player with the highest secured area wins the game and otherwise the game ends in a tie. Earlier research has shown that, if an analogous game is played on disjoint circles, the second mover advantage is in place only if K = 1, while for K > 1 both players have a tying strategy. It was also shown that these results hold for line segments of identical length when rules of the game additionally require players to take exactly one location in the first round. In this paper we show that the second mover advantage is still in place for K ≥ 1 and 2K − 1 ≤ N, even if the additional restriction is dropped, while K ≤ N < 2K − 1 results in the first mover advantage. Our results allow us to draw conclusions about a natural variant of the game, where the resource mobility constraint is more stringent so that in each round each player chooses a single location and we show that the second mover advantage re-appears for K ≤ N < 2K − 1 if K is an even number. In all the cases the losing player has a strategy guaranteeing him arbitrarily small loss.     

关于“一类最优指派问题的动态规划模型”的注记

考虑一类较一般的最优指派问题 :欲指派 m个人做 n项工作 (m≥n) ,要求每个人只做一项工作 ,第j项工作可以由 bj个人共同去做 ,其中 bj是待求未知数 ,满足 dj≤ bj≤ ej(即 ej,dj为第 j项工作所需人数的上下限 )及 ∑nj=1bj=m(即每个人都有工作 ) ,dj,ej为已知常数 ,j =1 ,… ,n.第 i人做第 j项工作的效益为 cij≥ 0 ,i =1 ,… ,m;j =1 ,… ,n.本文建立求解上述最优指派问题 (使总的效益最大 )的动态规划模型 ,并将文 [1]作为本文的特例 .     

Location of retail facilities under conditions of uncertainty

Models for the optimal location of retail facilities are typically premised on current market conditions. In this paper we incorporate future market conditions into the model for the location of a retail facility. Future market conditions are analyzed as a set of possible scenarios. We analyze the problem of finding the best location for a new retail facility such that the market share captured at that location is as close to the maximum as possible regardless of the future scenario. The objective is the minimax regret which is widely used in decision analysis. To illustrate the models an example problem is analyzed and solved in detail.     

Lot sizing with carbon emission constraints

This paper introduces new environmental constraints, namely carbon emission constraints, in multi-sourcing lot-sizing problems. These constraints aim at limiting the carbon emission per unit of product supplied with different modes. A mode corresponds to the combination of a production facility and a transportation mode and is characterized by its economical costs and its unitary carbon emission. Four types of constraints are proposed and analyzed in the single-item uncapacitated lot-sizing problem. The periodic case is shown to be polynomially solvable, while the cumulative, global and rolling cases are NP-hard. Perspectives to extend this work are discussed.     

Location problems

Recent developments for several location problems are surveyed. These include: graph theoretic and combinatorial formulations of the simple plant location problem, the NP-hardness of some p-center problems, worst-case bounds for several polynomial-time heuristics for some p-center problems, and a general solution to a class of one facility network problems with convex cost functions.     

A dynamic programming approach for batch sizing in a multi-stage production process with random yields

This paper proposes a dynamic programming approach to modeling and determining batch sizes in a single period, multi-stage production process with random yields for each stage. To improve the computational performance of the proposed approach, a statistical bound is developed. A key decision incorporated into the model is whether to continue onto the next stage of processing or to scrap the entire current batch of product. This decision is based on the expected total profit from the remaining items for processing following the removal of all defectives. The decisions involving the locations of test stations after stages are also incorporated into the modeling approach.     

Scheduling at coal handling facilities using Simulated Annealing

The main thrust of this study is the operational scheduling of the continuous coal handling and blending processes when considering multiple, and sometimes conflicting, objectives. A widely applicable generic goal programming model is proposed. Furthermore, assumptions regarding the certainty of demand during different periods are challenged, endeavoring to provide more robust schedules in a largely stochastic environment. As the study aims to provide scheduling solutions to any coal handling facility, the Simulated Annealing metaheuristic is proposed to ensure that acceptably good solutions for large instances of the generic model can be found in reasonable computational time. The generic approach and its suggested application will be valuable not only in the coal handling environment, but also in the continuous product manufacturing/blending or continuous material handling environment.     

Uniqueness of certain polynomials constant on a line

We study a question with connections to linear algebra, real algebraic geometry, combinatorics, and complex analysis. Let p(x,y) be a polynomial of degree d with N positive coefficients and no negative coefficients, such that p=1 when x+y=1. A sharp estimate d?2N-3 is known. In this paper we study the p for which equality holds. We prove some new results about the form of these “sharp” polynomials. Using these new results and using two independent computational methods we give a complete classification of these polynomials up to d=17. The question is motivated by the problem of classification of CR maps between spheres in different dimensions.     

The elixir of life: using a maintenance, repair and replacement model based on virtual and operating age in the water industry

Processing equipment in the water industry is subject to decayand requires maintenance, repair and eventual replacement. Thechallenge of competition within the water industry and the accompanyingregulatory regime requires that actions be integrated and costeffective. This is an industry, which has considerable dataon the failure of its equipment, but until recently very fewmodels of the maintenance process have been built. This paper describes the context of this problem for cleanwater processing where the equipment is that required to purifywater. It proposes a model based on the virtual and operatingage of the components. The operating age reflects the true ageof the equipment while the virtual age allows for the cumulativeeffect of maintenance actions performed on the equipment. Themodel also allows for different types of equipment by describingdegradation by Cox's proportional hazards model. Thus the specialfeatures of the equipment and environment in which the equipmentoperates are described by a set of characteristics, which modifythe hazard rate of the failure time of the equipment. This approachusing Cox's model with virtual and operating age can be appliedto other processing industries including the gas industry andthe ‘dirty water’ side of the water industry. The model is formulated as a stochastic dynamic programmingor Markov decision process and the form of the optimal policyis determined. This shows that repair and replacement shouldonly be performed when the equipment has failed and describesgeneral conditions when replacement is appropriate. The optimalpolicy is calculated numerically using the value iteration algorithmfor a specific example based on data on failure.