Locating Facilities in the Presence of Disruptions and Incomplete Information*

In this article, we analyze a location model where facilities may be subject to disruptions. Customers do not have advance information about whether a given facility is operational or not, and thus may have to visit several facilities before finding an operational one. The objective is to locate a set of facilities to minimize the total expected cost of customer travel. We decompose the total cost into travel, reliability, and information components. This decomposition allows us to put a value on the advance information about the states of facilities and compare it to the reliability and travel cost components, which allows a decision maker to evaluate which part of the system would benefit the most from improvements. The structure of optimal solutions is analyzed, with two interesting effects identified: facility centralization and co‐location; both effects appear to be stronger than in the complete information case, where the status of each facility is known in advance.     

Location and reliability problems on a line: Impact of objectives and correlated failures on optimal location patterns

In this paper we study a class of locations models where facilities are not perfectly reliable and failures may be correlated. We analyze problems with Median and Center objectives under complete and incomplete customer information regarding the state of facilities. The goal is to understand how failure probabilities, correlations, availability of information, and problem objective affect the optimal location patterns. In particular, we want to find analytical confirmations for location patterns observed in numerical experiments with network location models. To derive closed-form analytical results the analysis is restricted to a simple (yet classic) setting: a 2-facility problem on a unit segment, with customer demand distributed uniformly over the segment (results can be extended to other demand distributions as well). We derive explicit expressions for facility trajectories as functions of model parameters, obtaining a number of managerial insights. In addition we provide the decomposition of the optimal cost into the closed form components corresponding to the cost of travel, the cost of facility unreliability and the cost of incomplete information. Most of the theoretical insights are confirmed via numerical experiments for models with larger (3–5) number of facilities.     

Capacity Sharing and Cost Allocation among Independent Firms with Congestion

We analyze the benefit of production/service capacity sharing for a set of independent firms. Firms have the choice of either operating their own production/service facilities or investing in a facility that is shared. Facilities are modeled as queueing systems with finite service rates. Firms decide on capacity levels (the service rate) to minimize delay costs and capacity investment costs possibly subject to service‐level constraints on delay. If firms decide to operate a shared facility they must also decide on a scheme for sharing the capacity cost. We formulate the problem as a cooperative game and identify settings under which capacity sharing is beneficial and there is a cost allocation that is in the core under either the first‐come, first‐served policy or an optimal priority policy. We show that capacity sharing may not be beneficial in settings where firms have heterogeneous work contents and service variabilities. In such cases, we specify conditions under which capacity sharing may still be beneficial for a subset of the firms.     

Flexible Servers in Understaffed Tandem Lines

We study the dynamic assignment of cross‐trained servers to stations in understaffed lines with finite buffers. Our objective is to maximize the production rate. We identify optimal server assignment policies for systems with three stations, two servers, different flexibility structures, and either deterministic service times and arbitrary buffers or exponential service times and small buffers. We use these policies to develop server assignment heuristics for Markovian systems with larger buffer sizes that appear to yield near‐optimal throughput. In the deterministic setting, we prove that the best possible production rate with full server flexibility and infinite buffers can be attained with partial flexibility and zero buffers, and we identify the critical skills required to achieve this goal. We then present numerical results showing that these critical skills, employed with an effective server assignment policy, also yield near‐optimal throughput in the Markovian setting, even for small buffer sizes. Thus, our results suggest that partial flexibility is sufficient for near‐optimal performance, and that flexibility structures that are effective for deterministic and infinite‐buffered systems are also likely to perform well for finite‐buffered stochastic systems.     

基于双层规划的反恐应急设施选址模型及算法

恐怖袭击常以人流密集地区的平民作为袭击目标，并存在突发性和随机性等特点，极易造成严重的袭击后果。通过反恐应急设施的合理布局可以缩短救援人员和物资的到达时间，从而减轻袭击后果。首先，对反恐应急设施选址问题进行描述，并将其构造为一类离散双层规划模型。其中，上层规划是关于政府选址的0-1规划问题，下层规划则是关于恐怖分子袭击目标选择的0-1规划问题。其次，结合模型和问题的特征设计算法，利用分支定界算法实现上层选址变量的隐枚举，同时通过下层问题的求解来确定上下界并判断是否满足分枝或剪枝的条件。最后，结合南疆地区的交通拓扑网络进行算例分析，结果证明有效的选址方案可以大大降低袭击损失。     

Optimal Workforce Mix in Service Systems with Two Types of Customers

We consider a service system with two types of customers. In such an environment, the servers can either be specialists (or dedicated) who serve a specific customer type, or generalists (or flexible) who serve either type of customers. Cross‐trained workers are more flexible and help reduce system delay, but also contribute to increased service costs and reduced service efficiency. Our objective is to provide insights into the choice of an optimal workforce mix of flexible and dedicated servers. We assume Poisson arrivals and exponential service times, and use matrix‐analytic methods to investigate the impact of various system parameters such as the number of servers, server utilization, and server efficiency on the choice of server mix. We develop guidelines for managers that would help them to decide whether they should be either at one of the extremes, i.e., total flexibility or total specialization, or some combination. If it is the latter, we offer an analytical tool to optimize the server mix.     

服务水平保证下应急抢修点选址模型及求解算法研究

本文研究了一类故障率低但重要性较高设备的应急抢修点选址问题。设备的故障发生过程和从应急抢修点到故障设备的通行时间是随机的,每个设备被分配给一个应急抢修点进行抢修,并且整个应急抢修系统的服务水平要大于给定标准。本文以应急抢修点总开设成本最小作为目标,同时考虑了设备覆盖约束、抢修分配关系约束和抢修系统服务水平约束,在合理的假设下证明设备发生故障且应急抢修小组迟到的总次数服从泊松分布,最终将应急抢修点选址问题描述为一个0-1整数规划模型。通过对模型中的覆盖约束和抢修系统服务水平约束进行松弛,设计了相应的拉格朗日启发式算法。最后通过对大量随机算例进行计算,证明了该模型和算法的有效性。     

On tie breaking in competitive location under binary customer behavior

Ties in customer facility choice may occur when the customer selects the facility with maximum utility to be served. In the location literature ties in maximum utility are broken by assigning a fixed proportion of the customer demand to the facilities with maximum utility which are owned by the entering firm. This tie breaking rule does not take into account the number of tied facilities of both the entering firm and its competitors. In this paper we introduce a more realistic tie breaking rule which assigns a variable proportion of customer demand to the entering firm depending on the number of tied facilities. We present a general framework in which optimal locations for the old and the new tie breaking rules can be obtained through Integer Linear Programming formulations of the corresponding location models. The optimal locations are obtained for the old tie breaking rule for different values of the fixed proportion and a comparison with the results obtained for the new tie breaking rule is drawn with data of Spanish municipalities in a variety of scenarios. Finally, some conclusions are presented.     

Facility Location: A Robust Optimization Approach

In this research, we apply robust optimization (RO) to the problem of locating facilities in a network facing uncertain demand over multiple periods. We consider a multi‐period fixed‐charge network location problem for which we find (1) the number of facilities, their location and capacities, (2) the production in each period, and (3) allocation of demand to facilities. Using the RO approach we formulate the problem to include alternate levels of uncertainty over the periods. We consider two models of demand uncertainty: demand within a bounded and symmetric multi‐dimensional box, and demand within a multi‐dimensional ellipsoid. We evaluate the potential benefits of applying the RO approach in our setting using an extensive numerical study. We show that the alternate models of uncertainty lead to very different solution network topologies, with the model with box uncertainty set opening fewer, larger facilities. Through sample path testing, we show that both the box and ellipsoidal uncertainty cases can provide small but significant improvements over the solution to the problem when demand is deterministic and set at its nominal value. For changes in several environmental parameters, we explore the effects on the solution performance.     

层次型应急设施布局模型及其应用

应急设施的特殊性决定了应急设施布局作为特殊的设施布局问题,必须更加注重及时性。应急服务的级别决定应急布局模型的考虑因素,现实中往往同时布局多个层次的应急设施,本文基于一个p-中心重心的混合模型,建立了层次型应急设施布局模型。根据应急服务的真实情况,该模型对距离的测算进行了改进,以交通网络距离代替欧氏距离。最后,将其应用于上海市上海某区的医疗设施布局。     

A Bicriterion Maximal Covering Location Formulation Which Considers the Satisfaction of Uncovered Demand

There have been many applications of the maximal covering location problem (MCLP). An underlying assumption of the MCLP is that demand not covered (i.e., not within a prespecified maximal distance of a facility) is not served. This may be an unrealistic assumption in many location planning scenarios, especially in the public sector. For example, in cases such as fire protection or ambulance service, calls not technically covered will still be serviced. The MCLP, however, does not consider the distances or travel times necessary to service such demand. This paper presents a bicriterion locational covering model which explicitly considers the travel distance or time necessary to service demand not within the maximal covering distance of a facility. The model may be used to generate noninferior (Pareto optimal) siting configurations which demonstrate the inherent trade-offs between a siting scheme designed to maximize total coverage and one designed to minimize total travel time for uncovered demand to reach its nearest facility. In addition, it is shown that for any particular weighting scheme on the two objectives, the problem can be solved as a p-median problem; a problem for which several efficient solution methods exist.     

考虑最坏中断损失下的P-中位设施选址问题的模型与算法研究

蓄意突袭以及恐怖袭击会造成设施服务的突然中断成为网络系统的主要危害之一,因此网络设施选址决策应该同时考虑正常和紧急状态下系统的运作成本.本文研究考虑最坏中断损失下的网络设施选址问题,建立了该问题的双层规划模型,上层规划涉及设施选址决策,下层规划研究确定设施位置后,设施中断产生最大损失的问题.本文运用基于拉格朗日松弛的混合遗传算法来求解该双层规划问题.将European150数据集作为研究对象,对比研究了本文研究问题与传统的P-中位选址问题的结果,分析不同选址策略下网络系统的效率被中断影响的程度是不同的.最后通过改变一些关键参数,比如常规运作权重、设施数量、中断设施数量,对相关结果进行了分析.     

设施失灵风险下不确定需求应急定位-路径鲁棒优化研究

为抵御突发灾害对路网造成的破坏性和设施失灵风险,降低系统成本,并快速完成应急救援任务,本文考虑到受灾点物资需求量的不确定和风险对救援系统的影响,采用直升机进行物资运送以规避路径风险。建立了最小化应急物流系统总成本和物资到达需求点总救援时间为双目标的应急物流定位-路径鲁棒优化模型,基于相对鲁棒优化方法处理需求不确定,采用偏差鲁棒优化思想描述设施失灵风险损失,采用遗传算法进行求解。通过对三个算例进行数据仿真实验,证明了相对鲁棒优化方法在处理需求不确定和偏差鲁棒优化方法在处理设施失灵风险方面的有效性,进而为解决应急设施点的开设和救援物资的安全及时准确配送,增强应急物流系统的风险应对能力提供了有效的方法。     

The Use of Flexible Manufacturing Capacity in Pharmaceutical Product Introductions*

This work considers the value of the flexibility offered by production facilities that can easily be configured to produce new products. We focus on technical uncertainty as the driver of this value, while prior works focused only on demand uncertainty. Specifically, we evaluate the use of process flexibility in the context of risky new product development in the pharmaceutical industry. Flexibility has value in this setting due to the time required to build dedicated capacity, the finite duration of patent protection, and the probability that the new product will not reach the market due to technical or regulatory reasons. Having flexible capacity generates real options, which enables firms to delay the decision about constructing product‐specific capacity until the technical uncertainty is resolved. In addition, initiating production in a flexible facility can enable the firm to optimize production processes in dedicated facilities. The stochastic dynamic optimization problem is formulated to analyze the optimal capacity and allocation decisions for a flexible facility, using data from existing literature. A solution to this problem is obtained using linear programming. The result of this analysis shows both the value of flexible capacity and the optimal capacity allocation. Due to the substantial costs involved with flexibility in this context, the optimal level of flexible capacity is relatively small, suggesting products be produced for only short periods before initiating construction of dedicated facilities.     

Quality‐Speed Competition in Customer‐Intensive Services with Boundedly Rational Customers

We consider a system in which two competing servers provide customer‐intensive services and the service reward is affected by the length of service time. The customers are boundedly rational and choose their service providers according to a logit model. We demonstrate that the service provider revenue function is unimodal in the service rate, its decision variable, and show that the service rate competition has a unique and stable equilibrium. We then study the price decision under three scenarios with the price determined by a revenue‐maximizing firm, a welfare‐maximizing social planner, or two servers in competition. We find that the socially optimal price, subject to the requirement that the customer actual utility must be non‐negative, is always lower than the competition equilibrium price which, in turn, is lower than the revenue‐maximizing monopoly price. However, if the customer actual utility is allowed to be negative in social optimization, the socially optimal price can be higher than the other two prices in a large market.     

The min-p robust optimization approach for facility location problem under uncertainty

Improper value of the parameter p in robust constraints will result in no feasible solutions while applying stochastic p-robustness optimization approach (p-SRO) to solving facility location problems under uncertainty. Aiming at finding the lowest critical p-value of parameter p and corresponding robust optimal solution, we developed a novel robust optimization approach named as min-p robust optimization approach (min-pRO) for P-median problem (PMP) and fixed cost P-median problem (FPMP). Combined with the nearest allocation strategy, the vertex substitution heuristic algorithm is improved and the influencing factors of the lowest critical p-value are analyzed. The effectiveness and performance of the proposed approach are verified by numerical examples. The results show that the fluctuation range of data is positively correlated with the lowest critical p-value with given number of new facilities. However, the number of new facilities has a different impact on lowest critical p-value with the given fluctuation range of data. As the number of new facilities increases, the lowest critical p-value for PMP and FPMP increases and decreases, respectively.

     

Flexibility Structure and Capacity Design with Human Resource Considerations

Most service systems consist of multidepartmental structures with multiskill agents that can deal with several types of service requests. The design of flexibility in terms of agents' skill sets and assignments of requests is a critical issue for such systems. The objective of this study was to identify preferred flexibility structures when demand is random and capacity is finite. We compare structures recommended by the flexibility literature to structures we observe in practice within call centers. To enable a comparison of flexibility structures under optimal capacity, the capacity optimization problem for this setting is formulated as a two‐stage stochastic optimization problem. A simulation‐based optimization procedure for this problem using sample‐path gradient estimation is proposed and tested, and used in the subsequent comparison of the flexibility structures being studied. The analysis illustrates under what conditions on demand, cost, and human resource considerations, the structures found in practice are preferred.     

Increasing the Revenue of Self‐Storage Warehouses by Facility Design

Self‐storage is a booming industry. Both private customers and companies can rent temporary space from such facilities. The design of self‐storage warehouses differs from other facility designs in its focus on revenue maximization. A major question is how to design self‐storage facilities to fit market segments and accommodate volatile demand to maximize revenue. Customers that cannot be accommodated with a space size of their choice can be either rejected or upscaled to a larger space. Based on data of 54 warehouses in America, Europe, and Asia, we propose a new facility design approach with models for three different cases: an overflow customer rejection model and two models with customer upscale possibilities, one with reservation and another without reservation. We solve the models for several real warehouse cases, and our results show that the existing self‐storage warehouses can be redesigned to generate larger revenues for all cases. Finally, we show that the upscaling policy without reservation generally outperforms the upscaling policy with reservation.     

DUAL-RESOURCE PARALLEL QUEUES WITH SERVER TRANSFER AND INFORMATION ACCESS DELAYS*

Dual-resource constrained queuing systems contain fewer servers than service facilities. This study uses computer simulation to evaluate several server assignment procedures in a dual-resource system. A field study serves as the basis for developing a model with two service facilities in parallel, a single server, and deterministic information access and transfer delays that can be applied to job shops, computer operating systems, and elevators. Several findings, useful in server assignment decision making, resulted from the study. If first-come, first-served sequencing is used, delaying server assignment at a facility until all jobs are completed reduces both the mean and the variance of job flow time. If shortest-process-time-first sequencing is used, an assignment rule is tested that delays a server at a facility until a sufficiently short job is estimated to have arrived elsewhere. This rule performs best overall in terms of both the mean and variance of flow time. Methods to implement this decision rule easily are discussed.     

An integrated system for capacity planning and facility layout

In order to achieve efficient facility design for service type activities, operating under dynamic conditions and a large number of constraints, the use of a traditional approach has proved to be tedious and time consuming. Development of an efficient decision support system for such a situation calls for the consideration of the complex nature of interaction between the system parameters and the relationship between the working environment and the resources within the system. Mathematical programming techniques, e.g. linear and integer programming as well as queuing models, though useful in handling combinatorial optimization problems, are incapable of dealing with stochastic utilization problems normally encountered in the design of facilities of a fast changing environment. This paper makes use of a pattern search algorithm for the optimal allocation of service facility resources. The layout of the facilities has then been optimized by the use of the CLASS algorithm. The two separate algorithms have suitably been integrated together into a single simulation-based system. The effectiveness of the proposed methodology has been demonstrated by means of a real case study pertaining to design and layout optimization of a multi-functional gasoline service station in Bangkok.