Optimal Capacity Allocation Research Articles

Customer Acquisition, Retention, and Service Access Quality: Optimal Advertising, Capacity Level, and Capacity Allocation

Problem definition We provide guidelines on three fundamental decisions of customer relationship management (CRM) and capacity management for profit-maximizing service firms that serve heterogeneous repeat customers, whose acquisition, retention, and behavior depend on their service access quality to bottleneck capacity: how much to spend on customer acquisition, how much capacity to deploy, and how to allocate capacity and tailor service access quality levels to different customer types. Academic/ practical relevance These decisions require a clear understanding of the connections between customers’ behavior and value, their service access quality, and the capacity allocation. However, existing models ignore these connections. Methodology We develop and analyze a novel fluid model that accounts for these connections. Simulation results suggest that the fluid-optimal policy also yields nearly optimal performance for large stochastic queueing systems with abandonment. Results First, we derive new customer value metrics that extend the standard ones by accounting for the effects of the capacity allocation, the resulting service access qualities, and customer behavior: a customer’s lifetime value; her Vμ index, where V is her one-time service value and μ her service rate; and her policy-dependent value, which reflects the Vμ indices of other served types. Second, we link these metrics to the profit-maximizing policy and to new capacity management prescriptions, notably, optimality conditions for rationing capacity and for identifying which customers to deny service. Further, unlike standard index policies, the optimal policy prioritizes customers based not on their Vμ indices, but on policy- and type-dependent functions of these indices. Managerial implications First, our study highlights the importance of basing decisions on more complete metrics that link customer value to the service access quality; marketing-focused policies that ignore these links may reduce profits significantly. Second, the proposed metrics provide guidelines for valuing customers in practice. Third, our decision guidelines help managers design more profitable policies that effectively integrate CRM and capacity management considerations. The online appendix is available at https://doi.org/10.1287/msom.2017.0635 .

Setting production capacities for production agents making selfish routing decisions

ABSTRACTTraditionally, the capacity dimensioning step within the manufacturing system design process takes a known and fixed distribution of production flow across path alternatives to derive capacity demand based on a desired target utilisation rate. Setting target rates for machine utilisation provides limits on throughput times and allows to provide capacity buffers against changes in the production mix. In this contribution, we transfer this rationale into the world of Industry 4.0, where Cyber-Physical Systems can make autonomous and selfish routing decisions. Under this new framework, non-cooperative agents make decisions based on the capacity allocation and the decisions of all other agents, thus creating a feedback between flow and capacity distribution that makes existing methods for capacity dimensioning inapplicable. We use methods and insight from algorithmic game theory and operations research to investigate the capacity dimensioning process in this context. We prove properties of the throughput-time optimal allocation of production capacity under fixed target utilisation rates for important queue classes. Our findings not only provide a quantitative, easy to operationalise tool for production system designers, but also explore a trade-off between cost and flexibility that arises naturally in this regime.

Joint optimisation of capacity and safety stock allocation

We study the joint optimisation of capacity and safety stock allocation in assembly systems. Particularly, we consider capacitated systems with base-stock policies and periodic review. Capacity allocation is restricted by budget constraints, which can connect multiple systems. Our objective is to minimise overall inventory holding costs while satisfying service level as well as budget constraints. We propose an algorithm to jointly approximate optimal capacity allocation and base-stock levels. To this end, we introduce a set of convex approximations for this non-convex optimisation problem. In order to solve the resulting convex programmes, we analytically compute sample path derivatives via infinitesimal perturbation analysis. By iteratively adapting the approximations, we achieve good capacity allocations and base-stock levels for the original problem. Furthermore, we introduce a heuristic to allocate capacity, which originates from link capacity allocation in communication networks and use it as a benchmark. The algorithm is applied to small illustrative examples as well as cases motivated by the semiconductor manufacturing process at IBM Systems. It turns out that particularly for high utilisation levels, our algorithm can achieve significant improvements compared to the capacity allocation heuristic.

Optimal capacity allocation for sampled networked systems

We consider the problem of estimating the states of weakly coupled linear systems from sampled measurements. We assume that the total capacity available to the sensors to transmit their samples to a network manager in charge of the estimation is bounded above, and that each sample requires the same amount of communication. Our goal is then to find an optimal allocation of the capacity to the sensors so that the time-averaged estimation error is minimized. We show that when the total available channel capacity is large, this resource allocation problem can be recast as a strictly convex optimization problem, and hence there exists a unique optimal allocation of the capacity. We further investigate how this optimal allocation varies as the available capacity increases. In particular, we show that if the coupling among the subsystems is weak, then the sampling rate allocated to each sensor is nondecreasing in the total sampling rate, and is strictly increasing if and only if the total sampling rate exceeds a certain threshold.

Forest-based biofuel production in the Nordic countries: Modelling of optimal allocation

Biofuels have been promoted as a likely avenue for the future transportation energy mix. Hence, production of biofuels using lignocellulosic feedstocks, such as forest-based biomass, is expected to increase globally. Forest biomass abundance and experience with applying biomass conversion technologies gives the Nordic countries an advantage in catering to biofuel production capacity investment. Yet, given uncertainties in the techno-economic variables of biofuel conversion technologies, as well as differences between the Nordic countries in terms of labor costs, bioheat market prices and electricity and forest biomass costs and prices, it is unclear which of the Nordic countries are comparatively attractive for future investment in forest-based biofuel production capacity. In this paper, we quantify how techno-economic cost components of a novel forest-based biofuel production technology affect optimal allocation of biofuel production capacity in the Nordic countries at a regional level. We apply a scenario analysis approach using an endogenous biofuel capacity investment module in the Nordic Forest Sector Model (NFSM). In each scenario, we alter the techno-economic features of the technology and quantify total biofuel production allocation volume in each region and at a national level. We find that optimal capacity allocation is affected by the type of feedstock used in the technology and will affect existing industries dependent on forest feedstocks. Electricity selling or purchasing will have little effect on allocation because it comprises a small revenue or cost proportion. Bioheat may affect allocation, but this will depend on local demand. Finally, labor costs may affect allocation, but this will depend on the labor intensity, which changes with scale. The results are relevant for policy incentives to proliferate future forest-based biofuel production in the Nordic countries.

Optimal Portfolio Selection of GenCo Under Congestion Risk in Multimarket Environment

In a restructured electricity market derivative instruments help in reducing price risk. This paper proposes a portfolio optimization model considering uncertainty of electricity spot prices. Using this model, a thermal generation company (GenCo) holding contracts within and outside its jurisdiction can maximize its profit with limited risk exposure. The proposed model is formulated using mean variance portfolio theory, considering spot market, bilateral contracts and options with the possibility of managing congestion risk while trading between different locations. To handle uncertainties scenario generation and reduction techniques are used. The spot price inaccuracies are further represented as scenario tree. The producers risk preference is expressed by a utility function as the trade-off between expectation and variance of the return. For multiple scenarios the optimization problem is solved to obtain a stochastic solution to the optimal capacity allocation problem. The work addresses price variability of zonal transaction considering both physical and financial contracts to schedule the output of an opportunistic GenCo for maximizing its profit by creating hedging strategy through multiple scenarios. The results indicate that the proposed model is capable of improving the profit risk trade-off of the portfolios. GenCos profit seeking behavior during congestion relieving situation has also been demonstrated in the proposed risk modeling. Study is performed on a GenCo situated in NORDPOOL market.

Reducing energy consumption in serial production lines with Bernoulli reliability machines

This paper is devoted to developing an integrated model to minimise energy consumption while maintaining desired productivity in Bernoulli serial lines with unreliable machines and finite buffers. For small systems, such as three- and four-machine lines with small buffers, exact analysis to optimally allocate production capacity is introduced. For medium size systems (e.g. three- and four-machine lines with larger buffers, or five-machine lines with small buffers), an aggregation procedure to evaluate line production rate is introduced. Using it, optimal allocation of machine efficiency is searched to minimise energy consumption. Insights and allocation principles are obtained through the analyses. Finally, for larger systems, a fast and accurate heuristic algorithm is presented and validated through extensive numerical experiments to obtain optimal allocation of production capacity to minimise energy consumption while maintaining desired productivity.

Optimizing Allocation of Battery Energy Storage System Capacity in Coordination with Contract Price in Distribution Network

This paper presents a double-layer synergistic optimization method for battery energy storage system (BESS) allocation considering contract price. From the point of view of the distribution company (DISCO) operator, the upper layer explores the potential benefits of the BESS configuration and set reasonable BESS charge and discharge price. From the BESS operator point of view, the lower layer on the basis of the upper layer given contract price, to determine BESS optimal capacity and optimal power allocation, as well as the charge and discharge power at any times. This paper uses the improved particle swarm optimizer to solve the problem and introduces Cauchy-Gaussian reduction mutation factor to adjust the local optimal extremum. An improved IEEE-33 nodes system is studied. Cases analysis shows that the method proposed in this paper allows both DISCO and BESS operators to be profitable.

Optimal Allocation of Flood Control Capacity for Multi-Reservoir Systems Using Multi-Objective Optimization Approach

Operation of multi-reservoir systems during flood periods is of great importance in the field of water resources management. This paper proposes a multi-objective optimization model with new formulation for optimal operation of multi-reservoir systems. In this model, the release rate and the flood control capacity of each reservoir is considered as decision variable and the resulting nonlinear non-convex multi-objective optimization problem is solved with e-constraint method through the mixed integer linear programming (MILP). Objective functions of the model are minimizing the flood damage at downstream sites and the loss of hydropower generation. The developed model is used to determine optimal operating strategies for Karkheh multi-reservoir system in southwestern Iran. For this purpose, the model is executed in two scenarios based on “two-reservoir” and “six-reservoir” systems and for floods with return periods of 25 and 50 years. The results show that in two-reservoir system, flood damage is at least about 114 million dollars and cannot be mitigated any further no matter how hydropower generation is managed. But, in the case of developing all six reservoirs, optimal strategies of coordinated operation can mitigate and even fully prevent flood damage.

Scheduling Operating Rooms with Elective and Emergency Surgeries

The issue of allocating capacity to accommodate emergent surgery cases while scheduling elective patients has major policy implications for Level-1 trauma centers including most large academic medical centers. This is because operating rooms (ORs) are the greatest source of revenues for hospitals, while also being the largest cost centers. However, scheduling ORs, especially at level-1 trauma hospitals, is challenging due to significant uncertainty in the arrivals of patients requiring emergent surgery. When scheduling surgeries, hospitals face a trade-off between the need to be responsive to emergency cases and the need to conduct scheduled elective surgeries as planned. We develop a model that allocates the OR capacity to elective patients so that the emergency patients who arrive randomly can be accommodated without incurring any excessive delays. The objective is to develop a framework for aggregate weekly schedules and generate detailed daily schedules that minimize a weighted sum of the ORs’ operating time, idle time, and overtime. Optimization procedures are developed to devise effective block schedules while a rescheduling procedure schedules elective patients who are affected by an emergency arrival. Initially, the procedures are based on deterministic surgery times for the elective patients and then they are extended to stochastic surgery times. We illustrate our methodology on specialized ORs for trauma cases related to neurosurgery. We show that for a given arrival rate of emergency patients, the total expected cost is convex in the weekly load of the elective surgeries scheduled. Numerical experiments are devised to obtain the total expected cost curves for various arrival rates of emergency patients. Using these cost curves the optimal capacity allocation of ORs to elective patients can be determined as a function of the arrival rate of emergency patients.

Enhanced Situational Awareness through a Decision Support Service for Optimal Allocation of Resources and Response Capacity

Enhanced Situational Awareness through a Decision Support Service for Optimal Allocation of Resources and Response Capacity

Capacity Allocation of Hydrogen Production and Fuel Cells in Wind Farm Based on Stochastic Prediction Error

Hydrogen production system is special energy storage device. Hydrogen production using wind power and electricity generation using hydrogen fuel cells can reduce wind power grid-connected power fluctuation. The optimal capacity allocation is determined based on the hydrogen production and fuel cells energy conversion efficiency. With the target of hydrogen throughput and stabilizing power fluctuation effect, the optimal internal configuration of electrolyzers and fuel cells is determined by comparing the different parameters of them. In the case studies, without the aid of other sources of energy, the system can achieve the goal of reducing wind power fluctuation by the optimal capacity allocation and the internal configuration, which verifies the accuracy and effectiveness of the method in this paper.

Optimal allocation of surplus gas and suitable capacity for buffer users in steel plant

Byproduct gases are an important secondary energy source in the iron and steel industry. A novel mathematical programming model was established in this paper to study the optimal allocation of surplus gas in buffer users in the byproduct gas system, on the basis of which a new method for calculating the suitable capacities of gasholders and boilers was also proposed. The validity and practicability of the model and the design method were tested in an iron and steel enterprise. The results show that gas emissions were controlled, boiler efficiency was improved, and surplus gas-related power generation was increased by approximately 5×104kWh in each hour compared with the actual data from the iron and steel enterprise. Finally, fitting curves of the relationship between the designed fuel load of the boiler and the capacity of the gasholder were obtained. Scientific guidance is thus provided for the improvement of buffer users in steel plants in the future.

Allocation of Wind Capacity Subject to Long Term Voltage Stability Constraints

Increasing wind capacity integration results in displacement of active power from conventional generators and a reduction in reactive power sources available. As such, voltage stability may become a concern in certain periods for power system operation particularly in weaker areas of the network. Thus, it is of importance to consider the AC constraints for optimal wind generation planning (long term) in order to decrease the possibility of a wind capacity allocation that requires costly remedies from the power system operation perspective (short term). In this work, a procedure is proposed for wind capacity allocation with the aim of benefiting from the potential of an optimal wind capacity allocation for enhancing the voltage stability margin. The procedure is based on a multi operating conditions voltage stability constrained optimal power flow. The wind capacity target is set and the loadability margin is tracked. The results will show the applicability of the proposed procedure and will emphasize the effects of the pattern of wind capacity allocation on the loadability margin. This will result in a wind capacity allocation that enhances the minimum loadability margin among the possible future operating conditions considered for planning. The procedure uses the Maximin concept for this purpose.

Multi-echelon Supply Chain Flexibility Enhancement Through Detecting Bottlenecks

This study suggests a supply chain design deploying a novel idea from production planning. The idea of capacity bottlenecks is used to improve flexibility in a multi-echelon multi-product supply chain. We suggest an optimization model that focuses on optimal capacity allocations to bottleneck points in order to enhance overall flexibility. The proposed mixed-integer linear programming model minimizes the total cost of facility establishment as well as their utilization and transportation cost. The performance of suggested model is investigated by several test problems with uncertainty in demand, cost, capacity, and product specifications. The results indicate the superiority of the suggested model to the previous flexibility formulation method. According to the numerical results, the proposed model decreases the total supply chain cost by up to 16 % on average. Another advantageous feature of the proposed model is its capability of solving previously insolvable test problems by optimizing flexibility levels.

Optimal Placement of Distributed Energy Storage in Power Networks

We formulate the optimal placement, sizing and control of storage devices in a power network to minimize generation costs with the intent of load shifting. We assume deterministic demand, a linearized DC approximated power flow model and a fixed available storage budget. Our main result proves that when the generation costs are convex and nondecreasing, there always exists an optimal storage capacity allocation that places zero storage at generation-only buses that connect to the rest of the network via single links. This holds regardless of the demand profiles, generation capacities, line-flow limits and characteristics of the storage technologies. Through a counterexample, we illustrate that this result is not generally true for generation buses with multiple connections. For specific network topologies, we also characterize the dependence of the optimal generation cost on the available storage budget, generation capacities and flow constraints.

Revenue Maximization with Optimal Capacity Control in Infrastructure as a Service Cloud Markets

Infrastructure-as-a-Service cloud providers offer diverse purchasing options and pricing plans, namely on-demand, reservation, and spot market plans. This allows them to efficiently target a variety of customer groups with distinct preferences and to generate more revenue accordingly. An important consequence of this diversification however, is that it introduces a non-trivial optimization problem related to the allocation of the provider's available data center capacity to each pricing plan. The complexity of the problem follows from the different levels of revenue generated per unit of capacity sold, and the different commitments consumers and providers make when resources are allocated under a given plan. In this work, we address a novel problem of maximizing revenue through an optimization of capacity allocation to each pricing plan by means of admission control for reservation contracts, in a setting where aforementioned plans are jointly offered to customers. We devise both an optimal algorithm based on a stochastic dynamic programming formulation and two heuristics that trade-off optimality and computational complexity. Our evaluation, which relies on an adaptation of a large-scale real-world workload trace of Google, shows that our algorithms can significantly increase revenue compared to an allocation without capacity control given that sufficient resource contention is present in the system. In addition, we show that our heuristics effectively allow for online decision making and quantify the revenue loss caused by the assumptions made to render the optimization problem tractable.

Optimal Map Reduce Job Capacity Allocation in Cloud Systems

We are entering a Big Data world. Many sectors of our economy are now guided by data-driven decision processes. Big Data and business intelligence applications are facilitated by the MapReduce programming model while, at infrastructural layer, cloud computing provides flexible and cost effective solutions for allocating on demand large clusters. Capacity allocation in such systems is a key challenge to provide performance for MapReduce jobs and minimize cloud resource costs. The contribution of this paper is twofold: (i) we provide new upper and lower bounds for MapReduce job execution time in shared Hadoop clusters, (ii) we formulate a linear programming model able to minimize cloud resources costs and job rejection penalties for the execution of jobs of multiple classes with (soft) deadline guarantees. Simulation results show how the execution time of MapReduce jobs falls within 14% of our upper bound on average. Moreover, numerical analyses demonstrate that our method is able to determine the global optimal solution of the linear problem for systems including up to 1,000 user classes in less than 0.5 seconds.

Radiation Queue: Meeting Patient Waiting Time Targets

This article proposes a queueing and patient pooling approach for radiotherapy capacity allocation with heterogeneous treatment machines called linear accelerators (LINACs), different waiting time targets (WTTs), and treatment protocols. We first propose a novel queueing framework with LINAC time slots as servers. This framework leads to simple single-class queues for the evaluation of WTT satisfaction that would, otherwise, require an analysis of complicated multiclass queues with reentrance. Mixed-integer programming models are proposed for capacity allocation and case-mix optimization under WTT constraints. We then extend the queueing framework by pooling the basic patient types into groups sharing the same slot servers. A mathematical programming model and a pairwise merging heuristic are proposed for patient pooling optimization to minimize the overall LINAC capacity needed to meet all WTT requirements. Extended numerical experiments are conducted to assess the efficiency of our approach and to show the properties of optimal capacity allocation and patient pooling.

Reconciling quality and cost: A case study in interventional radiology.

To provide a method to calculate delay cost and examine the relationship between quality and total cost. The total cost including capacity, supply and delay cost for running an interventional radiology suite was calculated. The capacity cost, consisting of labour, lease and overhead costs, was derived based on expenses per unit time. The supply cost was calculated according to actual procedural material use. The delay cost and marginal delay cost derived from queueing models was calculated based on waiting times of inpatients for their procedures. Quality improvement increased patient safety and maintained the outcome. The average daily delay costs were reduced from 1275 € to 294 €, and marginal delay costs from approximately 2000 € to 500 €, respectively. The one-time annual cost saved from the transfer of surgical to radiological procedures was approximately 130,500 €. The yearly delay cost saved was approximately 150,000 €. With increased revenue of 10,000 € in project phase 2, the yearly total cost saved was approximately 290,000 €. Optimal daily capacity of 4.2 procedures was determined. An approach for calculating delay cost toward optimal capacity allocation was presented. An overall quality improvement was achieved at reduced costs. • Improving quality in terms of safety, outcome, efficiency and timeliness reduces cost. • Mismatch of demand and capacity is detrimental to quality and cost. • Full system utilization with random demand results in long waiting periods and increased cost.