Service Completion Estimates for Cross‐trained Workforce Schedules under Uncertain Attendance and Demand

Although cross‐trained workers offer numerous operational advantages for extended‐hour service businesses, they must first be scheduled for duty. The outcome from those decisions, usually made a week or more in advance, varies with realized service demand, worker attendance, and the way available cross‐trained workers are deployed once the demands for service are known. By ignoring the joint variability of attendance and demand, we show that existing workforce scheduling models tend to overstate expected schedule performance and systematically undervalue the benefits of cross‐training. We propose a two‐stage stochastic program for profit‐oriented cross‐trained workforce scheduling and allocation decisions that is driven by service completion estimates obtained from the convolution of the employee attendance and service demand distributions. Those estimates, reflecting optimal worker allocation decisions over all plausible realizations of attendance and demand, provide the gradient information used to guide workforce scheduling decisions. Comparing the performance of workforce scheduling decisions for hundreds of different hypothetical service environments, we find that solutions based on convolution estimates are more profitable, favor proportionately more cross‐trained workers and fewer specialists, and tend to recommend significantly larger (smaller) staffing levels for services under high (low) contribution margins than workforce schedules developed with independent expectations of attendance and demand.     

多因素扰动情景下应急数量弹性契约的供应链协调

研究突发事件发生导致多种因素干扰的情景下,数量弹性契约是否能实现二级供应链协调,并寻找供应链协调时最优订货与定价策略。针对市场价格稳定和随机两种情况,设定契约弹性系数为常量,分别建立市场价格稳定不变与随机波动两种情况下的应急数量弹性契约模型,寻找它们实现协调的内在约束条件,并与基准模型下的结论进行比较。然后将契约弹性系数由常量拓展为变量,判断是否同时存在最优的弹性系数和订货量,分析弹性系数的变化对于生产、订货决策及供应链整体收益的影响。研究结果证明：当弹性系数为常量时,只要对基准契约的批发价进行适当调整,供应链就能协调应对两种情景下的突发事件,此时,可以找到唯一的最优订货决策。当弹性系数为变量时,两种情景下的供应链均不存在唯一的最优订货决策,但存在唯一的最优供货决策,并且契约弹性系数的改变不会影响供应链期望收益。最后通过算例验证了上述结论的正确性。     

Dynamic Assignment of Flexible Service Resources

Resource flexibility is an important tool for firms to better match capacity with demand so as to increase revenues and improve service levels. However, in service contexts that require dynamically deciding whether to accept incoming jobs and what resource to assign to each accepted job, harnessing the benefits of flexibility requires using effective methods for making these operational decisions. Motivated by the resource deployment decisions facing a professional service firm in the workplace training industry, we address the dynamic job acceptance and resource assignment problem for systems with general resource flexibility structure, i.e., with multiple resource types that can each perform different overlapping subsets of job types. We first show that, for systems containing specialized resources for individual job types and a versatile resource type that can perform all job types, the exact policy uses a threshold rule. With more general flexibility structures, since the associated stochastic dynamic program is intractable, we develop and test three optimization‐based approximate policies. Our extensive computational tests show that one of the methods, which we call the Bottleneck Capacity Reservation policy, is remarkably effective in generating near‐optimal solutions over a wide range of problem scenarios. We also consider a model variant that requires dynamic job acceptance decisions but permits deferring resource assignment decisions until the end of the horizon. For this model, we discuss an adaptation of our approximate policy, establish the effectiveness of this policy, and assess the value of postponing assignment decisions.     

Designing Service Level Contracts for Supply Chain Coordination

Supply contracts are used to coordinate the activities of the supply chain partners. In many industries, service level‐based supply contracts are commonly used. Under such a contract, a company agrees to achieve a certain service level and to pay a financial penalty if it misses it. The service level used in our study refers to the fraction of a manufacturer's demand filled by the supplier. We analyze two types of service level‐based supply contracts that are designed by a manufacturer and offered to a supplier. The first type of contract is a flat penalty contract, under which the supplier pays a fixed penalty to the manufacturer in each period in which the contract service level is not achieved. The second type of contract is a unit penalty contract, under which a penalty is due for each unit delivered fewer than specified by the parameters of the contract. We show how the supplier responds to the contracts and how the contract parameters can be chosen, such that the supply chain is coordinated. We also derive structural results about optimal values of the contract parameters, provide numerical results, and connect our service level measures to traditional service level measures. The results of our analyses can be used by decision makers to design optimal service level contracts and to provide them with a solid foundation for contract negotiations.     

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.     

An Advanced Heuristic for Multiple‐Option Spare Parts Procurement after End‐of‐Production

After‐sales service is a major source of profit for many original equipment manufacturers in industries with durable products. Successful engagement in after‐sales service improves customer loyalty and allows for competitive differentiation through superior service like an extended service period during which customers are guaranteed to be provided with service parts. Inventory management during this period is challenging due to the substantial uncertainty concerning demand over a long time horizon. The traditional mechanism of spare parts acquisition is to place a large final order at the end of regular production of the parent product, causing major holding costs and a high level of obsolescence risk. With an increasing length of the service period, more flexibility is needed and can be provided by adding options like extra production and remanufacturing. However, coordinating all three options yields a complicated stochastic dynamic decision problem. For that problem type, we show that a quite simple decision rule with order‐up‐to levels for extra production and remanufacturing is very effective. We propose a heuristic procedure for parameter determination which accounts for the main stochastic and dynamic interactions in decision making, but still consists of relatively simple calculations that can be applied to practical problem sizes. A numerical study reveals that the heuristic performs extremely well under a wide range of conditions, and therefore can be strongly recommended as a decision support tool for the multi‐option spare parts procurement problem. A comparison with decision rules adapted from practice demonstrates that our approach offers an opportunity for major cost reductions.     

Strategies for Addressing the Nursing Shortage: Coordinated Decision Making and Workforce Flexibility

In this article, we present strategies to help combat the U.S. nursing shortage. Key considerations include providing an attractive work schedule and work environment—critical issues for retaining existing nurses and attracting new nurses to the profession—while at the same time using the set of available nurses as effectively as possible. Based on these ideas, we develop a model that takes advantage of coordinated decision making when managing a flexible workforce. The model coordinates scheduling, schedule adjustment, and agency nurse decisions across various nurse labor pools, each of differing flexibility levels, capabilities, and costs, allowing a much more desirable schedule to be constructed. Our primary findings regarding coordinated decision making and how it can be used to help address the nursing shortage include (i) labor costs can be reduced substantially because, without coordination, labor costs on average are 16.3% higher based on an actual hospital setting, leading to the availability of additional funds for retaining and attracting nurses, (ii) simultaneous to this reduction in costs, more attractive schedules can be provided to the nurses in terms of less overtime and fewer undesirable shifts, and (iii) the use of agency nurses can help avoid overtime for permanent staff with only a 0.7% increase in staffing costs. In addition, we estimate the cost of the shortage for a typical U.S. hospital from a labor cost perspective and show how that cost can be reduced when managers coordinate.     

Cross‐Training with Imperfect Training Schemes

Cross‐training workers is one of the most efficient ways of achieving flexibility in manufacturing and service systems for increasing responsiveness to demand variability. However, it is generally the case that cross‐trained employees are not as productive on a specific task as employees who were originally trained for that task. Also, the productivity of the cross‐trained workers depends on when they are cross‐trained. In this work, we consider a two‐stage model to analyze the effects of variations in productivity levels on cross‐training policies. We define a new metric called achievable capacity and show that it plays a key role in determining the structure of the problem. If cross‐training can be done in a consistent manner, the achievable capacity is not affected when the training is done, which implies that the cross‐training decisions are independent of the opportunity cost of lost demand and are based on a trade‐off between cross‐training costs at different times. When the productivities of workers trained at different times differ, there is a three‐way trade‐off between cross‐training costs at different times and the opportunity cost of lost demand due to lost achievable capacity. We analyze the effects of variability and show that if the productivity levels of workers trained at different times are consistent, the decision maker is inclined to defer the cross‐training decisions as the variability of demand or productivity levels increases. However, when the productivities of workers trained at different times differ, an increase in the variability may make investing more in cross‐training earlier more preferable.     

面向供应链协调的利润分享契约及其响应方法研究

针对收入分享契约未能使供应链中的风险在成员企业之间有效分担的情况,提出了一种利润分享契约及其在需求价格弹性变动情况下的响应方法。按照该契约,供应商与零售商之间采用中间产品的单位成本作为结算价格,并在销售期末对供应链系统利润进行适当分配。当需求价格弹性发生变化时,需要调整利润分享契约参数以引导零售商的决策。研究表明,利润分享契约能够协调供应链;对市场需求变化的合理响应,能够促使双方接受新的协调契约,使供应链系统利润始终处于最优水平。仿真实例表明了利润分享契约及其响应方法的有效性。     

The Role of Revenue‐Focused Managerial Performance Measures in Supply Chain Coordination

Many firms employ revenue‐focused managerial performance measures (RF‐MPMs) that cause managers to worry more about revenues than about costs. Although this can seemingly misalign the interests of a manager, we show that the use of such measures can help supply chain partners to overcome hold‐up issues with respect to capacity and promotion investments. We develop a game theoretic model in which two supply chain partners engage in repeated interactions in which the supplier invests in capacity and the buyer invests in demand promotion. Following the realization of demand in each period, the two firms negotiate over the output quantity and wholesale price. The novelty of our model is that we allow the owners of each firm to delegate decision‐making power and negotiating responsibility to a free‐agent manager. We characterize the conditions under which the owners of both firms employ RF‐MPMs in equilibrium and benefit from doing so. For a special case of our model, we show that for the owners of the buyer, an RF‐MPM is equivalent to a price only relational contract, and that it complements a price and quantity relational contract as a mechanism for mitigating hold‐up issues.     

供应链单向及双向期权柔性契约比较分析

在随机市场需求环境下,对于易逝品供应链合作契约的数量柔性问题,建立了两种不同期权模式的柔性契约模型。通过对模型的求解与分析,得出了不同契约下销售商的订货策略,而且销售商在双向期权契约下比在单向看涨期权契约时的期权购买量要小,初始订货量要大,但总的预期订货量要小。销售商在两种期权契约模式下的总的最优订货量均大于传统订货方式下总的最优订货量。两种期权契约均可以提高销售商总的订货量,但在具体契约参数下,两者在接近供应链最优订货量上存在差异。     

Pay‐Back‐Revenue‐Sharing Contract in Coordinating Supply Chains with Random Yield

We consider coordination issues in supply chains where supplier's production process is subject to random yield losses. For a simple supply chain with a single supplier and retailer facing deterministic demand, a pay back contract which has the retailer paying a discount price for the supplier's excess units can provide the right incentive for the supplier to increase his production size and achieve coordination. Building upon this result, we consider coordination issues for two other supply chains: one with competing retailers, the other with stochastic demand. When retailers compete for both demand and supply, they tend to over‐order. We show that a combination of a pay back and revenue sharing mechanism can coordinate the supply chain, with the pay back mechanism correcting the supplier's under‐producing problem and the revenue sharing mechanism correcting the retailers' over‐ordering problem. When demand is stochastic, we consider a modified pay‐back‐revenue‐sharing contract under which the retailer agrees to not only purchase the supplier's excess output (beyond the retailer's order), but also share with the supplier a portion of the revenue made from the sales of the excess output. We show that this contract, by giving the supplier additional incentives in the form of revenue share, can achieve coordination.     

Coordinating Service‐Sensitive Demand and Capacity by Adaptive Decision Making: An Application of Case‐Based Decision Theory*

The subject of this article is the simultaneous choice of product price and manufacturing capacity if demand is stochastic and service‐level sensitive. In this setting, capacity as well as price have an impact on demand because several aspects of service level depend on capacity. For example, delivery time will be reduced if capacity is increased given a constant demand rate. We illustrate the relationship between service level, capacity, and demand reaction by a stylized application problem from the after‐sales services industry. The reaction of customers to variations in service level and price is represented by a kinked price‐demand‐rate function. We first derive the optimal price‐capacity combination for the resulting decision problem under full information. Subsequently, we focus on a decision maker (DM) who lacks complete knowledge of the demand function. Hence the DM is unable to anticipate the service level and consequently cannot identify the optimal solution. However, the DM will acquire additional information during the sales process and use it in subsequent revisions of the price‐capacity decision. Thus, this decision making is adaptive and based on experience. In contrast to the literature, which assumes certain repetitive procedures somewhat ad hoc, we develop an adaptive decision process based on case‐based decision theory (CBDT) for the price‐capacity problem. Finally, we show that a CBDT DM in our setting eventually finds the optimal solution, if the DM sets the price based on absorption costs and adequately adjusts the capacity with respect to the observed demand.     

Designing Efficient Infrastructural Investment and Asset Transfer Mechanisms in Humanitarian Supply Chains

We analyze the efficacy of different asset transfer mechanisms and provide policy recommendations for the design of humanitarian supply chains. As a part of their preparedness effort, humanitarian organizations often make decisions on resource investments ex ante because doing so allows for rapid response if an adverse event occurs. However, programs typically operate under funding constraints and donor earmarks with autonomous decision‐making authority resting with the local entities, which makes the design of efficient humanitarian supply chains a challenging problem. We formulate this problem in an agency setting with two independent aid programs, where different asset transfer mechanisms are considered and where investments in resources are of two types: primary resources that are needed for providing the aid and infrastructural investments that improve the operation of the aid program in using the primary resources. The primary resources are acquired from earmarked donations. We show that allowing aid programs the flexibility of transferring primary resources improves the efficiency of the system by yielding greater social welfare than when this flexibility does not exist. More importantly, we show that a central entity that can acquire primary resources from one program and sell them to the other program can further improve system efficiency by providing a mechanism that facilitates the transfer of primary resources and eliminates losses from gaming. This outcome is achieved without depriving the individual aid programs of their decision‐making autonomy while maintaining the constraints under which they operate. We find that outcomes with centralized resource transfer but decentralized infrastructural investments by the aid programs are the same as with a completely centralized system (where both resource transfer and infrastructural investments are centralized).     

The Comparison of Two Vertical Outsourcing Structures under Push and Pull Contracts

In a three‐tier supply chain comprising an original equipment manufacturer (OEM), a contract manufacturer (CM), and a supplier, there exist two typical outsourcing structures: control and delegation. Under the control structure, the OEM contracts with the CM and the supplier respectively. Under the delegation structure, the OEM contracts with the CM only and the CM subcontracts with the supplier. We compare the two outsourcing structures under a push contract (whereby orders are placed before demand is realized) and a pull contract (whereby orders are placed after demand is realized). For all combinations of outsourcing structures and contracts, we derive the corresponding equilibrium wholesale prices, order quantities, and capacities. We find that the equilibrium production quantity is higher under control than under delegation for the push contract whereas the reverse holds for the pull contract. Both the OEM and the CM prefer control over delegation under the push contract. However, under the pull contract, the OEM prefers control over delegation whereas the CM and the supplier prefer delegation over control. We also show that for a given outsourcing structure, the OEM prefers the pull contract over the push contract. In extending our settings to a general two‐wholesale‐price (TWP) contract, we find that when wholesale prices are endogenized decision variables, the TWP contract under our setting degenerates to either a push or a pull contract.     

Definitions and linkages between operational and strategic flexibilities

This paper aims at clarifying the concept of strategic flexibility, starting from that much more common of manufacturing flexibility (or operational one). After characterizing the dimensions of the latter, a classification of strategic flexibility is presented which distinguishes four categories. The measures of strategic flexibility are also investigated. Then two analogies are pointed out with the operational flexibility. The first, of the cause-effect type, is on two levels: at the business level, the operational flexibility estimates the variation of practices, while the strategic flexibility measures the effect obtained on performances; at the corporate level, the operational flexibility estimates the variation of competences, while the strategic flexibility evaluates the change in business. The second analogy, related to the classification variables, permits the main types of operational and strategic flexibilities to be placed in a single framework. So this study seeks to provide a framework—which has not been proposed in prior literature—for analyzing and evaluating the correlated concepts of operational and strategic flexibilities, to create a theoretical foundation for future research and empirical testing.     

Managing High‐Tech Capacity Expansion via Reservation Contracts

We study capacity reservation contracts between a high‐tech manufacturer (supplier) and her OEM customer (buyer). The supplier and the buyer are partners who enter a ‘design‐win” agreement to develop the product, and who share the stochastic demand information. To encourage the supplier for more aggressive capacity expansion, the buyer reserves capacity upfront by paying a deductible fee. As capacity expansion demonstrates diseconomy of scale in this context, we assume convex capacity costs. We show that as the buyer's revenue margin decreases, the supplier faces a sequence of four profit scenarios with decreasing desirability. We examine the effects of market size and demand variability to the contract conditions. We propose two channel coordination contracts, and discuss how such contracts can be tailored for situations where the supplier has the option of not complying with the contract, and when the buyer's demand information is only partially updated during the supplier's capacity lead‐time.     

Home healthcare integrated staffing and scheduling

Workforce planning for home healthcare represents an important and challenging task involving complex factors associated with labor regulations, caregivers’ preferences, and demand uncertainties. This task is done manually by most home care agencies, resulting in long planning times and suboptimal decisions that usually fail to meet the health needs of the population, to minimize operating costs, and to retain current caregivers. Motivated by these challenges, we present a two-stage stochastic programming model for employee staffing and scheduling in home healthcare. In this model, first-stage decisions correspond to the staffing and scheduling of caregivers in geographic districts. Second-stage decisions are related to the temporary reallocation of caregivers to neighboring districts, to contact caregivers to work on a day-off, and to allow under- and over-covering of demand. The proposed model is tested on real-world instances, where we evaluate the impact on costs, caregiver utilization, and service level by using different recourse actions. Results show that when compared with a deterministic model, the two-stage stochastic model leads to significant cost savings as staff dimensioning and scheduling decisions are more robust to accommodate changes in demand. Moreover, these results suggest that flexibility in terms of use of recourse actions is highly valuable as it helps to further improve costs, service level, and caregiver utilization.     

Elective Patient Admission and Scheduling under Multiple Resource Constraints

We consider a patient admission problem to a hospital with multiple resource constraints (e.g., OR and beds) and a stochastic evolution of patient care requirements across multiple resources. There is a small but significant proportion of emergency patients who arrive randomly and have to be accepted at the hospital. However, the hospital needs to decide whether to accept, postpone, or even reject the admission from a random stream of non‐emergency elective patients. We formulate the control process as a Markov decision process to maximize expected contribution net of overbooking costs, develop bounds using approximate dynamic programming, and use them to construct heuristics. We test our methods on data from the Ronald Reagan UCLA Medical Center and find that our intuitive newsvendor‐based heuristic performs well across all scenarios.     

On multi-criteria chance-constrained capacitated single-source discrete facility location problems

This work aims at investigating multi-criteria modeling frameworks for discrete stochastic facility location problems with single sourcing. We assume that demand is stochastic and also that a service level is imposed. This situation is modeled using a set of probabilistic constraints. We also consider a minimum throughput at the facilities to justify opening them. We investigate two paradigms in terms of multi-criteria optimization: vectorial optimization and goal programming. Additionally, we discuss the joint use of objective functions that are relevant in the context of some humanitarian logistics problems. We apply the general modeling frameworks proposed to the so-called stochastic shelter site location problem. This is a problem emerging in the context of preventive disaster management. We test the models proposed using two real benchmark data sets. The results show that considering uncertainty and multiple objectives in the type of facility location problems investigated leads to solutions that may better support decision making.