Intelligent Procedures for Intra‐Day Updating of Call Center Agent Schedules

For nearly all call centers, agent schedules are typically created several days or weeks before the time that agents report to work. After schedules are created, call center resource managers receive additional information that can affect forecasted workload and resource availability. In particular, there is significant evidence, both among practitioners and in the research literature, suggesting that actual call arrival volumes early in a scheduling period (typically an individual day or week) can provide valuable information about the call arrival pattern later in the same scheduling period. In this paper, we develop a flexible and powerful heuristic framework for managers to make intra‐day resource adjustment decisions that take into account updated call forecasts, updated agent requirements, existing agent schedules, agents' schedule flexibility, and associated incremental labor costs. We demonstrate the value of this methodology in managing the trade‐off between labor costs and service levels to best meet variable rates of demand for service, using data from an actual call center.     

Benefactors and Beneficiaries: The Effects of Giving and Receiving on Cost‐Coalitional Problems

Motivated by supply chain collaborations in practice, we introduce a class of cost‐coalitional problems, which are based on a priori information about the cost faced by each agent in each set that it could belong to. Our focus is on problems with decreasingly monotonic coalitional costs. In this class of problems, we study the effects of giving and receiving when there exist players whose participation in an alliance always contributes to the savings of all alliance members (we refer to these players as benefactors), and there also exist players whose cost decreases in such an alliance (we call them beneficiaries). We use linear and quadratic norm cost games to analyze the role played by benefactors and beneficiaries in achieving stability of different cooperating alliances. We consider different notions of stability (the core and the bargaining set) and provide conditions for stability of an all‐inclusive alliance of agents which leads to minimum value of total cost incurred by all agents.     

A Model for Partial Product Complementarity and Strategic Production Decisions under Demand Uncertainty

This paper considers a general industrial setting where multiple manufacturers each produce a different product and sell it to the markets. These products are partially complementary in the sense that there is a common demand stream that requests all these products as complementary sets and there are streams of individual demands each requesting only one of the products. All demands are uncertain and may follow any general, joint distributions. Facing demand uncertainties, the manufacturers each choose a production quantity for its product with an objective to maximize its own expected profit. We formulate the problem as a non‐cooperative game to study the strategic interactions of such firms and their implications to supply chain performance. We show that such a game may have numerous equilibria. Among all the possible equilibria, however, we prove that there always exists a unique one that maximizes each and every manufacturer's profit, and we derive an explicit solution for this Pareto‐optimal equilibrium point. We further study the optimal solution for a centralized system and compare it with the decentralized solution. Managerial insights are drawn as to how system parameters and control mechanisms affect firms' decisions and performance.     

Skill Management in Large‐Scale Service Marketplaces

Large‐scale, web‐based service marketplaces have recently emerged as a new resource for customers who need quick resolutions for their short‐term problems. Due to the temporary nature of the relations between customers and service providers (agents) in these marketplaces, customers may not have an opportunity to assess the ability of an agent before their service completion. On the other hand, the moderating firm has a more sustained relationship with agents, and thus it can provide customers with more information about the abilities of agents through skill screening mechanisms. In this study, we consider a marketplace where the moderating firm can run two skills tests on agents to assess if their skills are above certain thresholds. Our main objective is to evaluate the effectiveness of skill screening as a revenue maximization tool. We, specifically, analyze how much benefit the firm obtains after each additional skill test. We find that skill screening leads to negligible revenue improvements in marketplaces where agent skills are highly compatible and the average service times are similar for all customers. As the compatibility of agent skills weakens or the customers start to vary in their processing time needs, we show that the firm starts to experience sizable improvements in revenue from skill screening. Apparently, the firm can reap the most of these substantial benefits when it runs only one test. For instance, in marketplaces where agents posses uncorrelated skills, the second skill test only brings an additional 2% improvement in revenue. Accounting for possible skill screening costs, we then show the optimality of offering only one test when the compatibility between agent skills is sufficiently low. The results of this study also have important implications in terms of the right level of intervention in the marketplaces we study.     

Market Good Flexibility in Capacity Auctions

We consider the allocation of limited production capacity among several competing agents through auctions. Our focus is on the contribution of flexibility in market good design to effective capacity allocation. The application studied is a capacity allocation problem involving several agents, each with a job, and a facility owner. Each agent generates revenue by purchasing capacity and scheduling its job at the facility. Ascending auctions with various market good designs are compared. We introduce a new market good that provides greater flexibility than those previously considered in the literature. We allow ask prices to depend both on agents’ utility functions and on the number of bids at the previous round of the auction, in order to model and resolve resource conflicts. We develop both optimal and heuristic solution procedures for the winner determination problem. Our computational study shows that flexibility in market good design typically increases system value within auctions. A further increase is achieved if each agent is allowed to bid for multiple market goods at each round. On average, the multiple flexible market goods auction provides over 95% of the system value found by centralized planning.     

Demand Functions in Decision Modeling: A Comprehensive Survey and Research Directions

A variety of mathematical forms have been developed to characterize demand functions which depend on a firm's operational and marketing activities. Such demand functions are being increasingly used by researchers in economics and different functional areas of business. We provide a comprehensive survey of commonly used demand models which depend on (i) price, (ii) rebate, (iii) lead time, (iv) space, (v) quality, and (vi) advertising. Our survey includes single firm–demand models in each category, as well as game theoretic multifirm models involving strategic interaction among the firms. We observe that certain types of functional forms, such as linear, power/iso‐elastic, multinomial logit, and multiplicative competitive interaction, have been widely used to construct various demand models in all six categories, but that a large majority of publications deal with categories (i) and (v) of demand models. For each of the six categories, we survey relevant functional forms in the representative papers, and discuss the main properties, the advantages, the disadvantages, and comment on possible future research directions. We also present discussions of the applications of these analytical demand models in empirical studies. The article ends with a summary of our major findings.     

Reducing Packaging Waste and Cost via Consumer Price Discounts

Low‐waste packaging may imply an inconvenience to consumers and cause firms to offer a compensating price discount. For example, Starbucks’ “Take the Mug Pledge” campaign provides a 10‐cent discount for customers who purchase coffee without a standard cup (i.e., customers provide their own cup). Understanding how such a discount drives demand and profit is the focus of this article. We consider a monopolist that can offer a reduced‐packaging option for its product at a variable cost savings. That option implies a transactional “inconvenience” cost for consumers. While that transactional cost is generally positive, our model also permits some consumers to associate convenience with reduced packaging. We derive the optimal price and discount that maximize profits. We show the optimal discount is bounded by the magnitude of the variable cost savings associated with the packaging reduction. We explore when the optimal discount is negative (a price premium), which requires a specific proportion of consumers to associate convenience with reduced packaging. We also derive conditions under which the firm should price to eliminate demand for the standard product, rather than segment the market, to leverage the variable cost savings of reduced packaging. When the variable cost savings are low (e.g., as is true for Starbucks), we show the profit curve for the segmenting policy is relatively flat for a discount up to several multiples of the cost differential. Finally, we demonstrate the potential for the reduced packaging option, with optimal discounting, to simultaneously increase profit and consumer surplus while reducing waste.     

Flexible Capacity Investments and Product Mix: Optimal Decisions and Value of Postponement Options

In this article, we study a firm's interdependent decisions in investing in flexible capacity, capacity allocation to individual products, and eventual production quantities and pricing in meeting uncertain demand. We propose a three‐stage sequential decision model to analyze the firm's decisions, with the firm being a value maximizer owned by risk‐averse investors. At the beginning of the time horizon, the firm sets the flexible capacity level using an aggregate demand forecast on the envelope of products its flexible resources can accommodate. The aggregate demand forecast evolves as a Geometric Brownian Motion process. The potential market share of each product is determined by the Multinomial Logit model. At a later time and before the end of the time horizon, the firm makes a capacity commitment decision on the allocation of the flexible capacity to each product. Finally, at the end of the time horizon, the firm observes the demand and makes the production quantity and pricing decisions for end products. We obtain the optimal solutions at each decision stage and investigate their optimal properties. Our numerical study investigates the value of the postponed capacity commitment option in supplying uncertain operation environments.     

Multiperiod Models with Capacities in Competitive Supply Chain

This paper considers a supply chain setting where several capacitated suppliers compete for orders from a single retailer in a multiperiod environment. At each period, the retailer places orders to the suppliers in response to the prices they announce. Each supplier has a fixed capacity. We consider a make‐to‐stock setting where the retailer can carry inventory. The retailer faces exogenous, price‐dependent demand. We study the problem using ideas from fluid models. In particular, we (i) analyze when there are pure equilibrium policies in this setting and characterize the structure of these policies; (ii) consider coordination mechanisms; and (iii) present some preliminary computational results. We also consider a modified model that uses option contracts to coordinate the supply chain.     

Benchmark Schedules for Subcontracted Operations: Decentralization Inefficiencies that Arise from Competition and First‐Come‐First‐Served Processing*

Subcontracting has become a prominent business practice across many industries. Subcontracting of industrial production is generally based on short‐term need for additional processing capacity, and is frequently employed by manufacturers to process customer orders more quickly than using only in‐house production. In this article, we study a popular business model where multiple manufacturers, each capable of processing his entire workload in‐house, have the option to subcontract some of their operations to a single third party with a flexible resource. Each manufacturer can deliver customer orders only after his entire batch of jobs, processed in‐house and at the third party, is completed. The third party facility is available to several manufacturers who compete for its use. Current business practice of First‐Come‐First‐Served (FCFS) processing of the subcontracted workloads as well as the competitive Nash equilibrium schedules developed in earlier studies result in two types of inefficiencies; the third party capacity is not maximally utilized, and the manufacturers incur decentralization cost. In this article, we develop models to assess the value created by coordinating the manufacturers' subcontracting decisions by comparing two types of centralized control against FCFS and Nash equilibrium schedules. We present optimal and/or approximate algorithms to quantify the third party underutilization and the manufacturers' decentralization cost. We find that both inefficiencies are more severe with competition than they are when the third party allocates capacity in an FCFS manner. However, in a decentralized setting, a larger percentage of the players prefer Nash equilibrium schedules to FCFS schedules. We extend our analysis to incomplete information scenarios where manufacturers reveal limited demand information, and find that more information dramatically benefits the third party and the manufacturers, however, the marginal benefit of additional information is decreasing. Finally, we discuss an extension wherein each manufacturer's objective takes into account asymmetries in subcontracting, in‐house processing, and delay costs.     

Optimal Quantity Discount Design with Limited Information Sharing*

In this article we address the optimal quantity discount design problem of a supplier in a two‐stage supply chain where the supplier and the buyer share annual demand information only. The supply chain faces a constant deterministic demand that is not price sensitive and operates with fixed setup costs in both stages. We show that the supplier can actually moderate a cost‐minimizing buyer to order in quantities different than the buyer's optimal order quantity in the traditional setting and develop a multi‐breakpoint quantity discount scheme that maximizes supplier's expected net savings. The proposed multi‐breakpoint discount scheme can be easily computed from the available information and, while also maximizing the supplier's net savings, is very effective in achieving high levels of supply chain coordination efficiency in the presence of limited information.     

Building Supply Chain Resilience through Virtual Stockpile Pooling

Stockpiling inventory is an essential strategy for building supply chain resilience. It enables firms to continue operating while finding a solution to an unexpected event that causes a supply disruption or demand surge. While extremely valuable when actually deployed, stockpiles incur large holding costs and usually provide no benefits until such a time. To help to reduce this cost, this study presents a new approach for managing stockpiles. We show that if leveraged intelligently, stockpiles can also help an organization better meet its own regular demand by enabling a type of virtual pooling we call virtual stockpile pooling (VSP). The idea of VSP is to first integrate the stockpile into several locations’ regular inventory buffers and then dynamically reallocate the stockpile among these locations in reaction to the demand realizations to achieve a kind of virtual transshipment. To study how to execute VSP and determine when it can provide the most value, we formulate a stylized multi‐location stochastic inventory model and solve for the optimal stockpile allocation and inventory order policies. We show that VSP can provide significant cost savings: in some cases nearly the full holding cost of the stockpile (i.e., VSP effectively maintains the stockpile for free), in other cases nearly the savings of traditional physical inventory pooling. Last, our results prescribe implementing VSP with many locations for large stockpiles, but only a few locations for small stockpiles.     

Reverse Auctions with Multiple Reinforcement Learning Agents*

Reverse auctions in business‐to‐business (B2B) exchanges provide numerous benefits to participants. Arguably the most notable benefit is that of lowered prices driven by increased competition in such auctions. The competition between sellers in reverse auctions has been analyzed using a game‐theoretic framework and equilibria have been established for several scenarios. One finding of note is that, in a setting in which sellers can meet total demand with the highest‐bidding seller being able to sell only a fraction of the total capacity, the sellers resort to a mixed‐strategy equilibrium. Although price randomization in industrial bidding is an accepted norm, one might argue that in reality managers do not utilize advanced game theory calculations in placing bids. More likely, managers adopt simple learning strategies. In this situation, it remains an open question as to whether the bid prices converge to the theoretical equilibrium over time. To address this question, we model reverse‐auction bidding behavior by artificial agents as both two‐player and n‐player games in a simulation environment. The agents begin the game with a minimal understanding of the environment but over time analyze wins and losses for use in determining future bids. To test for convergence, the agents explore the price space and exploit prices where profits are higher, given varying cost and capacity scenarios. In the two‐player case, the agents do indeed converge toward the theoretical equilibrium. The n‐player case provides results that reinforce our understanding of the theoretical equilibria. These results are promising enough to further consider the use of artificial learning mechanisms in reverse auctions and other electronic market transactions, especially as more sophisticated mechanisms are developed to tackle real‐life complexities. We also develop the analytical results when one agent does not behave strategically while the other agent does and show that our simulations for this environment also result in convergence toward the theoretical equilibrium. Because the nature of the best response in the new setting is very different (pure strategy as opposed to mixed), it indicates the robustness of the devised algorithm. The use of artificial agents can also overcome the limitations in rationality demonstrated by human managers. The results thus have interesting implications for designing artificial agents in automating bid responses for large numbers of bids where human intervention might not always be possible.     

Do Markets Favor Agents able to Make Accurate Predictions?

Blume and Easley (1992) show that if agents' have the same savings rule, those who maximize the expected logarithm of next period's outcomes will eventually hold all wealth (i.e. are ‘most prosperous’). However, if no agent adopts this rule then the most prosperous are not necessarily those who make the most accurate predictions. Thus, agents who make inaccurate predictions need not be driven out of the market. In this paper, it is shown that, among agents who have the same intertemporal discount factor (and who choose savings endogenously), the most prosperous are those who make accurate predictions. Hence, convergence to rational expectations obtains because agents who make inaccurate predictions are driven out of the market.     

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.     

Coalition Formation and Cost Allocation for Joint Replenishment Systems

This paper focuses on the issues of coalition formation and cost allocation in a joint replenishment system involving a set of independent and freely interacting retailers purchasing an item from one supplier to meet a deterministic demand. The papers dealing with this problem are mainly focused on supperadditive games, where the cost savings associated with a coalition increase with the number of players in the coalition. The most relevant question addressed then is how to allocate the savings to the players. In this paper, we propose to go further by dealing with a non‐supperadditive game, where a set of independent retailers have the common understanding to share the cost savings according to the cost‐based proportional rule. In this setting, the global cost optimization is no longer a relevant approach to identify appealing coalitions for any retailer. Here, we provide an iterative procedure to form the so‐called efficient coalition structure and we show that this coalition structure has the nice properties of being (i) weakly stable in the sense of the coalition structure core and (ii) strongly stable under a given assumption. An exact fractional programming based solution is also given to generate such efficient coalitions.     

Lead Time Management through Expediting in a Continuous Review Inventory System

We consider a continuous review inventory system where delivery lead times can be managed by expediting in‐transit orders shipped from the supplier. First, we propose an ordering/expediting policy and derive expressions for evaluating the operating characteristics of such systems. Second, using extensive numerical experiments, we quantify the benefits of such an expediting policy. Third, we investigate a number of managerial issues. Specifically, we analyze the impact of the number of expediting hubs and their locations along the shipment network on the performance of such systems and offer insights into the design of the shipment network. We show (i) a single expediting hub that is optimally located in a shipment network can capture the majority of cost savings achieved by a multi‐hub system, especially when expediting cost is not low or demand variability is not high; (ii) when expediting time is proportional to the time to destination, for small‐enough or large‐enough demand variations, a single expediting hub located in the middle of the shipment network can capture the majority of cost savings of an optimally located hub; and (iii) in general, hubs close to the retailer significantly drive down costs, whereas hubs close to the supplier may not offer much cost savings.     

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.     

Coordination of Supply Chains with Risk‐Averse Agents

The extant supply chain management literature has not addressed the issue of coordination in supply chains involving risk‐averse agents. We take up this issue and begin with defining a coordinating contract as one that results in a Pareto‐optimal solution acceptable to each agent. Our definition generalizes the standard one in the risk‐neutral case. We then develop coordinating contracts in three specific cases: (i) the supplier is risk neutral and the retailer maximizes his expected profit subject to a downside risk constraint; (ii) the supplier and the retailer each maximizes his own mean‐variance trade‐off; and (iii) the supplier and the retailer each maximizes his own expected utility. Moreover, in case (iii), we show that our contract yields the Nash Bargaining solution. In each case, we show how we can find the set of Pareto‐optimal solutions, and then design a contract to achieve the solutions. We also exhibit a case in which we obtain Pareto‐optimal sharing rules explicitly, and outline a procedure to obtain Pareto‐optimal solutions.     

Inventory‐Related Compensation in Decentralized Organizations

We consider a principal agent problem in a decentralized organization. The agent holds private precontracting information with respect to an uncertain demand in a single period setting. Being head of a profit center, his only task is to determine the optimal order quantity. We show that using a profit share as the only performance measure to incentivize the agent creates agency costs. In fact, offering a menu of profit‐sharing contracts to the agent to pick from, requires rent payments to motivate the agent to always choose the desired contract. This result still holds if a fixed payment is added. Using an inventory‐related component as a third measure, however, allows one to solve the agency problem and to achieve first best outcomes. Precisely, each contract needs to specify a bonus or a penalty conditioned on the inventory level at the end of the selling season combined with a profit share and a fixed pay. The paper not only demonstrates that first best can be achieved in the described setting, it also provides a theoretical explanation for the observed practice of using inventory‐related compensation elements, such as service‐level agreements, in organizations.