Provably Near-Optimal LP-Based Policies for Revenue Management in Systems with Reusable Resources

Motivated by emerging applications in workforce management, we consider a class of revenue management problems in systems with reusable resources. The corresponding applications are modeled using the well-known loss network systems. We use an extremely simple linear program (LP) that provides an upper bound on the best achievable expected long-run revenue rate. The optimal solution of the LP is used to devise a conceptually simple control policy that we call the class selection policy (CSP). Moreover, the LP is used to analyze the performance of the CSP policy. We obtain the _rst control policy with uniform performance guarantees. In particular, for the model with single resource and uniform resource requirements, the CSP policy is guaranteed to have expected long-run revenue rate that is at least half of the best achievable. More generally, as the ratio between the capacity of the system and the maximum resource requirement grows to in_nity, the CSP policy is asymptotically optimal, regardless of any other parameter of the problem. The asymptotic performance analysis that we obtain is more general than existing results in several important dimensions. It is based on several novel ideas that we believe will be useful in other settings

Approximation Algorithms for the Stochastic Lot-Sizing Problem with Order Lead Times

We develop new algorithmic approaches to compute provably near-optimal policies for multiperiod stochastic lot-sizing inventory models with positive lead times, general demand distributions, and dynamic forecast updates. The policies that are developed have worst-case performance guarantees of 3 and typically perform very close to optimal in extensive computational experiments. The newly proposed algorithms employ a novel randomized decision rule. We believe that these new algorithmic and performance analysis techniques could be used in designing provably near-optimal randomized algorithms for other stochastic inventory control models and more generally in other multistage stochastic control problems.National Science Foundation (U.S.) (Grant DMS-0732175)National Science Foundation (U.S.) (CAREER Award CMMI-0846554)United States. Air Force Office of Scientific Research (Award FA9550-08-1-0369)United States. Air Force Office of Scientific Research (Award FA9550-11-1-0150)Singapore-MIT AllianceSolomon Buchsbaum AT&T Research Fun

Supply Chain Management with Online Customer Selection

We consider new online variants of supply chain management models, where in addition to production decisions, one also has to actively decide on which customers to serve. Specifically, customers arrive sequentially during a selection phase, and one has to decide whether to accept or reject each customer upon arrival. If a customer is rejected, then a lost-sales cost is incurred. Once the selection decisions are all made, one has to satisfy all the accepted customers with minimum possible production cost. The goal is to minimize the total cost of lost sales and production. A key feature of the model is that customers arrive in an online manner, and the decision maker does not require any information about future arrivals. We provide two novel algorithms for online customer selection problems, which are based on repeatedly solving offline subproblems that ignore previously made decisions. For many important settings, our algorithms achieve small constant competitive ratio guarantees. That is, for any sequence of arriving customers, the cost incurred by the online algorithm is within a fixed constant factor of the cost incurred by the respective optimal solution that has full knowledge upfront on the sequence of arriving customers. Finally, we provide a computational study on the performance of these algorithms when applied to the economic lot sizing and joint replenishment problems with online customer selection.National Science Foundation (U.S.) (CMMI-0846554)United States. Air Force Office of Scientific Research (FA9550-11-1-0150)United States. Air Force Office of Scientific Research (FA9550-08-1-0369

From Cost Sharing Mechanisms to Online Selection Problems

We consider a general class of online optimization problems, called online selection problems, where customers arrive sequentially, and one has to decide upon arrival whether to accept or reject each customer. If a customer is rejected, then a rejection cost is incurred. The accepted customers are served with minimum possible cost, either online or after all customers have arrived. The goal is to minimize the total production costs for the accepted customers plus the rejection costs for the rejected customers. These selection problems are related to online variants of offline prize collecting combinatorial optimization problems that have been widely studied in the computer science literature. In this paper, we provide a general framework to develop online algorithms for this class of selection problems. In essence, the algorithmic framework leverages any cost sharing mechanism with certain properties into a poly-logarithmic competitive online algorithm for the respective problem; the competitive ratios are shown to be near-optimal. We believe that the general and transparent connection we establish between cost sharing mechanisms and online algorithms could lead to additional online algorithms for problems beyond the ones studied in this paper.National Science Foundation (U.S.) (CAREER Award CMMI-0846554)United States. Air Force Office of Scientific Research (FA9550-11-1-0150)United States. Air Force Office of Scientific Research (FA9550-08-1-0369)Solomon Buchsbaum AT&T Research Fun

The submodular joint replenishment problem

The joint replenishment problem is a fundamental model in supply chain management theory that has applications in inventory management, logistics, and maintenance scheduling. In this problem, there are multiple item types, each having a given time-dependent sequence of demands that need to be satisfied. In order to satisfy demand, orders of the item types must be placed in advance of the due dates for each demand. Every time an order of item types is placed, there is an associated joint setup cost depending on the subset of item types ordered. This ordering cost can be due to machine, transportation, or labor costs, for example. In addition, there is a cost to holding inventory for demand that has yet to be served. The overall goal is to minimize the total ordering costs plus inventory holding costs. In this paper, the cost of an order, also known as a joint setup cost, is a monotonically increasing, submodular function over the item types. For this general problem, we show that a greedy approach provides an approximation guarantee that is logarithmic in the number of demands. Then we consider three special cases of submodular functions which we call the laminar, tree, and cardinality cases, each of which can model real world scenarios that previously have not been captured. For each of these cases, we provide a constant factor approximation algorithm. Specifically, we show that the laminar case can be solved optimally in polynomial time via a dynamic programming approach. For the tree and cardinality cases, we provide two different linear programming based approximation algorithms that provide guarantees of three and five, respectively.National Science Foundation (U.S.) (CAREER Grant CMMI-0846554)United States. Air Force Office of Scientific Research (Award FA9550-11-1-0150)SMA GrantSolomon Buchsbaum AT&T Research Fun

Supply Chain Characteristics as Predictors of Cyber Risk: A Machine-Learning Assessment

This paper provides the first large-scale data-driven analysis to evaluate the predictive power of different attributes for assessing risk of cyberattack data breaches. Furthermore, motivated by rapid increase in third party enabled cyberattacks, the paper provides the first quantitative empirical evidence that digital supply-chain attributes are significant predictors of enterprise cyber risk. The paper leverages outside-in cyber risk scores that aim to capture the quality of the enterprise internal cybersecurity management, but augment these with supply chain features that are inspired by observed third party cyberattack scenarios, as well as concepts from network science research. The main quantitative result of the paper is to show that supply chain network features add significant detection power to predicting enterprise cyber risk, relative to merely using enterprise-only attributes. Particularly, compared to a base model that relies only on internal enterprise features, the supply chain network features improve the out-of-sample AUC by 2.3\%. Given that each cyber data breach is a low probability high impact risk event, these improvements in the prediction power have significant value. Additionally, the model highlights several cybersecurity risk drivers related to third party cyberattack and breach mechanisms and provides important insights as to what interventions might be effective to mitigate these risks

Modeling the impact of changing patient transportation systems on peri-operative process performance in a large hospital: insights from a computer simulation study

Transportation of patients is a key hospital operational activity. During a large construction project, our patient admission and prep area will relocate from immediately adjacent to the operating room suite to another floor of a different building. Transportation will require extra distance and elevator trips to deliver patients and recycle transporters (specifically: personnel who transport patients). Management intuition suggested that starting all 52 first cases simultaneously would require many of the 18 available elevators. To test this, we developed a data-driven simulation tool to allow decision makers to simultaneously address planning and evaluation questions about patient transportation. We coded a stochastic simulation tool for a generalized model treating all factors contributing to the process as JAVA objects. The model includes elevator steps, explicitly accounting for transporter speed and distance to be covered. We used the model for sensitivity analyses of the number of dedicated elevators, dedicated transporters, transporter speed and the planned process start time on lateness of OR starts and the number of cases with serious delays (i.e., more than 15 min). Allocating two of the 18 elevators and 7 transporters reduced lateness and the number of cases with serious delays. Additional elevators and/or transporters yielded little additional benefit. If the admission process produced ready-for-transport patients 20 min earlier, almost all delays would be eliminated. Modeling results contradicted clinical managers’ intuition that starting all first cases on time requires many dedicated elevators. This is explained by the principle of decreasing marginal returns for increasing capacity when there are other limiting constraints in the system.National Science Foundation (U.S.) (DMS-0732175)National Science Foundation (U.S.) (CMMI-0846554)United States. Air Force Office of Scientific Research (FA9550-08-1-0369)Singapore-MIT AllianceMassachusetts Institute of Technology. Buschbaum Research Fund

Base-stock policies for lost-sales models: Aggregation and asymptotics

This paper considers the optimization of the base-stock level for the classical periodic review lost-sales inventory system. The optimal policy for this system is not fully understood and computationally expensive to obtain. Base-stock policies for this system are asymptotically optimal as lost-sales costs approach infinity, easy to implement and prevalent in practice. Unfortunately, the state space needed to evaluate a base-stock policy exactly grows exponentially in both the lead time and the base-stock level. We show that the dynamics of this system can be aggregated into a one-dimensional state space description that grows linearly in the base-stock level only by taking a non-traditional view of the dynamics. We provide asymptotics for the transition probabilities within this single dimensional state space and show that these asymptotics have good convergence properties that are independent of the lead time under mild conditions on the demand distribution. Furthermore, we show that these asymptotics satisfy a certain ow conservation property. These results lead to a new and computationally efficient heuristic to set base-stock levels in lost-sales systems. In a numerical study we demonstrate that this approach performs better than existing heuristics with an average gap with the best base-stock policy of 0.01% across a large test-bed