Knowledge that Transforms

We investigate the optimal strategies for firms to invest in their suppliers when the benefits of such investments can spillover to other firms who also source from the same suppliers. We consider two Bayesian firms that can invest in improving the quality of their shared supplier; the firms do not have complete information on the true quality of the supplier, but they update their beliefs based on the supplier's performance. We formulate the problem as an investment game and obtain Markov perfect equilibria characterized by the investment thresholds of both firms. The equilibrium investment strategies of the two firms are characterized by a region of preemption and a region of war of attrition. We also examine how the interplay between spillover, competition, and returns from the investment at shared suppliers affect the investment threshold and the time to the leader's investment, and identify the conditions under which competition delays or hastens the first investment in a shared supplier.

We examine the critical role of evolving private information in managing supply risk. The problem features a dyadic channel where a dominant buyer operates a multiperiod inventory system with lost sales and fixed cost. He replenishes from a supplier, whose private state of production is vulnerable to random shocks and evolves dynamically over time. We characterize the optimal inventory policy with a simple semi‐stationary structure; it distorts order quantity for limiting information rent only in the initial period; the optimal payment compensates for production cost in every period but concedes real information rent only in the initial period. These properties allow us to derive an easy‐to‐implement revenue‐sharing contract that facilitates ex ante strategic planning and ex post dynamic execution. This work advances our understanding on when and how to use private information in dynamic risk management.

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.

We study a minimum total commitment (MTC) contract embedded in a finite‐horizon periodic‐review inventory system. Under this contract, the buyer commits to purchase a minimum quantity of a single product from the supplier over the entire planning horizon. We consider nonstationary demand and per‐unit cost, discount factor, and nonzero setup cost. Because the formulations used in existing literature are unable to handle our setting, we develop a new formulation based on a state transformation technique using unsold commitment instead of unbought commitment as state variable. We first revisit the zero setup cost case and show that the optimal ordering policy is an unsold‐commitment‐dependent base‐stock policy. We also provide a simpler proof of the optimality of the dual base‐stock policy. We then study the nonzero setup cost case and prove a new result, that the optimal solution is an unsold‐commitment‐dependent ( s , S ) policy. We further propose two heuristic policies, which numerical tests show to perform very well. We also discuss two extensions to show the generality of our method's effectiveness. Finally, we use our results to examine the effect of different contract terms such as duration, lead time, and commitment on buyer's cost. We also compare total supply chain profits under periodic commitment, MTC, and no commitment.

The construction of a software system requires not only individual coding effort from team members to realize the various functionalities, but also adequate team coordination to integrate the developed code into a consistent, efficient, and bug‐free system. On the one hand, continuous coding without adequate coordination can cause serious system inconsistencies and faults that may subsequently require significant corrective effort. On the other hand, frequent integrations can be disruptive to the team and delay development progress. This tradeoff motivates the need for a good coordination policy. Both the complexity and the importance of coordination is accentuated in distributed software development (DSD), where a software project is developed by multiple, geographically‐distributed sub‐teams. The need for coordination in DSD exists both within one sub‐team and across different sub‐teams. The latter type of coordination involves communication across spatial boundaries (different locations) and possibly temporal boundaries (different time zones), and is a major challenge that DSD faces. In this study, we model both inter‐ and intra‐sub‐team coordination in DSD based on the characteristics of the systems being developed by the sub‐teams, the deadline for completion, and the nature of division adopted by the sub‐teams with respect to development and integration activities. Our analysis of optimal coordination policies in DSD shows that integration activities by one sub‐team not only benefit that sub‐team (as is the case in co‐located development) but can also help the other sub‐teams by providing greater visibility, thereby resulting in a higher integration frequency relative to co‐located development. Analytical results are presented to demonstrate how the characteristics of the projects and the sub‐teams, and the efficiency of communication across the sub‐teams, affect coordination and productivity. We also investigate the pros and cons of using specialized integration sub‐teams and find that their advantage decreases as the project schedule becomes tighter. Decentralized decisions and asymmetric subsystems are also discussed.

Sharing common production, resources, and services to reduce cost are important for not for profit operations due to limited and mission‐oriented budget and effective cost allocation mechanisms are essential for encouraging effective collaborations. In this study, we illustrate how rigorous methodologies can be developed to derive effective cost allocations to facilitate sustainable collaborations in not for profit operations by modeling the cost allocation problem arising from an economic lot‐sizing (ELS) setting as a cooperative game. Specifically, we consider the economic lot‐sizing (ELS) game with general concave ordering cost. In this cooperative game, multiple retailers form a coalition by placing joint orders to a single supplier in order to reduce ordering cost. When both the inventory holding cost and backlogging cost are linear functions, it can be shown that the core of this game is non‐empty. The main contribution of this study is to show that a core allocation can be computed in polynomial time under the assumption that all retailers have the same cost parameters. Our approach is based on linear programming (LP) duality. More specifically, we study an integer programming formulation for the ELS problem and show that its LP relaxation admits zero integrality gap, which makes it possible to analyze the ELS game by using LP duality. We show that there exists an optimal dual solution that defines an allocation in the core. An interesting feature of our approach is that it is not necessarily true that every optimal dual solution defines a core allocation. This is in contrast to the duality approach for other known cooperative games in the literature.

Eroglu et al. (2013) study a retailer with limited shelf capacity and a backroom. They study a continuous review ( r , q ) ordering policy with a known order quantity, q . Assuming that backorders can be satisfied from the backroom inventory (if available), they find the expression for the optimal reorder level, r . Our work builds on Eroglu et al. (2013). We correct an erroneous derivation of the expected overflow term, as well as derive an exact expression for the expected cost function, and hence optimal reorder level, instead of the approximate one used by Eroglu et al. (2013).

We consider an assemble‐to‐order (ATO) system with multiple products, multiple components which may be demanded in different quantities by different products, possible batch ordering of components, random lead times, and lost sales. We model the system as an infinite‐horizon Markov decision process under the average cost criterion. A control policy specifies when a batch of components should be produced, and whether an arriving demand for each product should be satisfied. Previous work has shown that a lattice‐dependent base‐stock and lattice‐dependent rationing (LBLR) policy is an optimal stationary policy for a special case of the ATO model presented here (the generalized M‐system). In this study, we conduct numerical experiments to evaluate the use of an LBLR policy for our general ATO model as a heuristic, comparing it to two other heuristics from the literature: a state‐dependent base‐stock and state‐dependent rationing (SBSR) policy, and a fixed base‐stock and fixed rationing (FBFR) policy. Remarkably, LBLR yields the globally optimal cost in each of more than 22,500 instances of the general problem, outperforming SBSR and FBFR with respect to both objective value (by up to 2.6% and 4.8%, respectively) and computation time (by up to three orders and one order of magnitude, respectively) in 350 of these instances (those on which we compare the heuristics). LBLR and SBSR perform significantly better than FBFR when replenishment batch sizes imperfectly match the component requirements of the most valuable or most highly demanded product. In addition, LBLR substantially outperforms SBSR if it is crucial to hold a significant amount of inventory that must be rationed.

In retailing operations, retailers face the challenge of incomplete demand information. We develop a new concept named K‐approximate convexity, which is shown to be a generalization of K‐convexity, to address this challenge. This idea is applied to obtain a base‐stock list‐price policy for the joint inventory and pricing control problem with incomplete demand information and even non‐concave revenue function. A worst‐case performance bound of the policy is established. In a numerical study where demand is driven from real sales data, we find that the average gap between the profits of our proposed policy and the optimal policy is 0.27%, and the maximum gap is 4.6%.

Service quality is an important attribute that is used to characterize many service systems. In this study, we examine a service system with two consecutive steps that have shared resources. The service process consists of a base service (first step in the process) followed by a second step that adds additional value. We first look at a social surplus maximizing service provider (SP) who decides the optimal service capacity and re‐optimizes in response to changes in the speed of service of the first step due to local innovations. Our main objective is to explore using simple and stylized models, the effect on the service system of local innovations in step 1 that decrease this step's service times. We find that the effect of such innovations can sometimes lead to the worsening of certain critical service quality measures when SPs are monopolists. Next, using a model of competition, we find that this effect continues to hold in settings where SPs compete for arrivals. Our results have interesting consequences for many service systems and may help explain some of the unintended effects of service innovations reported in the literature.