Hossein Abouee-Mehrizi

Optimizing capacity, pricing and location decisions on a congested network with balking

In this paper, we consider the problem of making simultaneous decisions on the location, service rate (capacity) and the price of providing service for facilities on a network. We assume that the demand for service from each node of the network follows a Poisson process. The demand is assumed to depend on both price and distance. All facilities are assumed to charge the same price and customers wishing to obtain service choose a facility according to a Multinomial Logit function. Upon arrival to a facility, customers may join the system after observing the number of people in the queue. Service time at each facility is assumed to be exponentially distributed. We first present several structural results. Then, we propose an algorithm to obtain the optimal service rate and an approximate optimal price at each facility. We also develop a heuristic algorithm to find the locations of the facilities based on the tabu search method. We demonstrate the efficiency of the algorithms numerically.

Optimal Joint Replenishment and Transshipment Policies in a Multi-Period Inventory System With Lost Sales

Mismatch between supply and demand when the uncertainty of the demand is high and the supply lead time is relatively long such as seasonal good markets can result in high overstocking and understocking costs. In this paper we propose proactive transshipment as a powerful mechanism to mitigate the mismatch between the supply and demand. We consider a finite horizon multi-period inventory system where in each period two retailers have the options to replenish their inventory from a supplier (if there is any supply) or via proactive transshipment from the other retailer. Each retailer observes non-negative stochastic demand with general distribution during the season and incurs overstocking/understocking costs as well as costs for replenishment and transshipment which may be time dependent. We study a stochastic control problem where the objective is to determine the optimal joint replenishment and proactive transshipment policies so as to minimize the total expected cost over the season. We characterize the structure of the optimal policy, and show that, unlike the known order-up-to level inventory policy, the optimal ordering policy in each period is determined based on two switching curves. Similarly, the optimal transshipment policy is also identified by two switching curves. These four curves together partitions the optimal joint ordering and transshipment polices to eight regions where in each region the optimal policy is an order-up-to-curve policy. We demonstrate that the structure of the optimal policy holds for any known sequence and combination of ordering and proactive transshipment over time. We also show that in the optimal policy retailers try to share the risk of the overstocking and understocking costs.

Strategies for a Centralized Single Product Multiclass M/G/1 Make-to-Stock Queue

Make-to-stock queues are typically investigated in the M/M/1 settings. For centralized single-item systems with backlogs, the multilevel rationing (MR) policy is established as optimal and the strict priority (SP) policy is a practical compromise, balancing cost and ease of implementation. However, the optimal policy is unknown when service time is general, i.e., for M/G/1 queues. Dynamic programming, the tool commonly used to investigate the MR policy in make-to-stock queues, is less practical when service time is general. In this paper we focus on customer composition: the proportion of customers of each class to the total number of customers in the queue. We do so because the number of customers in M/G/1 queues is invariant for any nonidling and nonanticipating policy. To characterize customer composition, we consider a series of two-priority M/G/1 queues where the first service time in each busy period is different from standard service times, i.e., this first service time is exceptional. We characterize the required exceptional first service times and the exact solution of such queues. From our results, we derive the optimal cost and control for the MR and SP policies for M/G/1 make-to-stock queues.

Reducing the age of transfused red blood cells in hospitals: ordering and allocation policies.

Although recent randomized controlled trials have not found increased risk of morbidity/mortality with older red blood cells (RBCs), several large trials will be completed soon providing power to detect smaller risks if indeed they exist. Hence, there may still be a need for inventory management policies that could reduce the age of transfused RBCs without compromising availability or resulting in excessive outdates.

Designing Production-Inventory-Transportation Systems with Capacitated Cross-Docks

We consider a two-echelon supply chain problem, where the demand of a set of retailers is satisfied from a set of suppliers and shipped through a set of capacitated cross-docks that are to be established. The objective is to determine the number and location of cross-docks and the assignment of retailers to suppliers via cross-docking so that the total cost of pipeline and retailers inventory, transportation, and facility location is minimized. We formulate the problem as a nonlinear mixed integer programming. We first derive several structural results for special cases of the problem. We also demonstrate that the Capacitated Plant Fixed-Charge Transport Location Problem is a special case of our problem. To solve the general problem, we show that it can be written as a cutting stock problem and develop a column generation algorithm to solve it. We investigate the efficiency of the proposed algorithm numerically. We then extend the problem by allowing different truck capacities as decision variables.

Exact Analysis of Capacitated Two-Echelon Inventory Systems with Priorities

We consider a two-echelon inventory system with a capacitated centralized production facility and several distribution centers (DCs). Both production and transportation times are stochastic with general distributions. Demand arrives at each DC according to an independent Poisson process and is backlogged if the DC is out of stock. We allow different holding and backlog costs at the different DCs. We assume that inventory at DCs is managed using the one-for-one replenishment policy. The main objective of this paper is to investigate the control of the multiechelon M/G/1 setting with general transportation times. To achieve this objective, we analyze several decentralized allocation policies including the first-come, first-served (FCFS), strict priority (SP), and multilevel rationing (MR) policies. For our analytic results, we assume no order crossing. We derive the cost function for a capacitated two-echelon inventory system with general transportation times under these policies. Our numerical examples sho...

Can hospitals compete on quality

In this paper, we consider two hospitals with different perceived quality of care competing to capture a fraction of the total market demand. Patients select the hospital that provides the highest utility, which is a function of price and the patient’s perceived quality of life during their life expectancy. We consider a market with a single class of patients and show that depending on the market demand and perceived quality of care of the hospitals, patients may enjoy a positive utility. Moreover, hospitals share the market demand based on their perceived quality of care and capacity. We also show that in a monopoly market (a market with a single hospital) the optimal demand captured by the hospital is independent of the perceived quality of care. We investigate the effects of different parameters including the market demand, hospitals’ capacities, and perceived quality of care on the fraction of the demand that each hospital captures using some numerical examples.

Threshold-Based Allocation Policies for Inventory Management of Red Blood Cells

Under current regulations, red blood cell (RBC) units can be transfused to patients up to 42 days after donation. However, recent studies suggest an association between the age of transfused RBCs and adverse clinical outcomes for their recipients. Therefore, there is an interest in inventory management policies that could reduce the age of transfused RBCs without compromising their availability. In this work, we study the performance of a practical family of threshold-based allocation policies, designed to trade off the age of RBC transfusions with their availability at hospitals. To this end, we consider a stylized model of a hospital blood bank that procures its required blood from local donations. For this model, we develop a new method to exactly evaluate the performance of the threshold policy in terms of the distribution of the age of allocated units and the proportion of outdates and lost demand. Through numerical and structural results, we obtain new insights on the performance of the threshold po...

Joint pricing and location decisions in a heterogeneous market

In this paper we consider the problem of joint location and pricing optimization for a firm in a heterogeneous market producing a single product. We assume that customers have a different willingness to pay for the product. We consider two classes of customers who are not uniformly distributed in the market and develop an analytical framework to determine the relationship between the optimal price and location of the firm. We demonstrate that the optimal price and location are closely related to each other, and thus there is a need for simultaneous optimization of the price and location. We provide both analytical and numerical results to illustrate the impact of transportation cost and the level of heterogeneity on the firm’s strategic decisions. Our results show that simplifying the analysis of such markets with a uniform demand assumption and a homogeneity of customers may reduce the firm’s profit significantly.

Do Shareholders Really Prefer Their Executives to Maximize the Equity Value? A Newsvendor Case*

In this article, we study how the operational decisions of a firm manager depend on her own incentives, the capital structure, and financial decisions in the context of the newsvendor framework. We establish a relationship between the firm’s cost of raising funds and the riskiness of the inventory decisions of the manager. We consider four types of managers, namely, profit, equity, firm value, and profit-equity maximizers, and initially assume that they may raise funds to increase the inventory level only by issuing debt. We show that the shareholders are indifferent between the different types of managers when the coefficient of variation (CV) of demand is low. However, this is not the case when the CV of demand is high. Based on the demand and the firm’s specific characteristics such as profitability, leverage, and bankruptcy costs, the shareholders might be better off with the manager whose compensation package is tied to the firm value as opposed to the equity value. We, then, extend our model by allowing the manager to raise the required funds by issuing both debt and equity. For this case we focus on the equity and firm value maximizer managers and show that our earlier results (for the debt only case) still hold subject to the cost of issuing equity. However the benefit of the firm value maximizer manager over the equity maximizer manager for shareholders is considerably less in this case compared to the case where the manager can only issue debt. The Board of Directors can take these factors into consideration when establishing/modifying the right incentive package for the managers. We also incorporate the notion of the asymmetric information to capture its impact on the board of directors’ decision about the managers’ incentive package.