Demand Arrival Rates Research Articles

An Optimal Two-Dimensional Maintenance Policy for Self-Service Systems with Multi-Task Demands and Subject to Competing Sudden and Deterioration-Induced Failures

Self-service systems, such as electric vehicle charging piles (EVCPs), are typically deployed without on-site personnel. While frequent maintenance ensures high service revenue, it also leads to significant maintenance setup costs. Therefore, balancing service revenue and maintenance costs is essential for profit maximization. In this paper, we develop a maintenance policy optimization framework to maximize the profit rate of a fleet of self-service systems. First, we propose a maintenance policy that ensures sufficient functional systems while preventing high corrective maintenance costs. Next, we model the fleet's state transition process and its profit rate by characterizing two unique failure-induced demand-and-system interactions: demand switching and stepwise demand arrival rates, where the demands involve multiple tasks and systems are subject to multiple failure modes with non-constant occurrence rates. We develop a Tabu-search algorithm with random exploration to optimize the maintenance policy. Building on this, we investigate the impacts of key model parameters through a case study of thirteen EVCPs in Hong Kong and draw implications for profit maximization.

Blind Dynamic Resource Allocation in Closed Networks via Mirror Backpressure

We study the problem of maximizing payoff generated over a period of time in a general class of closed queueing networks with a finite, fixed number of supply units that circulate in the system. Demand arrives stochastically, and serving a demand unit (customer) causes a supply unit to relocate from the “origin” to the “destination” of the customer. The key challenge is to manage the distribution of supply in the network. We consider general controls including customer entry control, pricing, and assignment. Motivating applications include shared transportation platforms and scrip systems. Inspired by the mirror descent algorithm for optimization and the backpressure policy for network control, we introduce a rich family of mirror backpressure (MBP) control policies. The MBP policies are simple and practical and crucially do not need any statistical knowledge of the demand (customer) arrival rates (these rates are permitted to vary in time). Under mild conditions, we propose MBP policies that are provably near optimal. Specifically, our policies lose at most [Formula: see text] payoff per customer relative to the optimal policy that knows the demand arrival rates, where K is the number of supply units, T is the total number of customers over the time horizon, and η is the demand process’ average rate of change per customer arrival. An adaptation of MBP is found to perform well in numerical experiments based on data from NYC Cab. This paper was accepted by Gabriel Weintraub, revenue management and market analytics. Funding: Y. Kanoria was supported by the National Science Foundation’s Division of Civil, Mechanical, and Manufacturing Innovation [Grant CMMI-1653477]. Supplemental Material: The data files and online appendices are available at https://doi.org/10.1287/mnsc.2023.4934 .

A multi-objective fuzzy facility location problem with congestion and priority for drone-based emergency deliveries

Emergency medical service (EMS) plays an essential role in modern emergency and health systems; however, the delivery service via traditional ground vehicles faces enormous challenges, e.g., traffic congestion and poor road conditions, especially for time-critical products. Fortunately, drones provide an alternative solution for EMS due to faster speed, fewer road restrictions, and fewer workforce requirements, compared to ground vehicles. This paper develops a drone-based queuing-location model with stochastic demands and congestion for EMS, where drones perform as mobile servers with a generally distributed service time. In practice, delivery decisions are often made in the presence of imprecise information, and customer requests often have different priorities. However, to our best knowledge, limited research has addressed these issues. Thus, this paper employs fuzzy theory to cope with the vague drone endurance and demand arrival rate under a priority queuing strategy. A multi-objective optimization approach is adopted to balance the total cost, system efficiency, and equitable response time. As the resulting model is challenging to solve, we apply chance-constrained, second-order conic, fuzzy, and weighted goal programming approaches to recast the model as a crisp mixed-integer second-order conic program, which can be efficiently solved via off-the-shelf solvers. Results based on a case study show that our method can help decision-makers to better balance various objectives, make more flexible decisions with desirable fuzzy degrees, and significantly improve the service level of high priority demands for EMS.

A comparative study of different pull control strategies in multi-product manufacturing systems using discrete event simulation

Pull production control strategies coordinate manufacturing operations based on actual demand. Up to now, relevant publications mostly examine manufacturing systems that produce a single type of a product. In this research, we examine the CONWIP, Base Stock, and CONWIP/Kanban Hybrid pull strategies in multi-product manufacturing systems. In a multi-product manufacturing system, several types of products are manufactured by utilizing the same resources. We develop queueing network models of multi-stage, multi-product manufacturing systems operating under the three aforementioned pull control strategies. Simulation models of the alternative production systems are implemented using an open-source software. A comparative evaluation of CONWIP, Base Stock and CONWIP/Kanban Hybrid in multi-product manufacturing is carried out in a series of simulation experiments with varying demand arrival rates, setup times and control parameters. The control strategies are compared based on average wait time of backordered demand, average finished products inventories, and average length of backorders queues. The Base Stock strategy excels when the manufacturing system is subjected to high demand arrival rates. The CONWIP strategy produced consistently the highest level of finished goods inventories. The CONWIP/Kanban Hybrid strategy is significantly affected by the workload that is imposed on the system.

On State-Independent Policies in Network Revenue Management

Problem definition: We study the following seminal stochastic multiproduct dynamic-pricing problem, analyzed originally in Gallego and Van Ryzin (1997) – GVR, for short. A firm has a finite inventory of a set of resources needed to produce products that can be sold over a finite horizon. The demand for each product arrives according to a Poisson process for which the rate, at any time, is a function of the current prices of all the products. The firm's goal is to obtain a pricing policy that maximizes its expected revenue over the sales horizon. Results and Managerial implications: GVR's analysis of the above problem implicitly assumes that the demand-price relationship is separable among the products (that is, the demand rate of a product depends only on its own price and is independent of the prices of the other products). However, for pricing problems in many industries, e.g. fashion retail and travel, the separability assumption does not hold (due to, say, substitution or complementarity among the products). In this paper, we derive GVR's results for the more general setting where the demand-price relationship need not be separable. Specifically, we analyze two state-independent policies and show that they are both asymptotically optimal. Similar to GvR, we consider a sequence of scaled versions of the original problem in which the demand-arrival rates of the products and the capacities of the resources are both scaled by a factor $k\in \mathbb{N}$, and show that an upper bound on the optimal revenue scales proportional to $k$, while the optimality gaps of the two policies scale proportional to $\sqrt{k}$. This ''square root effect'' is widely viewed as a cornerstone in Network Revenue Management. Our analysis introduces a bounding technique that uses a Poisson concentration inequality – this technique can potentially be applied to other OM problems.

Optimal charging facility location and capacity for electric vehicles considering route choice and charging time equilibrium

In this study, the optimal design of location and capacity of charging facilities for electric vehicles (EVs) is investigated. A bi-level mathematical model is proposed to derive optimal design considering the equilibrium of route choice and waiting time for charging. The objective is to minimize the joint cost of facility constructions and EV drivers’ travel and waiting time over the network. The upper-level model allocates the facilities and their capacity, while the lower-level model characterizes equilibrium behavior of drivers’ route and charging facility choices. In particular, we model drivers at each charging facility as the M(t)/M/n queue and approximate the average queuing time and probability of waiting time as functions of facility capacity and demand arrival rate. The bi-level model is then converted into a single-level model, and the solution algorithm is proposed for iteratively solving the relaxed problems. Comprehensive experiments are conducted on three networks to evaluate algorithm performances, assess solution robustness and understand the scalability of the solution approach on large networks.

Transshipment policies for systems with multiple retailers and two demand classes

Many retailers discriminate among their customers based on their value to the firm. Instead of losing a customer due to this discrimination or lack of inventory, a retailer might prefer to place a transshipment request with other retailers to satisfy the customer’s demand. The system as a whole can benefit from this type of transshipments. In this paper, we study a problem of a centrally controlled system with multiple retailers. Each retailer serves two types of customers: high priority and low priority. Each retailer employs a rationing policy with a rationing level k in the context of a continuous-review (r, Q) inventory replenishment model. The overall policy is referred to as an (r, k, Q) policy. Retailers can transship items from either other retailers or a more expensive central depot. We propose an enumeration-based approximation to find the cost-minimizing policy parameters for the individual retailers and an approximation procedure to solve the combined rationing and transshipment problem. The latter relies on adjusting the demand arrival rates and the unit transshipment costs for both types of customers at all retailers. An extensive numerical study highlights the impact of transshipments on the retailers’ rationing policies. Without transshipment opportunities among each other, retailers set their policy parameters so that the resulting service levels are high for both types of customers. Allowing transshipments results in more aggressive rationing policies, and retailers with aggressive rationing policies benefit from the transshipments the most.

Technical Note—Managing Nonperishable Inventories with Learning About Demand Arrival Rate Through Stockout Times

We study a periodic review inventory model with a nonperishable product over an infinite planning horizon. The demand for the nonperishable product arrives according to a Poisson process. Lost sales are unobservable but the stockout times are observable. We formulate the problem as a dynamic programming model with learning on arrival rate according to stockout times and further simplify it by using unnormalized probabilities. We then compare the system performance with those under other two information scenarios where lost sales are observable or both lost sales and stockout times are unobservable. We show that the optimal inventory order-up-to level with observable stockout times is larger than the one with observable lost sales. We also show that more information improves the system performance.

A performance comparison of single product kanban control systems

This paper presents a simulation experiment comparing the Single Stage, Single Product Base Stock (BS), Traditional Kanban Control System (TKCS) and Extended Kanban Control System (EKCS). The results showed that BS incurs the highest cost in all scenarios; while EKCS is found to be effective only in a very niche scenario. TKCS is still a very powerful factory management system to date; and EKCS did not perform exceptionally well. The only time EKCS did outperform TKCS was during low demand arrival rates and low Backorder (C b ) and Shortage costs (C s ). That is because during then, it holds no stock. The most important discovery made here is that EKCS becomes TKCS once it has base stock (or dispatched kanbans). The results have also evinced the strength of the pure kanban system, the TKCS over BS. Hence managers using BS should consider upgrading to TKCS to save cost.

Optimal production and pricing policies in a combined make-to-order/make-to-stock system

In this paper, we consider a production system which is capable to produce two types of products. The first type of products is make-to-order, while the second type is make-to-stock whose demand is satisfied by the on-hand inventory. The demand arrival rates of both types of products are price-sensitive. The excess demand that cannot be satisfied immediately is either backlogged or lost. The system costs include the holding costs of product inventories and shortage costs of unsatisfied demand. The objective is to maximise the total discounted profit over an infinite planning horizon by coordinating the production process and pricing decisions. By analysing the properties of objective functions, we characterise the optimal control policy by two switch curves and the optimal price is also given for different ordering and inventory levels. We also explore the monotonicity of both switch curves which will reduce the computation effort. Numerical experiments are conducted to demonstrate the use of the switch curves in managing the production system and illustrate that compared with the static pricing policy, the optimal integrated price and inventory control policy can result in a significant profit improvement in the make-to-order/make-to-stock system that is much higher than in a single-product system.

Lateral Transshipment and Rationing Policies for Multi-Retailer Systems

Many retailers discriminate among their customers based on their value to the firm. Instead of losing a customer due to this discrimination or lack of inventory, a retailer might prefer to request that other retailers satisfy the customer's demand. The system as a whole can benefit from this types of transshipments. In this paper, we study a multi-retailer system with each retailer serving two types of customers: high and low priority. Each retailer employs a rationing, critical-level policy in the context of a continuous-review (r,Q) inventory model with lost sales. Retailers can transship items from either other retailers or a central depot. Therefore, no demand is lost; all demand is satisfied by the system. We propose an approximate iterative procedure to find the cost-minimizing policy parameters for individual retailers and propose an iterative heuristic, which relies on adjusting the demand arrival rates and the transshipment costs for both types of customers at all retailers, to solve the overall rationing and transshipment problem. Via numerical analysis, we identify the conditions under which a retailer can benefit from transshipments by changing its rationing policy. In addition, we study the sensitivity of the cost benefit resulting from transshipments with regard to different system parameters.

A mathematical model for order splitting in a multiple supplier single-item inventory system

In this paper we develop a mathematical model which considers multiple-supplier single-item inventory systems. The lead times of the suppliers and demand arrival rate are random variables. All shortages are backordered. Continuous review (s, Q) policy has been assumed. When the inventory level hits the reorder level, the total order is split among n suppliers. The problem is to determine the reorder level and order quantity for each supplier so that the expected total cost per time unit, including ordering cost, procurement cost, inventory holding cost and shortage cost is minimized. We also conduct extensive numerical experiments to show the advantages of our model compared to the relevant models in the literature. In addition, some managerial insights are observed.

Optimal configuration of a decentralized, market-driven production/inventory system

Pull systems are inherently easier to implement on the shop-floor; however, they are quite difficult to plan and design for optimal operation, leaving little guidelines to system designers and practitioners. In this paper we use an effective and relatively fast numerical method to understand the optimal configuration of a multi-stage, multi-product, decentralized, market-driven production/inventory system that minimizes average inventory holding subject to a service level constraint through selection of various production and procurement control parameters. We have also conducted a number of numerical experiments to understand how the control policies respond to changes in the system parameters, such as the number of stages, system workload, demand arrival rates of products, and inventory holding costs.

Capability flexibility: a decision support methodology for parallel service and manufacturing systems with flexible servers

To obtain improved performance, many firms pursue operational flexibility by endowing their production operations with multiple capabilities (e.g., multi-skilled workers, flexible machines and/or flexible plants). This article focuses on the problem of ranking (according to average wait in queue) alternative system designs that vary by capacity and the structure of capabilities for open, parallel queueing networks with partially flexible servers. Prior literature introduced the Structural Flexibility (SF) concept and because the SF method was intended for a strategic context with very little information, it did not incorporate mean service times by demand type, server speeds, or wide ranges in demand arrival rates. This article develops the Capability Flexibility (CF) index methodology to extend the range of operational environments and designs that can be ranked. By showing the effectiveness of a deterministic, second-order approximation of a capability-design's relative flexibility/performance—the CF index—it proved possible to establish the insight that the proposed simple deterministic approximation of these complex stochastic is able to capture the dominant drivers of congestion of one design relative to another.

Optimal bundle formation and pricing of two products with limited stock

In this study, we consider the stochastic modeling of a retail firm that sells two types of perishable products in a single period not only as independent items but also as a bundle. Our emphasis is on understanding the bundling practices on the inventory and pricing decisions of the firm. One of the issues we address is to decide on the number of bundles to be formed from the initial product inventory levels and the price of the bundle to maximize the expected profit. Product demands follow a Poisson Process with a price dependent rate. Customer reservation prices are assumed to have a joint distribution. We study the impact of reservation price distributions, initial inventory levels, product prices, demand arrival rates and cost of bundling. We observe that the expected profit decreases as the correlation between the reservation prices of two products increases. With negative correlation, bundling cost has a significant impact on the number of bundles formed. When the product prices are low, the retailer sells individual products as well as the bundle (mixed bundling), when they are high, the retailer sells only bundles (pure bundling). The expected profit and the number of bundles offered decrease as the variance of the reservation price distribution increases. For high starting inventory levels, the retailer reduces bundle price and offers more bundles. The number of bundle sales decreases and the number of individual product sales increases when the arrival rate increases since the need for bundling decreases. Impacts of substitutability and complementarity of products are also investigated. The retailer forms more bundles, or charges higher prices for the bundle or both as the products become more complementary and less substitutable.

Dynamic Truckload Truck Routing and Scheduling in Oversaturated Demand Situations

The problem considered is dynamic online truckload routing and scheduling with time windows operating in oversaturated conditions, that is, when the demand for service exceeds the system’s average capacity. The relationship between computation time and the solution quality, measured by system efficiency and response time, is discussed. A dynamic operation process for implementing various algorithms and procedures is described, with the aim of fully utilizing computational resources without wasting available time between successive demand requests. In addition, particularly when demand arrival rates result in oversaturated system conditions, application of intelligent acceptance and filtering decision procedures that consider system status and demand characteristics can result in significant operational benefits. Simulation experiments conducted to evaluate the relative performance of the proposed approaches confirm the existence of significant improvement potential in terms of both system efficiency and response time over previous approaches.

Optimal preventive maintenance in a production inventory system

We consider a production inventory system that produces a single product type, and inventory is maintained according to an (S, s) policy. Exogenous demand for the product arrives according to a random process. Unsatisfied demands are not back ordered. Such a make-to-stock production inventory policy is found very commonly in discrete part manufacturing industry, e.g., automotive spare parts manufacturing. It is assumed that the demand arrival process is Poisson. Also, the unit production time, the time between failures, and the repair and maintenance times are assumed to have general probability distributions. We conjecture that, for any such system, the down time due to failures can be reduced through preventive maintenance resulting in possible increase in the system performance. We develop a mathematical model of the system, and derive expressions for several performance measures. One such measure (cost benefit) is used as the basis for optimal determination of the maintenance parameters. The model application is explained via detailed study of 21 variants of a numerical example problem. The optimal maintenance policies (obtained using a numerical search technique) vary widely depending on the problem parameters. Plots of the cost benefit versus the system characteristic parameters (such as, demand arrival rate, failure rate, production rate, etc.) reveal the parameter sensitivities. The results show that the actual values of the failure and maintenance costs, and their ratio are significant in determining the sensitivities of the system parameters.

Optimal preventive maintenance in a production inventory system

We consider a production inventory system that produces a single product type, and inventory is maintained according to an (S, s) policy. Exogenous demand for the product arrives according to a random process. Unsatisfied demands are not back ordered. Such a make-to-stock production inventory policy is found very commonly in discrete part manufacturing industry, e.g., automotive spare parts manufacturing. It is assumed that the demand arrival process is Poisson. Also, the unit production time, the time between failures, and the repair and maintenance times are assumed to have general probability distributions. We conjecture that, for any such system, the down time due to failures can be reduced through preventive maintenance resulting in possible increase in the system performance. We develop a mathematical model of the system, and derive expressions for several performance measures. One such measure (cost benefit) is used as the basis for optimal determination of the maintenance parameters. The model application is explained via detailed study of 21 variants of a numerical example problem. The optimal maintenance policies (obtained using a numerical search technique) vary widely depending on the problem parameters. Plots of the cost benefit versus the system characteristic parameters (such as, demand arrival rate, failure rate, production rate, etc.) reveal the parameter sensitivities. The results show that the actual values of the failure and maintenance costs, and their ratio are significant in determining the sensitivities of the system parameters.

Some structural properties of a Markovian storage/production system

We consider a storage/production system with state-dependent production rate and state-dependent demand arrival rate. Every arriving demand gives rise to a ‘peak’ in the trajectory of the content process. We characterize the processes N_0(x) and N_1(x), defined as the number of peaks and the number of record peaks, respectively, before the content reaches the level x. The results are applied to the virtual waiting time process W(t) of a M/G/1 queue. Assuming that W(0)=x_0, M(x) is defined to be the number of arrivals before the virtual waiting time drops from x_0 to x_0-x (0\leq x\leq x_0)s in particular, M(x_0) is the number of customers arriving during the first busy period. It is shown that (M(x))_{0\leq x\leq x_0} is a compound Poisson process, and its jump size distribution is derived in closed form.