Search

We address the problem of optimising the intensity of online advertising. In contrast to the classical literature, we tackle the advertising interaction between the firm and the potential customer, for the sale of a onetime event, in a very limited time horizon. The problem is intrinsically dynamic due to two conflicting situations: the first arises when the customer is subjected to intense advertising pressure, which may lead to customer saturation and even irritation, while the second is the tendency for customers to forget if they are not reminded systematically through advertising. In order to determine an optimal event-advertising policy and develop an efficient enumerative shooting algorithm to solve the problem, we suggest a hazard rate-based approach to modelling the conflicting factors. Our analysis shows that the initial level of customer interest in the event has a non-trivial effect on the dynamics of the optimal advertising policy. In particular, this advertising policy consists of a monotonic increase over time prior to the event in the case of high initial interest and a concave, peak-wise form in the case of low initial interest.

We study the effect of appending regular, wholesale prices with a conventional, single price-break point quantity discount offered by a supplier to multiple retailers engaged in a Cournot–Nash competition. It is commonly observed in real-life supply chains that the retail price does not drop at once to the extent of the wholesale price discount. We capture this inertia with an evolutionary analysis which assumes that not every retailer immediately adopts a discounting strategy. We find that evolutionary dynamics then might alter the expected final outcome of the competition and show that the supplier will not be able to induce simultaneously both perfect coordination and perfect competition regardless of the type of retailers he is dealing with. Moreover, though the profits the supply chain gains are highest when the supplier perfectly coordinates it, we show that the retailers retain a non-zero profit margin in such a case. As a result, the supplier will not necessarily want to coordinate the supply chain, preferring instead to gain the same amount of profit from the perfect competition between the retailers attracted by the discount.

This paper investigates how current and future generations are affected by commitment-based Nash equilibrium environmental strategies when the environmental absorption efficiency is susceptible to switch from a pollution sink to a source. We formulate a two-player differential game model of transboundary pollution that includes the environmental absorption efficiency as a state variable that can be enhanced thanks to restoration efforts. Based on a logarithmic specification for the instantaneous revenue function, we characterize the cooperative solution and the commitment-based Nash equilibrium strategy, and examine their differences in terms of steady state and transient behavior. We notably show that a commitment-based Nash equilibrium strategy makes it possible to prevent a definitive switching of the environmental absorption efficiency from a pollution sink to a source but imposes greater economic sacrifices on current generations than on future generations. In comparison, the cooperative solution imposes greater sacrifices on current generations in terms of revenues but it imposes lower environmental costs on both current and future generations than commitment-based Nash equilibrium strategy.

We address the effect of uncertainty on a manufacturer’s dynamic production and pricing decisions over a finite planning horizon. The demand for products, which depends on their price, is characterized by two stochastic processes: potential demand and customer price sensitivity. An optimal policy for coordinating production and pricing is a time-dependent feedback rule with respect to the state of the manufacturer’s inventories. We show that when the volatility of customer sensitivity to the product price is negligible, the optimal policy can be obtained analytically. Moreover, our simulations demonstrate that the volatility of stochastic customer price sensitivity does not have a strong effect on the manufacturer’s expected profit. Therefore, the solution derived for the case of customer price sensitivity with zero volatility can serve as a good approximation heuristic for the optimal policy if the true volatility of customer price sensitivity is within 40 % of its mean and the volatility of potential demand is within 25 % of its mean. Moreover, under these conditions, a simplified, time-independent control rule deteriorates expected profits by only 1.5 %.

We consider a two-echelon supply chain involving one manufacturer and one supplier who collaborate on improving both design and conformance quality. Design quality is supposed to increase product desirability, and therefore market demand, while conformance quality should reduce the proportion of defective items, and therefore increase the manufacturer’s sales revenue. We investigate how the supply chain parties allocate effort between design and conformance quality under both cooperative and non-cooperative settings in an intertemporal framework. Furthermore, we evaluate wholesale price contracts and revenue-sharing contracts in terms of their performance and coordination power. We show that although a revenue-sharing contract enables the manufacturer to effectively involve the supplier in quality improvement, neither contract type allows for perfect coordination resulting in the quality that can be achieved by a cooperative supply chain. We thus suggest a reward-based extension to the revenue-sharing contract, to ensure system-wide optimal quality performance. Importantly, we find that the supplier would be better off adopting a reward-based revenue sharing contract and refusing a standard revenue-sharing contract, while the opposite would be true for the manufacturer.

This paper is motivated by inventory problems arising in supply chains characterized by continuous replenishment programs based on information exchanged (reviewed) only intermittently between a manufacturing system (supplier) and a customer (retailer). When the replenishment is once-per-period, rather than at any point of time, a well-known result is the optimality of the so-called myopic base-stock policy. We generalize the notion of the base-stock policy and study the optimality of the corresponding class of dynamic myopic policies. We identify a myopic policy and prove that although the replenishment rule is dynamic, this policy is optimal when the demands are stationary and the number of review periods tends to infinity.

This paper considers co-investments in a supply chain infrastructure using an inter-temporal investment model. We assume that the supply chain firms' capital consists essentially of an investment in the supply chain's infrastructure. As a result, firms' policies consist in selecting both an optimal level of employment and the level of co-investment in the supply chain infrastructure. Recent papers by Kogan and Tapiero (Eur J Oper Res 2009; Supply chain games: Operations management and risk valuation. Springer, Boston 2007) have presented open-loop and feedback solutions for non-cooperating firms and have shown that these solutions differ from a unique system-wide optimal solution, which maximizes the overall supply chain profit. To overcome this problem and thereby improve the supply chain performance, this paper suggests a coordination approach. Such an approach is consistent with a recent practice which consists in the creation of a supply chain shared capital (or joint funding of selected activities) with a temporal reward (or penalties) offered to non-cooperating firms for each dollar investment they make. In addition, this paper provides a closed form expression for the time sensitive rewards function expressed in terms of the system parameters. We show that when these rewards are offered, the Nash co-investment equilibrium is equal to the system-wide optimal solution.

We generalize a static two-agent location problem into dynamic, asymmetric settings. The dynamics is due to the ability of the agents to move at limited speeds. Since each agent has its own objective (demand) function and these functions are interdependent, decisions made by each agent may affect the performance of the other agent and thus affect the overall performance of the system. We show that, under a broad range of system’s parameters, centralized (system-wide optimal) and non-cooperative (Nash) behavior of the agents are characterized by a similar structure. The timing of these trajectories and the intermediate speeds are however different. Moreover, non-cooperative agents travel more and may never rest and thus the system performance deteriorates under decentralized decision-making. We show that a static linear reward approach, recently developed in Golany and Rothblum (Nav. Res. Logist. 53(1):1–15, 2006), can be generalized to provide coordination of the moving agents and suggest its dynamic modification. When the reward scheme is applied, the agents are induced to choose the system-wide optimal solution, even though they operate in a decentralized decision-making mode.

This paper addresses the economic efficiency of water production and distribution in a vertical supply chain consisting of a water-provider and a consumer (municipality). The inherent conflicts over stocks and supply costs that emerge among the parties in the water supply chain are modeled as a zero-sum stochastic differential game. Consequently, the effects of collaboration and competition are contrasted as well as the application of block pricing and subsidies in overcoming potential conflicts between the water-provider and the municipality subject to political risks of not meeting demands for water. The effect of uncertainty is elaborated as well. In particular, we show that when the supply variance depends on the mean supply, the effect of uncertainty depends on the intensity of the conflict between the municipality and the water-provider.

The assignment problem is a well-known operations research model. Its various extensions have been applied to the design of distributed computer systems, job assignment in telecommunication networks, and solving diverse location, truck routing and job shop scheduling problems. This paper focuses on a dynamic generalization of the assignment problem where each task consists of a number of units to be performed by an agent or by a limited number of agents at a time. Demands for the task units are stochastic. Costs are incurred when an agent performs a task or a group of tasks and when there is a surplus or shortage of the task units with respect to their demands. We prove that this stochastic, continuous-time generalized assignment problem is strongly NP-hard, and reduce it to a number of classical, deterministic assignment problems stated at discrete time points. On this basis, a pseudo-polynomial time combinatorial algorithm is derived to approximate the solution, which converges to the global optimum as the distance between the consecutive time points decreases. Lower bound and complexity estimates for solving the problem and its special cases are found.

The paper analyzes a manufacturing system with tandem machines producing one part type. The system is periodically stopped for maintenance. The objective is to determine machine production rates so that the inventory and backlog-related expenses could be minimized. We show only a few so-called restricting machines need to be considered. A numerical example is used to demonstrate the solution approach proposed in the paper.

The paper analyzes a manufacturing system made up of one-machine which produces N-product-types with controllable production rates in response to product demands. The demands are characterized by different amounts of each product-type to be produced and a common due date. The objective is to minimize inventory and backlog costs which are incurred when meeting the due date results in inventory surpluses and shortages. With the aid of the maximum principle, the continuous-time scheduling problem is studied as an optimal control model and is reduced to a combinatorial one, polynomially solvable when the costs are either ``agreeable'' or when the number of the non-agreeable costs is limited.

The problems of M-machine, J-product, N-time point preemptive scheduling in parallel and serial production systems are the focus of this paper. The objective is to minimize the sum of the costs related to inventory level and production rate along a planning horizon. Although the problem is NP-hard, the application of the maximum principle reduces it into a well-tractable type of the two-point boundary value problem. As a result, algorithms of O(NMJk(N-L)+1) and O(N(MJ)k(N-L)+1) time complexities are developed for parallel and serial production systems, respectively, where L is the time point when the demand starts and k is the ratio of backlog cost MN over the inventory cost. This compares favorably with the time complexity O((J+1MN) of a naive enumeration algorithm.

This paper discusses a continuous‐time approach to production control of parallel assembling complexes under maintenance activities specified in advance in order to avoid machine failures along the planning horizon. Every complex includes multiple machines and a tandem storage and retrieval station. Each machine performs a number of assembling operations with negligible setups and controllable production rates subject to time windows in which predetermined maintenance actions are to be carried out. The objective is to control simultaneous assembling of different items in every complex in order to track dynamic demands for the items as closely as possible, without exceeding the capacity of the tandem storage and retrieval stations. With the aid of the maximum principle, optimal production regimes are derived and a fast iterative time‐decomposition algorithm is developed to locate those regimes along the planning horizon with a given accuracy.

The paper addresses problems of allocating continuously divisible resources among multiple production activities. The resources are allowed to be doubly constrained, so that both usage at every point of time and cumulative consumption over a planning horizon are limited as it is often the case in project and production scheduling. The objective is to track changing in time demands for the activities as closely as possible. We propose a general continuous-time model that states the problem in a form of the optimal control problem with non-linear speed-resource usage functions. With the aid of the maximum principle, properties of the solutions are derived to characterize optimal resource usage policies. On the basis of this analytical investigation, numerical scheduling methods are suggested and computationally studied.

The Generalized Assignment Problem (GAP) is a well-known operations research model. Given a set of tasks to be assigned to a group of agents and the cost of performing each task by each agent, the model allocates tasks to agents to minimize the total cost subject to the availability of a single resource type. The single resource is consumed by the agents when performing these tasks. In this paper, we add the impact of time to the model assuming that each task has a due date, and inventory cost as well as shortage cost is incurred when a task is finished ahead or after its due date, respectively. We formulate the continuous-time op-timal control model of the problem where identical tasks are grouped into jobs (or batches), each job is performed by each agent with a fixed (production) rate, while due dates are transformed into demand. As a result, analytical properties of the optimal behavior of such a dynamic system are derived. Based on those properties, an efficient time-decomposition procedure is developed to solve the problem.

The paper deals with the scheduling of a robotic cell in which jobs are processed on two tandem machines. The job transportation between the machines is done by a transportation robot. The robotic cell has limitations on the intermediate space between the machines for storing the work-in-process. What complicates the scheduling problem is that the loading/unloading operation times are non-negligible. Given the total number of operationsn, an optimalO(n logn)-time algorithm is proposed together with the proof of optimality.

A continuous time dynamic model of discrete scheduling problems for a large class of manufacturing systems is considered in the present paper. The realistic manufacturing based on multi-level bills of materials, flexible machines, controllable buffers and deterministic demand profiles is modeled in the canonical form of optimal control. Carrying buffer costs are minimized by controlling production rates of all machines that can be set up instantly. The maximum principle for the model is studied and properties of the optimal production regimes are revealed. The solution method developed rests on the iterative approach generalizing the method of projected gradient, but takes advantage of the analytical properties of the optimal solution to reduce significantly computational efforts. Computational experiments presented demonstrate effectiveness of the approach in comparison with pure iterative method.