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In addition to the fact that goods and services typically become scarce because resources are scarce, scarcity involves a psychological aspect. When a product is limited in availability, or perceived as being limited, it becomes more attractive. As a result, as long as the product is viewed as scarce, a surplus in supplies implies an increase in consumption. Motivated by fresh-water scarcity, we address the problem of dynamic interaction between two firms committing to provide water supply within a limited time horizon. We find that competition does not necessarily reduce product scarcity compared to the monopolistic industry. In particular, commitment-based market equilibrium is characterized by a critical duration of the supply contract. Duopolistic competition within this duration is reminiscent of the conventional quantity competition—the supply grows and the price drops compared to the monopolistic output. On the other hand, a longer contract leads to a different operational outcome—the monopoly becomes gradually more beneficial in terms of supplies and, as the time horizon grows, even overwhelmingly advantageous, thereby resulting in lower scarcity of the products.

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.

False quality claims have recently rocked the automobile industry. To promote customer demand while seemingly complying with regulations, manufacturers may cheat even at the risk of incurring sever...

Retailers are sources of environmental pollution, 80–90% of which is ultimately due to the processes that retailers set in motion by their orders for the products they carry and sell. The goal of t...

We consider the effect of competition between a firm and its potential suppliers on their decisions, including the firm's decision regarding which supplier to choose. The supply-chain parties interact via a wholesale-price contract with risk sharing via compensation payments paid by the supplier to the firm for early/late supplies. Both the demand for products and the delivery lead time are stochastic. We use Nash and Stackelberg scenarios to model the competition with a game theoretic approach depending on the level of information available to the supply-chain parties. The firm determines the order quantity and the planned delivery time, whereas the supplier controls the accuracy of the delivery times. We show the supplier's leadership has no effect on the supply-chain equilibrium only if the system conditions are such that the demand is known and an order should be placed as soon as possible. Unexpectedly, the Stackelberg solution, and therefore information asymmetry, may be more profitable for both supply-chain parties; that is, it may be Pareto-improving. We also find that by agreeing to greater compensation for early and late deliveries, the supplier may increase its expected profit, as well as the profit of the entire supply chain, thereby coordinating it.

Motivated by rising product insecurity during the initial waves of the COVID-19 pandemic, and the resultant need for consumers to travel further to buy scarce products, we address the possibility of shortages as a result of panic buying. In particular, we study the effect of competition on inventory and pricing by considering the case in which a manufacturer apportions a scarce product to two competing retailers. We find that competition does not always effectively respond to panic buying and can cause frequent price oscillations when the market is shared equally between the two retail firms. On the other hand, in contrast to the case of monopolistic retailing, competition enables the manufacturer to regulate the cost that consumers incur even if the wholesale price is fixed. Specifically, when the market location is biased towards one of the two firms, the manufacturer can apportion supplies to the firms in such a way as to increase the average cost (which includes the retail price and the consumers’ traveling costs), thereby mitigating panic buying and reducing the risk of shortage. Alternatively, when the panic is not severe, the manufacturer can apportion in a way that decreases the average cost, thereby meeting a social welfare-oriented goal in the framework of distributing a scarce product.

We explore how reliance on part-time medical staff affects operational and medical outcome performance in two general surgery departments Whereas prior research has indicated that operational performance is positively associated with medical performance, we find that heavier reliance on part-time practice may deteriorate operational performance but not necessarily medical-outcome performance. For so-called "complex" patients, reliance on part-time practice may even override the effect of patients' characteristics on medical-outcome performance. This result calls into question common perceptions in behavior marketing literature regarding part-time employees' working patterns and efficiency, and thereby provides a new perspective regarding current labor-market trends.

We consider an industry consisting of a large number of firms producing substitutable products and engaged in a dynamic Cournot-type competition. The firms are able to reduce their marginal production costs by accumulating their own experience as well as the experience spillovers from other firms. In particular, firms accumulate production experience through proprietary learning, which, however, depreciates over time. We determine steady-state Nash equilibrium policies that are based on the assumption that the firms do not have precise information about each competitor and therefore are unable to respond to a specific firm’s dynamics. The firms, however, do react to overall industry trends. We show that in such a case, though the information used for production control is incomplete, in the long run the firms tend to the output they would converge to under complete information. We also find that industry growth due to more firms entering the market results in decreasing long-run equilibrium output of each firm when the depreciation of experience is higher than the rate of spillovers. Otherwise, the opposite result can emerge, i.e., the steady-state output will grow.

Despite the widely reported speculation in the 1990s that the era of small medical practices would end within a short period of time, the majority of physicians today still work as solo practitioners or in groups of five or fewer. Personal goals and values in addition to a lack of room for negotiation and difficulties in “being heard” in large organizations are just a few of the potential reasons why physicians resist consolidation and mergers. In this paper, we study the impact of different levels of cooperation on independent medical practices (healthcare providers) in the context of a healthcare supply chain to look into operational reasons why providers are reluctant to merge. In particular, we consider the competition for patients between two providers via insurance reimbursement rate and drug procurement contracts related to demand uncertainties. Assuming that the provider forms a conjecture about its competing provider’s response to its action, we analyze different levels of cooperation between these two providers—from no cooperation to full consolidation in terms of market shares. Our results show that (1) operational costs and demand uncertainties may prevent healthcare providers from pursuing a full consolidation strategy; (2) there exists a unique level of consistent and evolutionarily stable cooperation, and the parties may suffer losses if they consolidate beyond that level; and (3) even when the stable level of cooperation increases, the providers, the drug supplier, and the entire supply chain do not necessarily improve their profits.

This paper analyzes how faculty members dynamically allocate their efforts between improving their research and teaching skills, taking into account the organizational structures and incentives implemented by academic institutions. The model builds on the assumption that organizational structures have an impact on the nature of spillover effects between teaching and research competencies. We analyze the dynamic equilibrium under unilateral and bilateral spillovers, using the no-spillover case as a benchmark. The bilateral spillover case is the most appealing as it achieves the highest overall performance; however, the nature of the equilibrium and the career paths can be quite different depending on the parameters of the problem such as the obsolescence of competencies or the strength of the spillover effect. This finding provides interesting insights on what could be the most productive configuration of a higher education institution.

We consider a monopolistic producer offering software that is updated periodically, but, by the end of one period, a pirated version is available at a transaction cost. This presents the consumers, who are different in terms of their willingness to pay for the original compared to the pirated version, with possible strategies for either buying a new product or pirating it. We address pricing and protection investment strategies to regain the profits affected by the piracy. In particular, we find that even when the transaction cost is exogenous, the producer does not necessarily want to fully price out the piracy. The decisive factor in such a case is the level of product newness relative to the transaction cost. If the producer is able to achieve high newness for the updated product relative to the transaction cost, then a high retail price ensures that he will gain the largest profit possible even though some of the demand will be lost due to piracy. On the other hand, when the transaction cost is endogenous, the producer may have two alternatives, in terms of profit, for dealing with the piracy—pricing the software out or investing heavily in software protection. As newness levels rise, the option of pricing out the piracy becomes increasingly preferable.

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.

We address the issue of contract breachability in a supply chain involving a retailer and a manufacturer operating under ship-to-order contract terms and stochastic demands. The manufacturer is required to fulfill the retailer’s demands on a continuous basis with little or no advance notice. The issue in such an environment is whether the retailer can “naively” assume that she will get a very high fill rate from the manufacturer and therefore has no need for contract penalties in case the manufacturer’s inventory falls short. We suggest a stochastic calculus framework to study the problem and derive a condition when the retailer’s naive assumption is justified since the probability of stock-outs of the manufacturer is negligible. That is, the ship-to-order contract will not be breached and the fill rate will be more than a predetermined threshold. Furthermore we find that although the manufacturer-owned direct channel generates more revenue and may reduce the volatility of both inventory and production orders, the ratio between expected direct channel and retail sales affects the benefits.

We consider a monopolistic supply chain consisting of a manufacturer and a retailer (service provider) who in addition to selling new durables, buy and resell used ones. The supply chain provides services for both new and used goods. Accordingly, consumers incur service charges for all types of goods. This study is motivated by the modern trend in cell phone businesses where retailers commence buying used phones from customers willing to upgrade their phones. The used phones are then refurbished and resold along with the services. The question that this trend gives rise to is how the interaction with the secondary market affects the performance of the supply chain in terms of its intracompetition and thereby its profit. We show that for a wide range of service rates, the second-hand market coordinates the supply chain by either reducing the double marginalization effect or by offsetting it with extra profits gained by servicing the used goods. This, however, does not imply that both parties always improve their profits. Furthermore, we find that when the service rates are low, the supply chain would be better off if the goods were not durable thereby precluding the very existence of the second-hand market.

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.

In this technical note we study continuous-time stochastic control of a dynamic production and replenishment system characterized by bounded control and an additive type of uncertainty. The study is motivated by problems arising in supply chains involving periodic exchange of information between a manufacturing system (supplier) and a customer (retailer). As a result, the inventories are only observed periodically while the replenishment is possible at any point of time. We identify replenishment policies for different operational conditions and show that, even for one-product-type system, the consideration of random demand over multiple update periods leads to a non-intuitive, and nontrivial, optimal production control.

In this paper, we consider inventory outsourcing by a producer to a distributor. The distributor charges a cost for each unit it handles and the manufacturer responds with a production and inventory policy over a finite contract period. As a result, the two parties enter a noncooperative differential game. We address the effect of information asymmetry in such a game under a stochastic demand when the inventory level can only be observed by the manufacturer intermittently.

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.

We consider a retailer who orders products before the price for them becomes known. The price is an outcome of perfect competition in a complete market. Since the demand is price sensitive, the uncertainty in prices induces uncertain profits and associated risks. In this paper we show that if the retailer is risk averse and, as a result, selects a utility function of profit to maximize, then his subjective assessment of future prices is affected by the risk attitude. This, in turn, introduces a bias in retailer’s ordering policies. By considering coordinated pricing and ordering policies we derive a relationship between risk aversion, retailer’s subjective (private) assessment and the market implied, risk neutral forecast. This relationship and the induced bias are then illustrated for two typical operations management strategies which involve either inventory considerations or promotions avoiding accumulation of stocks.

This paper addresses a problem encountered by a large-scale health service supply chain operating in a periodic review mode. Due to the vital nature of the products it provides, the number and timing of urgent orders are not limited. As a result, increasingly high transportation costs are incurred and the problem is to select an inventory replenishment (review) period that minimizes the transportation cost. Moreover, the supply chain involves multiple retailers which inevitably and independently respond to any change in replenishment policy since it may affect their inventory costs. Such a relationship results in a game between a distribution centre and retailers. Since the problem is intractable due to its scale and stochastic nature, we combine a game theoretic approach with an empirical analysis. We show that this system is predictable using equilibria and that the current replenishment equilibrium of the health service supply chain is close to the Nash solution. Numerical analysis shows that the transportation costs are cut if the distribution centre implements in reality its formal (Stackelberg) leadership by reducing the replenishment period. However, this does not coordinate the supply chain and greater system-wide savings are possible by increasing the replenishment period if the supply chain is vertically integrated or the parties cooperate.

This paper provides a quantitative and comparative economic and risk approach to strategic quality control in a supply chain, consisting of one supplier and one producer, using a random payoff game. Such a game is first solved in a risk-neutral framework by assuming that both parties are competing with each other. We show in this case that there may be an interior solution to the inspection game. A similar analysis under a collaborative framework is shown to be trivial and not practical, with a solution to the inspection game being an ‘all or nothing’ solution to one or both the parties involved. For these reasons, the sampling random payoff game is transformed into a Neyman–Pearson risk constraints game, where the parties minimize the expected costs subject to a set of Neyman–Pearson risk (type I and type II) constraints. In this case, the number of potential equilibria can be large. A number of such solutions are developed and a practical (convex) approach is suggested by providing an interior (partial sampling) solution for the collaborative case. Numerical examples are developed to demonstrate the procedure used. Thus, unlike theoretical approaches to the solution of strategic quality control random payoff games, the approach we construct is both practical and consistent with the statistical risk Neyman–Pearson approach.

In this note, we consider a manufacturing system with random machine breakdowns, which is characterized by a fairly general probability distribution. The demand is not known during the finite planning horizon except the probability distribution of the cumulative demand at the end of the horizon. We propose a decomposition method that features a feedback control. Simulation is used to compare the average cost of the proposed method and that of the optimal solution. Our results of more than a hundred examples show that the difference between the two is less than 2.4%.

This paper considers the problem of co-investment in a supply chain infrastructure using an inter-temporal model. We assume that firms’ capital is essentially the supply chain's infrastructure. As a result, firms’ policies consist in selecting an optimal level of employment as well as the level of co-investment in the supply chain infrastructure. Several applications and examples are presented and solutions found for non-cooperating firms and centralized investment. Non-simultaneous moves (Stackelberg) firms are treated in an extended version of this paper.

In many manufacturing systems prone to random interference, such as machine breakdowns and fluctuating yield, information about the interference as well as other system states, e.g., inventory levels, may not be available in a timely manner. Therefore an online feedback control will be difficult to implement, and a good offline control strategy may be the only alternative. In this note we develop such a strategy for a production system with random yield, which is characterized by a Wiener process. Assuming the initial inventory level is known, we derive closed form expressions of the optimal production control to minimize the expected inventory and backlog costs over a production horizon.

In this note, we consider a single-machine, single-part-type production system, operating in a defect-prone environment. It is assumed that there is a random yield proportion of nondefective parts, with known probability distribution. Over each production cycle, it is assumed that there is a single realization of the yield random variable. Furthermore, it is assumed that the system is operated under a periodic-review policy. Thus, the particular realization of the yield proportion cannot be determined prior to the end of the production horizon. The optimal production control, that minimizes a linear combination of expected surplus and shortage costs over the planning horizon is shown to be piecewise constant, and the appropriate production levels and control break-points are determined as functions of the yield rate distribution.

Human resource planning has always been a key issue to professional companies. To help professional firms cope with demands, a dynamic approach for planning human resources in a continuous time frame is proposed. We analytically determine an exact and globally optimal solution to a firm's human resources by explicitly considering its hierarchical structure, costs of recruiting and hiring, workload, contract delays, loss of revenues, and an over-capacity issue. Managerial implications of this study are also discussed.

We address the problem of managing the intensity, sequence and timing of inspection effort in an N-stage production system with M inspection activities possible at each stage. The objective is to minimize the sum of the inspection costs and the penalties caused by undetected defects. By means of the maximum principle we prove several properties or the optimal solution, which allow us to reduce the continuous-time inspection effort allocation problem to a combinatorial one. We suggest an efficient algorithm that solves the problem in 0(NM2 + N2) time.

This paper considers a manufacturing system where multiple-product-types are produced on a set of parallel machines. The production quantity for each product-type in a planning horizon is predetermined. However, the planning horizon is not fixed, and a cost must be paid for each unit of time in the horizon. Inventory holding costs are incurred due to storing products in the buffer placed after each machine. In addition, a production cost is incurred if a machine is not idle. Our objective is to schedule the production so that inventory, production, and planning horizon costs are minimized. With the aid of the maximum principle, this continuous-time scheduling problem is studied, and the conditions such that the problem can be decomposed into a set of well-structured, discrete-time sub-problems are derived. Consequently, several solvable cases are identified, and their corresponding polynomial-time algorithms are suggested.

We develop a model for determining the economically optimal amount of control effort required to manage a homogeneous project (one consisting of a large number of similar activities). The model is formulated in terms of the losses generated by deviations from the plan and of the costs associated with carrying out control activities. It accounts for changing levels of project activities and includes parameters that represent control effectiveness and project management effectiveness. The model is studied by applying optimal control theory, which yields the optimal control effort described by a number of control functions and switching points at which they change over. We identify three analytically solvable cases for the most commonly used forms of control cost and deviation loss functions. Our analysis of the model leads to several specific conclusions regarding the extent and timing of managerial attention that should be devoted to keep projects on track. We also point out how the optimal off-line policy can be adapted for on-line control and real-time decision making throughout the project life cycle.

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.

This paper addresses the production control problems created in the scheduling of a flexible manufacturing cell consisting of groups of identical machines. An actual manufacturing system, drawn from Sikorsky Aircraft Corporation, was used as a prototype for modeling the cell to study its optimal behavior. The model, stated in the form of optimal production flow control combines classical machine-part scheduling and scheduling of part fixtures. Such an extension induces three problem formulations comprising practical production issues important for many modern plants other than Sikorsky. These formulations are related to three production cases covering different degrees of fixture availability. With the aid of the maximum principle, a numerical scheduling method is constructed for all three problem formulations, and case studies are presented.

This paper develops a method for continuous-time scheduling problems in flexible manufacturing systems. The objective is to find the optimal schedule subject to different production constraints: precedence constraints (bills of materials), sequence-dependent setup times, finite machine capacities, and pressing demands. Differential equations along with mixed constraints are used to model production and setup processes in a canonical form of optimal control. The proposed approach to the search for the optimal solution is based on the maximum principle analysis and time-decomposition methodology. To develop fast near-optimal solution algorithms for sizable problems, we replace the general problem with a number of sub-problems so that solving them iteratively provides tight lower and upper estimates of the optimal solution.

This paper analyzes how faculty members dynamically allocate their efforts between improving their research and teaching skills, taking into account the organizational structures and incentives implemented by academic institutions. The model builds on the assumption that organizational structures have an impact on the nature of spillover effects between teaching and research competencies. We analyze the dynamic equilibrium under unilateral and bilateral spillovers, using the no-spillover case as a benchmark. The bilateral spillover case is the most appealing as it achieves the highest overall performance; however, the nature of the equilibrium and the career paths can be quite different depending on the parameters of the problem such as the obsolescence of competencies or the strength of the spillover effect. This finding provides interesting insights on what could be the most productive configuration of a higher education institution.

An optimal control approach to continuous-time aggregate production planning problems is presented. The proposed approach describes the production and capacity evolution (expansion, sell and deterioration) processes in the form of differential equations with regular production, subcontracting and capacity change rates controllable on one hierarchical level. In this way, the traditional disadvantages of the two-level problem consideration (one level for strategic capacity planning and the other for production smoothing) are avoided. Analytical properties for optimal production and capacity control regimes and conditions for their changeover are derived by the maximum principle. Based on these results, an insight into the optimal behaviour of the production system is gained and a fast numerical method is developed to identify and sequence the optimal regimes for arbitrary demand profiles. A computational example illustrates the effectiveness of the approach.

Rapid changes in the market environment, customer demands and technological advancement all cause the traditional, closed-loop MRP approach to lose efficiency. This paper suggests a solution for companies in which an end product of the same quality can be produced in different ways. In such an environment changes could be accommodated by an extended (multi) bill of material. The present solution is based on the hypergraph approach for modelling and optimizing multi-bills of material in the MRP system, and achieves cost reduction while maintaining the quality and service levels required by the company.

This paper introduces a new approach to continuous-time optimal scheduling problems for a large class of manufacturing systems. This class belongs to a make-to-order production environment, based on multilevel bills of materials, flexible flow shops with setup effects and finite capacities on the shop floor. So far the setup and production planning had to be decomposed into two levels; the present model allows treating these two issues on one level, thus potentially achieving better production results. The proposed approach states the problem in terms of optimal control and investigates control strategies by means of the maximum principle for the problems with constraints on state variables. >

This book is devoted to classifying and solving scheduling problems in the production systems of simple machine configurations. Although such configurations as job-shop, open-shop, and re-entrant lines are not within the book’s scope, the maximum principle applied to scheduling problems in complex machine configurations may still result in efficient combinatorial algorithms. This chapter deals with scheduling of multiple tandem machines with limited production capacity and demand concentrated at a due date. Among the various scheduling problems, this one is chosen to illustrate the solution methodology suggested in this book for those cases when configuration of the production system is not as simple as a parallel-machine cell.

Aggregate production planning is the problem of deciding about a firm’s production policy, i.e. on the quantity of products to be produced during a period of time. This decision is made on the basis of a product demand forecasted over a given planning horizon, as well as on the basis of many other factors within the manufacturing environment: costs, equipment and manpower flexibility, inventory constraints, etc. Since aggregate planning is a fundamental part of the firm’s overall business strategy, its optimization can lead to major improvement in the fiirm’s profits.

This chapter presents seven case studies of practical scheduling implemented at several manufacturing plants located in the northeast of the United States. Production engineers managing the manufacturing helped us to gather data on the shop floor. To study these cases we developed a scheduling software which is based on the numerical methods presented in Chapter 7. The software has an easy graphical user interface and runs under a Windows environment. The software as well as a tutorial can be found in the disk attached to this book (see file “Readme” for details of the disk).

We address quality control of products undergoing multiple transshipment stages handled by different parties. Depending on the transportation modes, the stages may expose the products to hostile environments, such as extreme temperatures, which could influence quality. We incorporate the effect of quality on demand with the Neyman–Pearson statistical framework to study the effect of intra-competition between supply chain parties on inspection policies and thereby product quality. Specifically, we compare these policies with that of a centralized supply chain, where a single decision maker chooses the optimal inspection policies for all stages. We find that in terms of inspection policy, a party with the higher probability of nonconformance tends to inspect less under competition compared to the system-wide optimal inspection policy. Conversely, the other party may inspect more than under the system-wide optimal policy. We determine when intra-competition impacts conformance quality so that regulations are of particular importance for protecting consumers.

We address a quality control problem frequently encountered in multi-stage pharmaceutical supply chains transporting drugs from a producer to a wholesaler and eventually to retailers (pharmacies). Depending on the transportation modes and storage methods used, the stages may expose the drugs to hostile environments, such as extreme temperatures, which may impact the quality. To study the performance of such a supply chain, we incorporate the effect of quality on demand with the Neyman?Pearson statistical framework. We show that in a centralised supply chain the optimal inspection strategies for the parties depend on parameters, which signify the relative importance of price and the impact of quality on demand. In particular, we find that the ratio between the customer demand under perfect product quality and the customer sensitivity to quality plays a critical role in selecting optimal inspection policies.

We consider rough products produced by a factory. Each product coming from the plant has \(m\) vital elements and some elements can be damaged. To obtain a perfect product (i.e. all the constitutive \(m\) elements are safe) all the damaged elements are repaired and a test phase follows. The result of this two-steps procedure is random. We suppose that the number \(Z_k\) of non-damaged elements is a Markov chain valued in the set \(\{0,1,\ldots ,m\}\), where \(k\) is the number of applied repairing-test phases. We have a qualitative result which says that if the repair phase is efficient then \(P(Z_k=m)\) is close to \(1\). As for production of a large number \(n\) of products, the former result allows us to give conditions under which either the \(n\) elements or a fraction of these \(n\) elements are (is) safe after the application of \(k\) previous maintenance phases.