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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...

In many manufacturing systems the production rate cannot be instantaneously adjusted in response to inventory updates. This article addresses such a system under price-dependent stochastic demand. The objective of the system is to choose a time-invariant production rate and time-dependent product price that maximize the expected profit. This manufacturing system is compared to a benchmark system where both production rate and product price are adjustable. It is shown that the expected inventory level does not necessarily increase when the manufacturer can handle stock spikes only by leveling the demand with the product price. Although the inability to adjust production rate under a high level of uncertainty is difficult to offset with dynamic pricing, the non-linear components of the production and inventory costs can make a difference. For example, by reducing the non-linear component of the production cost and increasing price volatility, the manufacturer may close the profit gap between the two systems...

A basic production system facing two types of uncertainty (shocks), multiplicative and additive, is considered. The former is due to a stochastic yield; the other to a stochastic demand. The objective of the production system is to choose a production rate (control) that minimizes expected inventory and production costs. Stochastic production control is typically considered the prerogative of closed-loop or on-line approaches. However, in certain manufacturing systems, information about inventory levels may at best be imprecise. Moreover, the production rate cannot be instantaneously adjusted in response to inventory updates. This warrants the exploration of an open-loop or off-line control methodology. In the comparative analysis of the two approaches presented in this paper, the probability distribution of inventories is characterized, the damage associated with the inability to adjust production is assessed, and the conditions at when the gap between the two approaches are insignificant are highlighted...

This paper focuses on advance orders and continuous-time production smoothing under uncertain demands. Similar to the classical newsboy problem, the demands may represent items that quickly become obsolete, spoil or have a future that is uncertain beyond a single period or selling season. The exact demand for items is unknown prior to the end of the selling season and may exceed the available capacity. To handle the uncertainty, initial inventories are accumulated by advance ordering or contracting out at a lower cost relative to the manufacturer's production cost. In contrast to the classical newsboy problem, the manufacturer's capacity is used to smooth inaccuracy in demand estimation during the selling season. The objective is to determine both the advance order quantity to be delivered by the beginning of the selling season and the production rates over the selling season to minimize advance order costs and expected inventory shortage or surplus costs as well as production costs during the season. The...

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.

This paper addresses the pricing policy of durable value goods that do not depreciate over time. This implies that demands for this type of goods fluctuate with respect to their market price and social interactions between customers rather than with respect to the time elapsed since they have been produced or created. We suggest an analytical approach for optimally setting durable value product prices with respect to the interdependency between two customer groups characterized by asymmetric intergroup externalities. We demonstrate that cyclic pricing policies of harmonic form become optimal when the company is prepared to compromise its short-run net profit to ensure its lasting reputation. Furthermore, we show that the greater the difference between the product of the price and the externality effect of the two customer groups, the greater the frequency of the harmonic fluctuation.

The paper focuses on the control decisions in the area of multi-period, aggregate production planning. The plan consists of a number of sequential planning periods stretching out to a particular time horizon. Owing to machine downtime, quality, supply, and maintenance problems, true productivity differs from the expected. Therefore, at the end of each planning period, the planner must have immediate feedback about production outcome. The results are analysed for variations from the plan (shortfalls or surpluses) and any differences are used to modify subsequent plans. The goal is to minimize the expected total costs including productivity, overtime as well as over- and under-production costs. Although the presented solution is generally not of base-stock type, a correspondence between it and the solution of the classical newsboy problem is revealed. This paper was developed during a consultation assignment in the food industry where the planning results were tested, and the case is presented.

A short selling season and highly uncertain demands prior to the season characterize production and selling of fashion goods. Once the season starts and demands turn up with a peak interest in the beginning, monopoly becomes under tremendous pressure to produce the required amount so as not to disappoint its customers. It motivates the monopoly to prepare significant inventories by the opening day. Unfortunately, even the most advanced techniques for demand forecasting are likely to induce either an overestimate or underestimate of the initial inventories. Both affect the monopoly's profit. Overestimation results in surplus, which may never be sold, and excessive inventory holding costs. Underestimation implies sales as well as customer loyalty losses. Given inventory level at the beginning of the selling season, we derive policies of handling this inventory, production capacity and product prices in order to maximize the profit and thus diminish the effect of inherent inaccuracy of initial inventory estimation of fashion goods. A case of bookstore management illustrates the effectiveness of the suggested strategies.

This paper focuses on a dynamic, continuous-time control generalization of the unbounded knapsack problem. This generalization implies that putting items in a knapsack takes time and has a due date. Specifically, the problem is characterized by a limited production horizon and a number of item types. Given an unbounded number of copies of each type of item, the items can be put into a knapsack at a controllable production rate subject to the available capacity. The demand for items is not known until the end of the production horizon. The objective is to collect items of each type in order to minimize shortage and surplus costs with respect to the demand. We prove that this continuous-time problem can be reduced to a number of discrete-time problems. As a result, solvable cases are found and a polynomial-time algorithm is suggested to approximate the optimal solution with any desired precision.

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.

In this paper, we consider a single part-type pull manufacturing system, which controls its production rates in response to periodic demand. When tracking the demand results in a product surplus, an inventory storage cost is incurred. Likewise, if an overall shortage occurs then a backlog cost is paid. In addition, production costs accrue when the system is not idle. Given an infinite planning horizon, the objective is to determine the cyclic production rates in order to minimize the total cost. With the aid of the maximum principle, extremal behavior of the system is studied and the continuous-time production planning problem is reduced to a discrete problem with a limited number of switching points at which time the production rates change. Using this result, an efficient numerical algorithm is proposed, which will yield an approximation to the optimal solution within any desired level of accuracy. In addition, we determine the analytical solution to the problem for three special cases: (i) the system c...

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.

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.

The paper concerns an optimal control approach to continuous-time aggregate production planning in make-to-stock and make-to-order environments. The dynamics of such a production system are modelled by purchased, in-process and finished inventory flows through multiple facilities of finite capacity. The objective of the make-to-order production is to track a given customer demand as closely as possible, while in the make-to-stock production it is to keep the purchased inventory minimal when filling the stocks with volumes of products scheduled to be completed by the end of the planning horizon. The optimal behaviour of the system is studied with the aid of the maximum principle which allows new analytical results to be derived. Consequently, fast numerical and analytical algorithms for balancing facilities in the two corresponding environments are suggested.

This paper introduces a continuous-time optimal control approach to cope with scheduling problems in complex manufacturing systems. These systems are controlled under arbitrary changing demand profiles with respect to multi-level bills of materials, flexible flow shops with setup effects and finite production capacities. The suggested methods extend a general optimal control approach to handle with partially sequence-dependent setups on one hierarchical level along with production scheduling. The optimal scheduling method and its enhanced modifications are derived based on the maximum principle analysis and compared to the traditional two-level hierarchical approach.

SUMMARY This paper concerns a new approach to continuous time optimal scheduling problems for a large class of manufacturing systems. The proposed approach states the problem in terms of optimal control with setup and production rates controllable on one hierarchical level. This allows for the traditional disadvantages of the two-level problem consideration (one level for defining the target production rates, and the other for scheduling the setup changes) to be avoided and stable control strategies to be obtained. Analysis of the maximum principle results in setup conditions of the optimal schedule and special regimes to which the optimal tends between subsequent setups. Based on these results, a numerical method is developed to define the sequence of the special regimes and the timing for getting into and out of them. An example illustrates the effectiveness of the approach.

A flexible manufacturing cell consisting of two machining centres, several automated storage/retrieval stations, and a mobile transporting robot is considered. The problem is to schedule jobs on machines so as to minimize the makespan, with the effects of transportation and set-ups to be taken into account. The problem is studied with the aid of a graph model, and an exact algorithm of cubic complexity is derived based on the Gilmore–Gomory algorithm for the travelling salesman problem.

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.