Periodic-review inventory systems with random yield and demand: Bounds and heuristics

We revisit the infinite-horizon decision problem of a single-stage single-item periodic-review inventory system under uncertain yield and demand. It is known that under some mild conditions the optimal replenishment policy is of the threshold type: an order is placed if and only if the starting inventory is below a threshold value. Although the structure of the optimal policy is well known, there has been little discussion about the optimal order quantities and the order threshold. In this paper, we construct upper and lower bounds for the optimal threshold value and the optimal order quantities through solving one-period problems with different cost parameters. These bounds provide interesting insights into the impact of yield uncertainty on the optimal policy. Heuristics are developed based on these bounds. Detailed computational studies show that, under some conditions, the performance of the heuristics is very close to that of the optimal solution and better than that of existing heuristics in the literature.     

Coordinating decentralised assembly systems with random yield and random demand

We study coordination of assembly systems with random supplier yields and random customer demand. We propose four contracts which are combinations of well-known contracts in the literature and show that the contracts can coordinate the chain under forced compliance. Our contracts have less payment schemes than the existing contracts given for coordination of assembly systems in the literature. We show that arbitrary profit allocation between the levels of the supply chain (the manufacturer or the suppliers) is possible. We also provide sufficient conditions which enable arbitrary profit allocation among the suppliers and illustrate the profit allocation with numerical examples.     

Supply management in assembly systems with random yield and random demand

In this paper, we consider an assembly system where a firm faces random demand for a finished product which is assembled using two critical components. The components are procured from the suppliers who, due to production yield losses, deliver a random fraction of the order quantity. We formulate the exact cost function where the decision variables are the target level of finished products to assemble, and the order quantity of the components from the suppliers. Since the exact cost function is analytically complex to solve, we introduce a modified cost function and derive bounds on the difference in the objective function values. Using the modified cost function, we determine the combined component ordering and production (assembly) decisions for the firm. The benefit of coordinating ordering and assembly decisions is numerically demonstrated by comparing the results with two heuristic policies commonly used in practice. In an extension to the model, we consider the case when the firm has the added option of ordering both the components in a set from a joint supplier. First, we consider the case when the joint supplier is reliable in delivery and obtain dominance conditions on the suppliers to be chosen. The maximum price a firm would be willing to pay to ensure reliable supply of components is determined. Later, we consider the uncertainty in the deliveries from the joint supplier and determine conditions under which there is no diversification, that is, either the individual suppliers are used, or the joint supplier is used, but never both.     

Joint production and maintenance planning with machine deterioration and random yield

Production, yield and maintenance are three key components for sustaining the competitiveness of a manufacturing firm. In this paper, we investigate a joint production and maintenance planning problem in a periodic review environment subject to stochastic demand and random yields. The manufacturing system deteriorates from period to period according to a discrete-time Markov chain. The objective is to find an integrated lot sizing and maintenance policy for the system such that the aggregate cost associated with production, holding, backlogging and maintenance is minimised. We formulate this integrated planning problem as a Markov decision process and analyse the structural properties of the optimal policies. We prove that the optimal production and the maintenance policies both exhibit a control limit structure and show that the solution to the finite-horizon problems converges to that of the infinite-horizon problem.     

A production scheduling problem with uncertain sequence-dependent set-up times and random yield

A scheduling problem in a real production line with uncertain sequence-dependent set-up times and a random yield is considered. The production line can produce multiple product types as production lots, each of which is composed of a number of products of the same product type. To changeover product types, a sequence-dependent set-up operation should be performed, and only the lower and upper bounds are known for the sequence-dependent set-up times. Moreover, the processing time to produce the required number of product for each production lot is uncertain due to the random yield. For the objective of minimising the average tardy probability of given production lots, a systematic approximation scheme to estimate tardy probabilities of lots in any given production sequence is developed by taking not only the uncertainties but also the computational efficiency into account. As practical solution approaches, a simulated annealing and a discrete particle swarm optimisation algorithms using the approximation scheme are developed, and their performance are evaluated by computational experiments. Since there has been no research on the scheduling problems with uncertain sequence-dependent set-up times and random yield, the authors expect this research will make an excellent contribution to develop practical scheduling methodologies in uncertain scheduling environments.     

Computational imaging systems: joint design and end-to-end optimality

A framework is proposed for optimal joint design of the optical and reconstruction filters in a computational imaging system. First, a technique for the design of a physically unconstrained system is proposed whose performance serves as a universal bound on any realistic computational imaging system. Increasing levels of constraints are then imposed to emulate a physically realizable optical filter. The proposed design employs a generalized Benders' decomposition method to yield multiple globally optimal solutions to the nonconvex optimization problem. Structured, closed-form solutions for the design of observation and reconstruction filters, in terms of the system input and noise autocorrelation matrices, are presented. Numerical comparison with a state-of-the-art optical system shows the advantage of joint optimization and concurrent design.     

Publisher Correction: Approaches for periodic inventory control under random production yield and fixed setup cost

OR Spectrum - In the original version of the article, operator symbols “⌊   ⌋” “⌈   ⌉” have been inadvertently processed as square...     

Approaches for periodic inventory control under random production yield and fixed setup cost

OR Spectrum - In this paper, we study a multi-period inventory control problem with random demand and stochastically proportional production yield. The model includes nonzero processing lead time...     

Supply chain coordination by risk sharing contracts under random production yield and deterministic demand

From numerous contributions to literature we know that properly designed contracts can facilitate coordinated decision making of multiple actors in a supply chain (SC) so that efficiency losses for the whole SC can be avoided. In a newsvendor-type SC with stochastic demand it is well-known that the double marginalization effect hampers the simple wholesale price contract to achieve coordination. More complex contracts however can bring about coordination, especially those which enable appropriate sharing of risks between the actors. While the effectiveness of risk sharing contracts is well understood for SC situations with random demand and reliable supply, less is known about respective problems if demand is deterministic but supply is unreliable due to random production yield. This paper shows how in a buyer-supplier SC the distribution of risks affects the coordination of buyer’s ordering and supplier’s production decision in a basic random yield, deterministic demand setting. Both parties are exposed to risks of over-production or under-delivery, respectively, if a simple wholesale price contract is applied. The resulting risk distribution always impedes SC coordination. However, more sophisticated contract types which penalize or reward the supplier can change risk distribution so that SC coordination is possible under random yield. Additionally, it is proven that the wholesale price contract will guarantee SC coordination if the supplier has a second (emergency) procurement source that is more costly, but reliable. Moreover, it is shown that under wholesale price contracts it can be beneficial to utilize this emergency source even if it is unprofitable from a SC perspective. However, if such an emergency option is available to the buyer as opposed to the supplier, a wholesale price contract will not be able to coordinate the SC.     

Dynamic systems with random initial state

Summary A perturbation scheme is described to treat time variable cryptodeterministic systems. According to Moyal's degree of randomness criteria the method provides a complete stochastic characterization of the system response. Certain digital computational features, when the perturbation scheme is not applicable, are also outlined. For an assumed random initial state, the results are then applied to describe the transient flapping oscillations of a helicopter blade which in forward flight has periodically varying aerodynamic damping and spring parameters.     

Coordinating a three-layer supply chain with uncertain demand and random yield

The paper considers a three-layer supply chain involving one raw-material supplier, one manufacturer and one retailer. The market demand is assumed to be stochastic and productions at the raw-material supplier and manufacturer are subject to random yield. The centralised model is studied as the benchmark case. The decentralised model is solved and Nash equilibrium solutions are obtained. It is shown that buyback contract fails to coordinate such a supply chain. However, a composite contract framed combining buyback, and sales rebate and penalty contracts is shown to coordinate the supply chain. Numerical examples are provided to illustrate the developed models.     

Control of a manufacturing system with random product yield and downward substitutability

We consider a manufacturing system where the quality of the end product is uncertain and is graded into one of several quality levels after production. We assume stochastic demand for each quality level, stochastic production times, and random quality yields. We also assume downward substitutability (i.e., customers who require a given product will be satisfied by a higher quality product at the same price). The firm produces to stock and has the option to refuse satisfying customers even when it has items in stock. We formulate this problem as a Markov Decision Process in the context of a simple M/M/1 make-to-stock queue with multiple customer classes to gain insight into the following questions: (i) how does the firm decide when to produce more units (i.e., what is the optimal production policy?) and (ii) how does the firm decide when to accept/reject orders and when to satisfy customers demanding lower quality products using higher quality products? In the case of two product classes, we completely characterize the structure of the optimal production and acceptance/substitution policies. However, the structure of the optimal policy is complicated and we therefore develop a simple heuristic policy for any number of classes which performs very well. We finally extend our heuristic to the system where production occurs in batches of size of larger than one, the system where there is a setup cost for initiating production, and the case where processing time distribution is Erlang.     

Transient responses of dynamical systems with random uncertainties

A new approach is presented for modeling random uncertainties by a nonparametric model allowing transient responses of mechanical systems submitted to impulsive loads to be predicted in the context of linear structural dynamics. The probability model is deduced from the use of the entropy optimization principle whose available information involves the algebraic properties related to the generalized mass, damping and stiffness matrices which have to be positive-definite symmetric matrices, and the knowledge of these matrices for the mean reduced matrix model. An explicit construction and representation of the probability model have been obtained and are very well suited to algebraic calculus and to Monte Carlo numerical simulation in order to compute the transient responses of structures submitted to impulsive loads. Finally, a simple example is presented.     

Vehicle routing with compartments: applications, modelling and heuristics

Despite the vast amount of literature about vehicle routing problems, only very little attention has been paid to vehicles with compartments that allow transportation of inhomogeneous products on the same vehicle, but in different compartments. We motivate a general vehicle routing problem with compartments that is essential for several industries, like the distribution of food or petrol. We introduce a formal model, an integer program formulation and a benchmark suite of 200 instances. A solver suite of heuristic components is presented, which covers a broad range of alternative approaches for construction, local search, large neighbourhood search and meta-heuristics. The empirical results for the benchmark instances identify effective algorithmic setups as well as essential components for achieving high solution quality. In a comparison on 23 specific and combinatorially less complex instances taken from literature, our algorithm showed to be competitive.     

Comparison of Bertrand and Cournot competitions under random yield

We look at a Bertrand model in which each firm may be unreliable with random yield, so the total quantity brought into market is uncertain. Under mild conditions, the Bertrand model with random yield has a unique Nash equilibrium, in which the prices and production quantities are determined by each firm’s production cost and reliability. In the case of symmetric firms, we compare Bertrand competition with Cournot competition by numerical examples, and find that Bertrand competition yields lower prices and less profits than Cournot competition. Furthermore, in the case of symmetric firms with 0–1 yields, we explicitly show that Bertrand competition yields lower prices and less profits than Cournot competition, and the comparison between the quantities of Bertrand and Cournot competition is dependent on the value of reliability. When the reliability is high, Cournot competition yields less quantities than Bertrand competition. Otherwise, the other hand holds.     

Recursive linear control of order release to manufacturing cells with random yield

One-piece flow job shop production environments in high labor turnover environments are oftentimes characterized by late shipments and incomplete orders due to random and variable yield. The problem addressed in this paper is that of determining an order release policy for a one-piece flow prototype production line in order to meet demand in an environment subject to random and variable yield induced by high labor turnover. This paper is motivated by a problem encountered in a facility that produces prototype parts. The problem at hand can be denned as that of determining a lot size to release into the line lo minimize deviations from the demand (i.e., target batch quota) for single-piece flow production in an environment characterized by random and variable yield. The objective of this research was to investigate the utility of recursive linear control as a mechanism for releasing parts into a single-piece flow production cell, and to develop a control algorithm using a Kalman filter. The methodology is evaluated via simulation using actual demand and yield data simulated from a distribution fit from historical data. Order release strategy and yield were found to be the dominant variables for complete and on-time orders without excess and shortages, and linear recursive control was found to be effective for tracking, monitoring and adjusting the release of parts into a single-piece flow job shop in an environment characterized by random and variable yield.     

On the optimality of exhaustive service policies in multiclass queueing systems with modulated arrivals and switchovers

Consider a single-server multiclass queueing system withK classes where the individual queues are fed byK-correlated interrupted Poisson streams generated in the states of aK-state stationary modulating Markov chain. The service times for all the classes are drawn independently from the same distribution. There is a setup time (and/or a setup cost) incurred whenever the server switches from one queue to another. It is required to minimize the sum of discounted inventory and setup costs over an infinite horizon. We provide sufficient conditions under which exhaustive service policies are optimal. We then present some simulation results for a two-class queueing system to show that exhaustive, threshold policies outperform non-exhaustive policies. This research was supported in part by the Office of Naval Research and the Department of Science and Technology grant N00014-93-1017.     

Optimal acquisition decision in a remanufacturing system with partial random yield information

When making decisions to acquire used products or components (cores), a remanufacturer faces limited information on the quality or proportional yield of cores during the recovery process. In this paper, we propose and analyse a robust optimisation model for studying the remanufacturing decision problem with partial random yield information, that is, when the quality information of cores is partly unknown in a remanufacturing system. Regarding the impacts of unknown yield information, we only require the support and mean of the proportional yield rather than the true distributions. The closed-form solutions of acquisition quantities are derived based on the minimax regret approach. In addition, to validate the effectiveness of the analytical results, particularly the acquisition of yield information, numerical experiments are designed and implemented using (1) the support and mean of the proportional yield based on the manufacturer’s knowledge and (2) a sampling inspection to evaluate the performance of the robust optimisation approach, the benchmark, and the naïve approach. We observe that the minimax regret approach slightly underperforms compared to the benchmark but performs much better than the naïve approach. As an acceptable choice, this approach is less complicated and extremely easy to implement to meet the needs of practical situations based on its robust closed-form solutions.