Optimal batch ordering policies for assembly systems with guaranteed service

For a supply chain modelled as a multi-echelon inventory system, effective management of its inventory at each stock is critical to reduce inventory costs while assuring a given service level to customers. In our previous work, we used the guaranteed-service approach (GSA) to design optimal echelon batch ordering policies for continuous-review serial systems with Poisson customer demand and fixed order costs. The approach assumes that the final customer demand is bounded and each stock has a guaranteed service time in the sense that the demand of its downstream stock can always be satisfied in the service time. This paper extends this work by considering more general assembly systems. We first derive an analytical expression for the total cost of the system in the long run. The problem of finding optimal echelon batch ordering policies for the system can then be decomposed into two independent sub-problems: order size decision sub-problem and reorder point decision sub-problem. We develop efficient dynamic programming algorithms for the two sub-problems. Numerical experiments on randomly generated instances show the effectiveness of the proposed approach.     

Evaluating assembly sequences for automatic assembly systems

Selecting the assembly sequence and associated automatic assembly stations necessary to assemble a candidate product design is a critical step in the life cycle of a product. We present a method that determines the best sequence and set of stations using cost and performance measures. The method uses a multi-echelon optimization procedure based on simulated annealing. We show how simulated annealing can be used for such problems and present examples in which we determine the optimal assembly sequence for a product in an automated manufacturing environment.     

Process-oriented tolerancing for multi-station assembly systems

In multi-station manufacturing systems, the quality of final products is significantly affected by both product design as well as process variables. Historically, however, tolerance research has primarily focused on allocating tolerances based on the product design characteristics of each component. Currently, there are no analytical approaches to optimally allocate tolerances to integrate product and process variables in multi-station manufacturing processes at minimum costs. The concept of process-oriented tolerancing expands the current tolerancing practices, which bound errors related to product variables, to explicitly include process variables. The resulting methodology extends the concept of “part interchangeability” into “process interchangeability,” which is critical due to increasing requirements related to the selection of suppliers and benchmarking. The proposed methodology is based on the development and integration of three models: (i) the tolerance-variation relation; (ii) variation propagation; and (iii) process degradation. The tolerance-variation model is based on a pin-hole fixture mechanism in multi-station assembly processes. The variation propagation model utilizes a state space representation but uses a station index instead of a time index. Dynamic process effects such as tool wear are also incorporated into the framework of process-oriented tolerancing, which provides the capability to design tolerances for the whole life-cycle of a production system. The tolerances of process variables are optimally allocated through solving a nonlinear constrained optimization problem. An industry case study is used to illustrate the proposed approach.     

Setting procurement safety lead-times for assembly systems

This paper describes a practical method for setting safety lead-times for purchased components in assembly systems with uncertainty in the supply process. The approach is specifically designed to be used in an MRP procurement environment. A two-stage production model in which suppliers were uncapacitated with stochastic lead times was developed. Then, a combinatorial optimization method that took advantage of structural properties was developed to produce an optimal integer solution of safety lead-times. In addition to yielding a practical lead-time setting tool, the model led to some interesting policy insights: (1) the flexibility achieved by bringing parts in early may have value even in situations with ideal suppliers; (2) purchasing components in batches offers some of the same protection as does safety lead time, but is less precise and subsequently more expensive; and (3) ignoring the complicating issues of MRP procurement results in far from optimal results.     

Optimal major and minimal maintenance policies for deteriorating systems

We present a maintenance model for a multi-state semi-Markovian deteriorating system. Our model allows one of three maintenance decisions (do-nothing, minimal maintenance or replacement) to be taken at each state of the system. We use control limit policy and the policy-iteration algorithm to find the optimal maintenance policies that minimizes the expected long-run cost rate of the system. Numerical examples are given to illustrate the proposed policies.     

Buffering unbalanced assembly systems

Many assembly systems are required to hold minimal work-in-process inventories because of space or capital limitations. Unfortunately, in the presence of variable processing times, output from an assembly line may be severely restricted if no work-in-process inventory is held. Thus, assembly lines often should be designed to have minimal, but not zero, buffer capacity. In this paper we address the issue of how one should optimally deploy limited buffer capacity in unbalanced assembly systems, and we find that the answer is sometimes counterintuitive. We study simple asynchronous assembly systems with random processing times and develop simple heuristic rules that can be used to improve existing operations and to support line designers who are faced with increasingly rapid cycles of new product introduction. We apply these heuristics to several larger systems and discover that they perform quite well.     

Buffering unbalanced assembly systems

Many assembly systems are required to hold minimal work-in-process inventories because of space or capital limitations. Unfortunately, in the presence of variable processing times, output from an assembly line may be severely restricted if no work-in-process inventory is held. Thus, assembly lines often should be designed to have minimal, but not zero, buffer capacity. In this paper we address the issue of how one should optimally deploy limited buffer capacity in unbalanced assembly systems, and we find that the answer is sometimes counterintuitive. We study simple asynchronous assembly systems with random processing times and develop simple heuristic rules that can be used to improve existing operations and to support line designers who are faced with increasingly rapid cycles of new product introduction. We apply these heuristics to several larger systems and discover that they perform quite well.     

Aggregate line capacity design for PWB assembly systems

In a multi-product, flexible manufacturing environment, line capacity of printed wiring board (PWB) assembly systems may need to be adjusted at the beginning of each aggregate planning period because of demand fluctuation over multiple periods. A model of production planning and equipment changeover scheduling at the aggregate level is developed. In the described model, three kinds of equipment changeover methods, i.e. adding machine, removing machine and transferring machine, are involved. Because the model is a large-scale integer programming problem, it cannot be solved directly. A solution approach is developed, which first solves a recursive linear programming problem to obtain a rough set of machines to be added and a rough set of machines to be removed for each machine line in each period, then applies a branch and bound heuristic to the rough sets to obtain near-optimal solutions to the equipment changeover scheduling problem. Computational studies show the financial benefit both on capital cost and equipment changeover costs.     

Stage due date planning for multistage assembly systems

Coordinating due dates of operations throughout all stages of manufacturing and assembly is a problem especially for complex product structures with uncertainties in process times. A recursive procedure is described to estimate distributions of completion times for each operation. Stage due dates are then calculated to meet specified service targets. Compared with plans from existing heuristic methods, there are considerable improvements in meeting service targets and reducing costs. Simulations demonstrate that the method is effective for complex assemblies produced in low volumes by capital goods companies.     

A methodology for the selection of assembly systems

The design of an assembly system for a particular product is a complex engineering effort involving many interrelated decisions. The wide range of alternative system configurations makes a detailed design of each alternative too expensive and time-consuming. In this work a methodology is developed which helps the decision maker by ranking possible alternatives according to ‘subjective’ cost/ benefit criteria.     

On sequencing policies for unit-load automated storage and retrieval systems

Automated Storage and Retrieval System (AS/RS) performance highly depends on the characteristics of the mechanical equipment. However, once the system has been physically implemented, achieving its maximum efficiency depends on the way the system is operated. This paper shows that request sequencing (i.e. planning the order in which storage and retrieval requests are performed) is of paramount importance in AS/RS performance. This paper reviews and adapts the most popular storage and sequencing policies to dynamic contexts, and then it proposes a ‘sequencing mathematical model’ (SMM) to simultaneously solve the sequencing and storage location problems. Extensive computational results based on a thorough simulation experiment plan confirm that performing the requests in the right sequence can have a positive impact on AS/RS performance. Our results show that the proposed SMM regularly outperforms other methods. When used in a dynamic context, the proposed SMM may yield up to a 25% reduction in average travel-time compared to the situation where a no-sequencing method is applied.     

Optimum condition-based maintenance policies for deteriorating systems with partial information

Systems are considered which deteriorate as time goes on and whose conditions can be observed. The optimum maintenance policy with respect to cost is determined, based on a continuous deterioration process, by formulating the decision process as a discrete Markov decision problem. Examples from the field of civil engineering are given. The relation between the type of deterioration and condition-based optimum inspection intervals, optimum repair level, minimum average maintenance costs and mean time to repair is shown, using some numerical results.     

In situ Interferometric alignment systems for the assembly of microchannel relay systems

An interferometric alignment technique developed for the assembly of microchannel relay systems is described. The method uses pairs of diffractive lenslets that are arranged to form compact in situ interferometers. The relative transverse, longitudinal, and rotational alignment of the two lenslet arrays can be quantitatively determined from the resulting interference patterns. The theoretical analysis is compared with the experimental performance.     

Economic control and inspection policies for high-speed unreliable production systems

In this paper, we consider a high-speed production process, which produces defects at a known rate while in control. When the process goes out of control, it produces defects at a higher rate. In this study, we revisit the role of the distribution of the process in-control time when managing such systems. Specifically, we focus on two management schemes, a control policy and an inspection policy. In the control policy, when the number of defects produced reaches a threshold, the process is stopped and inspected. In contrast, in the inspection policy, the process is stopped and inspected periodically. We derive the operating characteristics of the system and devise schemes for finding the optimal policy parameters for each policy. We also investigate the behavior of the optimal policy parameters, compare the performances of the control and inspection policies and identify the environments in which each of these policies out performs the other one using a numerical experiment.     

Dynamic release policies for software systems with a reliability constraint

We discuss the optimal release problem of computer software. A conditional non-homogeneous Poisson process model is used lo describe the software reliability growth behavior. By formulating with Markov decision programming, we show that, to minimize the total discounted cost, the optimal release policy is threshold-type, which is easy to obtain and to implement. It is then extended to the model with a constraint on the system reliability, for which a similar threshold-type control policy is proved to be optimal too.     

Maintenance policies for systems with condition monitoring and obvious failures

We investigate a maintenance optimization problem with condition monitoring, which allows the decision maker to observe some wear-related variable throughout a system's lifetime to more accurately determine its degree of deterioration. Specifically, we examine the problem of adaptively scheduling observations (both perfect and imperfect) and preventive maintenance actions for a multistate, Markovian deterioration system with obvious failures, such that the long-run average-cost per unit time is minimized. We establish structural properties of the perfect observation-information problem and adjust them for heuristic use in the imperfect observation-information problem. We model both cases as partially observed Markov decision processes and provide numerical examples of optimal and heuristic solutions for both cases.     

Comparison and evaluation of lot-to-order matching policies for a semiconductor assembly and test facility

This paper is motivated by the problem of assigning semiconductor fabrication wafer lots to customer orders of various sizes. The goal of this research is to develop a method for deciding, on a given day, which orders to fill and the assignment of available lots to orders. This problem can be formulated as an integer program with a non-linear objective and non-linear constraints. Because of the complexity of this formulation, the problem is decomposed into two integer linear programs and solved in sequence by heuristic methods. In this paper, heuristic solutions are selected for the two subproblems and the performances of these heuristics are analysed in an experimental design using a representative data set. Based on this analysis, it is shown that the greedy heuristics selected perform significantly better than current practice. Finally, future research is discussed.     

Combining items for lot sizing in multi-level assembly systems

Multi-level lot sizing problems are difficult to solve optimally when the product structure contains more than a few items. This paper identifies conditions on the cost parameters which, when applicable, allow items to be combined for purpose of optimization, thereby reducing the size of the problem.     

Modelling and optimization of proof testing policies for safety instrumented systems

This paper introduces a new development for modelling the time-dependent probability of failure on demand of parallel architectures, and illustrates its application to multi-objective optimization of proof testing policies for safety instrumented systems. The model is based on the mean test cycle, which includes the different evaluation intervals that a module goes periodically through its time in service: test, repair and time between tests. The model is aimed at evaluating explicitly the effects of different test frequencies and strategies (i.e. simultaneous, sequential and staggered). It includes quantification of both detected and undetected failures, and puts special emphasis on the quantification of the contribution of the common cause failure to the system probability of failure on demand as an additional component. Subsequently, the paper presents the multi-objective optimization of proof testing policies with genetic algorithms, using this model for quantification of average probability of failure on demand as one of the objectives. The other two objectives are the system spurious trip rate and lifecycle cost. This permits balancing of the most important aspects of safety system implementation. The approach addresses the requirements of the standard IEC 61508. The overall methodology is illustrated through a practical application case of a protective system against high temperature and pressure of a chemical reactor.     

State-age-dependent maintenance policies for deteriorating systems with Erlang sojourn time distributions

This paper investigates state-age-dependent maintenance policies for multistate deteriorating systems with Erlang sojourn time distributions. Since Erlang distributions are serial combinations of exponential phases, the deteriorating process can be modeled by a multi-phase Markovian model and hence easily analyzed. Based on the Markovian model, the optimal phase-dependent inspection and replacement policy can be obtained by using a policy improvement algorithm. However, since phases are fictitious and can not be identified by inspections, two procedures are developed to construct state-age-dependent policies based on the optimal phase-dependent policy. The properties of the constructed state-age-dependent policies are further investigated and the performance of the policy is evaluated through a numerical example.