Characterizing the optimal allocation of storage space in production line systems with variable processing times

We consider the optimal allocation of buffer storage spaces in unpaced production lines with variable processing times. It is known that for a fixed total number of buffer spaces, the production rate can often be improved by deliberately unbalancing the buffer allocations in an inverted bowl pattern (the storage bowl phenomenon), with more storage space allocated to the internal stations than to the end stations. It has been hypothesized that if the total number of buffer spaces is also a decision variable, then for a reasonable cost model the optimal allocation would have one additional storage space at each of the internal stations. This paper uses a cost model to show that the optimal allocation is more complicated than this. For balanced lines, the inverted bowl pattern is typically optimal, but the bowl shape becomes more and more pronounced (in an absolute sense) with larger numbers of buffer spaces. However, the relative shape of the bowl stays fairly constant. However, if the workload is unbalanced, the buffer space pattern deviates from the bowl pattern by reducing the number of buffer spaces in buffers that are not adjacent to the bottleneck machine.     

A Directly-Coupled Two-Stage Unpaced Line

For a directly-coupled two-stage production system whose stochastic processing times may follow any distribution form, we present a simple procedure for estimating its average cycle time. We then demonstrate systematically the effect of the skewness and kurtosis of processing times on this average cycle time. Finally, we consider a version of the “unbalancing” problem that is more realistic than the classical Hillier-Boling version; we found that for a two-stage directly-coupled system, one should perfectly balance the mean and the skewness of the stages' processing times, but the variance and the fourth moment need not be balanced. Also, if the stages have unequal mean processing times, the station with larger mean should also have larger skewness.     

An Analysis of Scheduling Policies In Multiechelon Production Systems

Results of a simulation study of the economics of frequency of rescheduling Material Requirements Planning (MRP) systems are presented for a single-product, two-stage system in which demand is uncertain. The results indicate that for systems with moderate demand uncertainty, frequent rescheduling to maintain customer service may be uneconomical when compared with the alternative of more stable schedules in conjunction with safety stock. This result arises primarily because the cost of “emergency” production setups which occur when rescheduling is frequent exceeds the cost of safety stock required to “protect” stable schedules.     

A fast procedure for computing the total system cost of an appointment schedule for medical and kindred facilities

Scheduling outpatients and medical operation rooms has the following structure: Nusers are given appointment times to use a facility, the duration required by the facility to service each user is stochastic. The system incurs a “user idle cost” if a user arriving at the appointed time finds the facility still engaged by preceding users, while a “facility idle cost” is incurred if the facility becomes free before the next user arrives. We develop an accurate procedure to compute the expected total system costs for any given appointment schedule. Compared to earlier related procedures, ours is much faster and can handle larger problems as well as very general service-time distributions. We then show that this fast computation procedure enables one to determine easily the “lowest-cost appointment schedule” for any given “job” (i.e., “user”) sequence. This in turn will enable one to search for the optimal job sequence that has the best “lowest-cost appointment schedule”.     

Allocating resources to research and development projects in a competitive environment

Firms who are involved in R&D activities are often “racing” against competitors to become the lirst to attain the desired breakthrough. The goal might indeed be to "beat" the competitors in as many such R&D races as possible. However, when resources are limited, and competitors' budget allocation to these R&D activities unknown, the challenge becomes to devise a method of allocating R&D budgets to activites in a strategically “optimal” way. We model the decision problem of a firm wishing to allocate a fixed budget among several activities, so as to maximize the expected profit from the activities it captures. The probability of capturing an activity is an increasing function of one's allocation to it, and a decreasing function of the competitor's allocation. For a specific plausible capture-probability function, we find the optimal allocation between two activities conditional on the competitor's allocation (the “reaction curve”). Nash and Stackelberg equilibria for that model are then characterized. Wc also briefly explore the implications of more general, or different, capture-probability functions.     

Optimal threshold control for failure-prone tandem production systems

We consider the flow dynamics of a tandem production system formed by two failure-prone machines separated by a buffer stock. The production rates of the machines are regulated by a feedback mechanism which solves an associated optimal control problem with an average cost criterion. The cost structure penalizes both the entrance into and the sojourn on the buffer boundaries. The generic structure of the optimal control involves four buffer content thresholds. When the buffer content crosses these thresholds, the production rates are tuned to reduce the tendency to enter into the buffer boundaries. Using the fluid modelling framework, we obtain analytical results for the stationary buffer level distribution in the case where an operating machine can produce with, either a “nominal” or a “reduced” rate. In the stationary regime, the optimal positions of the buffer thresholds, the throughput and the average buffer content are presented.     

A mechanistic model for the effect of stress ratio on the LEFM fatigue crack growth behavior of metals and alloys—II. Crack-brittle materials

A recently proposed mechanistic model for the effect of stress ratio, R, on the LEFM (long) fatigue crack growth behavior of “crack-ductile” materials is extended here to explain and predict similar behavior under similar conditions of “crack-brittle” materials characterised by the presence of “static” modes of fatigue fracture in stages II and III. It is shown that in these materials the stage I behavior is similar, but the stages II and III behave differently from crack-ductile materials. Mechanism-based existence of two types of stage II curves characterised respectively by “ pure shear mode ” (SM-II) and “mixed-mode” (MM-II), both plotting linear but having different slopes, is introduced. It is shown that while stage SM-II is insensitive, stage MM-II is significantly sensitive to R, in the same material. Similar to stage I, another “ moving pivot-point ” exists at the transition from SM-II to MM-II, which slides down the “ master shear-curve ” with increasing R. Assuming a critical K_max for the initiation of static modes, a critical R for saturation of these modes, and Paris-type growth relations, a quantitative predictive model containing growth equations for stages SM-II and MM-II, has been developed. Stage III is discussed only qualitatively. Reasonably good agreement was found between predicted curves at selected R-values and a relatively large volume of experimental data for steels, Al-alloys and Ti-alloys. This simple, alternative model may be used for obtaining quick, fairly accurate and conservative estimates of R-influenced crack growth rates for design applications in preference to crack-closure which frequently requires elaborate and tedious experimental procedures.     

A Relational Approach to Organization Design

The paper criticizes the currently dominant view of organization forms as “discrete alternatives” and “coherent” set attributes, and proposes a more refined and micro-analytic view of organization forms as particular combinations of coordination mechanisms and rights allocations. This view is relevant for understanding and devising “new” forms and proposing solutions for governing the composite and fast changing systems of today. The view is “relational” as it offers a procedure for devising “superior” configurations as combinations—relations between organizational components—in a quasi-continuous space of possibilities. The approach is sustained by the quantitative methods of network analysis as applied to relations among firm's resources and activities. Theoretically, the approach revisits organization design, integrating classic organization theory tenets with the new inputs provided by organizational economics. Substantively, it is argued that a mix of much differentiated coordination mechanisms is usually superior to the codified, “packaged”, allegedly “coherent”, forms of organization. The procedure presented in the paper is applied to a field experiment in a medium size firm.1     

Role of base plate rotational speed in controlling spheroid size distribution and minimizing oversize particle formation during spheroid production by rotary processing

The occurrence of material adhesion and formation of oversize particles in the product yield during one-pot spheroid production by rotary processing leads to a less predictable process and a decrease in the usable portion of the total product yield obtained from each production run. The use of variable speeds of the rotating frictional base plate during the spheronization run was investigated for achieving optimal spheroid production. When the base plate speed was increased during liquid addition, the greater centrifugal forces generated improved liquid distribution and the mixing of the moist powder mass, resulting in a decrease in the amount of oversize particles formed. When the base plate was maintained at a high speed throughout the run, the amount of oversize particles and mean spheroid size increased, and a greater “between batch” mean spheroid size variability was also observed. The findings showed that, when higher speeds were used, the residence time must be adjusted accordingly to avoid excessive coalescence and growth while maintaining even liquid distribution. A “low-high-low” speed variation during rotary processing may be used to produce spheroids with a narrow size distribution and with a minimal amount of oversize particles in the total product yield.     

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.     

THE OPTIMALITY OF THE “CUT ACROSS THE BOARD” RULE APPLIED TO AN INVENTORY MODEL

A common procedure in budget allocation is to let the different entities of an organization determine their optimal budgets. Once the individual requests are received, they are then cut by a common factor, as necessary, so that a global constraint is satisfied. We refer to this procedure as the “cut across the board” rule. In general, this method will not result in a globally optimal solution. In this paper we identify conditions that assure the global optimality of die “cut (or expand) across the board” rule. We specifically focus on a constrained multi-item inventory model and generalize results of Rosenblatt [10] and Plossl and Wight [8]. In addition, we briefly discuss applicability of the results to other areas.     

ECONOMIC PRODUCTION QUOTAS FOR PULL MANUFACTURING SYSTEMS

We consider the problem of using “safety capacity” to ensure due date integrity in a pull manufacturing system and quantify the basic tradeoff between lost revenue opportunity and overtime costs. In this context, we address the question of when it is economically attractive to use “under capacity scheduling” and the problem of setting economic production quotas.

We develop four models for addressing the quota setting problem. The first three assume that quota shortfalls cannot be carried over to the next regular time production period. Models 1 and 3 assume that these shortages are made up on overtime and incur fixed or fixed plus variable costs. Model 2 does not use a capacity buffer and treats shortages as lost sales. Finally, Model 4 assumes that shortages can be backlogged to the next regular time production period at a cost. For this model, we compute both an optimal quota and an overtime “trigger,” which represents the minimum shortage for which overtime is used. We give computational results that illustrate and contrast the various models.     

Centering of the ion trajectory in the cyclotron

In this paper we present the theory of the horizontal motion ions through the acceleration gap in the case of a static magnetic field and time-varying electric field. It also describes the motion of the center of the ion trajectory through the acceleration gap and also during the acceleration process. The result also describes analytically the angle through which the ion passed (so called “flying angle”) between two acceleration gaps. That angle can be measured from the center of the ion trajectory or from the center of the cyclotron. The analysis shows that the “flying angle” of the ions measured in these two reference systems is not same. Namely, the “flying angle” of the ion measured from the center of its trajectory is bigger than in the case when the “flying angle” is measured from the center of the cyclotron. It shows that difference between “flying angle” in these two reference systems becomes less and less during acceleration process.     

Heuristic Programming in Spatial System Design

A link is needed to transform and to demonstrate the methodology of heuristic programming to the environment of spatial systems design. A class of problems is proposed which appears to be particularly suitable for this purpose. These problems relate to complex decisions in which the allocation and use of space is a critical dimension. This paper describes a game which may be viewed as an abstraction of real systems involving the packing of smaller items into a larger space; i.e., problems somewhat similar to the knapsack problem. The game has been invented as a means of focusing the attention of student designers on “real” games as opposed to parlor games. A computer implementation of a space game is described which provides for the addition and testing of subroutines incorporating heuristics for making decisions in design problems related to space.     

OPTIMAL BURN-IN SIMULATION ON HIGHLY INTEGRATED CIRCUIT SYSTEMS

Bum-in, a screening technique to improve product reliability, is especially useful for highly integrated circuit systems. But, in most applications, the resulting systems reliability after burn-in is worse than what has been forecasted, because of “incompatibility” not only among components but also among different subsystems and at the system level. To deal with this phenomenon, we present a simulation method to compensate for the lack of field data. Also, a stress-strength model is implemented using weighted factors and a model based on nonlinear programming theory is designed to find the optimal burn-in policy that satisfies the reliability requirement and cost restriction. The program presented here can serve as an “IC Information Query System” for system designers to consider at the design stage.     

Supply chain capacity and outsourcing decisions: the dynamic interplay of demand and supply uncertainty

We study the interplay of demand and supply uncertainty in capacity and outsourcing decisions in multi-stage supply chains. We consider a firm's investment in two stages of a supply chain (Stage 1 models the “core” activities of the firm, while Stage 2 are the “non-core” activities). The firm invests in these two stages in order to maximize the multi-period, discounted profit. We consider how non-stationary stochastic demand affects the outsourcing decisions. We also consider how investment levels are affected by non-stationary stochastic supply when the market responds to the firm's investments. We characterize the optimal capacity investment decisions Tor the single- and multi-period versions of our model and focus on how changes in supply and demand uncertainly affect the extent of outsourcing. We find that as the responsiveness of the market to investments made by the firm increases, the reliance on outsourcing generally increases. While greater supply and greater demand have the expected effect on investments, decreases in variability are not as straightforward. Greater supply uncertainty increases the need for vertical integration while greater demand uncertainty increases the reliance on outsourcing. In the multi-period model, we find that the nature of adjustments in capacity based on changes in demand or supply follows from the comparative statics of the single-period model, although whether outsourcing increases or decreases depends on the costs of adjusting capacity.     

Analytical Results for Miniload Throughput and the Distribution of Dual Command Travel Time

We determine the throughput, the maximum rate at which a miniload automated storage and retrieval system can process requests, as a'function of the dimension of the storage racks, the speed of the s/r machine and the speed of die picker. As a byproduct, we determine the distribution function of me travel time for a storage/retrieval machine that stores one container and retrieves another container (“dual command cycle”) before returning to the I/O point. Our emphasis is on obtaining closed-form, computable expressions.     

Fractal properties of percolating film structures

We simulate nucleation and growth processes of thin films on the basis of the so-called rate equation approach allowing “atoms” to diffuse and rearrange whereby enhancing their co-ordination number. The resulting percolating structures are different from those obtained by the “pure” percolation model where “atomic diffusion” is not taken into account. However, the fractal properties for p = p_c are the same as for the percolation model with the fractal dimension of d_f = 1.896 and for random walks of d_w = 2.87. Moreover, d_f and d_w are independent on the diffusion time we choose for our simulations.     

Strategic Allocation of Inspection Effort In A Serial, Multi-Product Production System

For a multi-stage production system, optimal location of inspection activities is an important consideration in minimizing the inspection-related and salvage costs. Set-up and inventory carrying costs also become important factors when several products are produced on the same line due to the product changeovers involved.

In this paper we discuss the effect of these additional costs (set-up and inventory carrying) on the inspection strategy, i.e., “all or none” versus partial inspection. We suggest a shortest path heuristic to determine the strategic location of inspection activities and the production lot sizes.     

A dynamic measure of order in structural glasses

Although some patterns of physical behavior are common in the glass transition and in the properties of supercooled liquids and glasses (characteristic viscoelasticity, temperature dependence of viscosity and relaxation times, property evolution through “physical aging”, difficulties in performing equilibrium measurements or simulations, etc.), it is difficult to arrive at a definition of the glass transition which distinguishes it from other phenomena exhibiting similar features. The present paper addresses this problem by defining a dynamical measure of order involving the average “shape” of particle trajectories in supercooled liquids. This dynamic order parameter should provide a measure of “closeness” to the glass transition and some indirect insights into the physical nature of supercooled liquids and glasses. Arguments are given that the proposed dynamic measure of order [“generalized capacity”, C(T)] is related to the temperature-dependent “effective hydrodynamic radius” R_H(T) measured in supercooled liquids and model numerical calculations are given to support this view. Some consequences of the intermittent particle motion at low temperatures for stress relaxation are also discussed.