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.     

Sequencing n Products Involving m Independent Jobs on m Machines

This article considers the problem of scheduling n products over m distinct machines. Every product consists of a set of jobs, each requiring a known processing time on a designated machine. There are no precedence constraints, and simultaneous processing of jobs requiring different machines within a product is allowed. The object of scheduling is to minimize a regular measure of performance associated with the products. It is shown that there exists an optimal schedule with the “no passing property.” Branch and bound routines are developed for finding the optimal solution for the two measures of performance: (1) total penalty cost; and (2) sum of product completion times. Comparisons between the optimal solution and solutions obtained using dispatching rules are given in the penalty cost case.     

On the uncertainties of decentralized controllers in a transfer production line

In this paper, an information theoretic approach is applied to analyze the performance of a decentralized control system. The control system plays the role of a correcting device which decreases the uncertainties associated with state variables of a production line by applying an appropriate “correcting signal” for each deviation from the target. In particular, a distributed feedback control policy is considered to govern a transfer production line, which consists of machines and buffers and processes a single part type in response to a stochastic demand. It is shown how the uncertainty of the demand propagates dynamically into the production system, causing uncertainties associated with buffer levels and machine production rates. The paper proposes upper estimates for these uncertainties as functions of the demand variance, parameters of the distributed controllers and some physical properties of the production line. The bounds are based on dynamic entropy measures of the system state and the control variables. Some practical implications into the area of decentralized controller design are proposed, an information-economical analysis is presented and a numerical study is performed.     

The Effect of the Coefficient of Variation of Operation Times on the Allocation of Storage Space in Production Line Systems

This paper studies the effect of the coefficient of variation of operation times on the optimal allocation of storage space in production line systems. The operation times at each station are modelled by a two-stage Coxian distribution. This work extends the results of our previous study of the storage allocation problem with exponentially distributed operation times. Interpreting Stage 1 of the two-stage Coxian distribution as the normal service for an item at a station and Stage 2 as down time at the station, our model can also be used to study the effect of breakdowns on the allocation of storage space in production line systems. The results show that the “bowl effect” whereby the center stations should be given preferential treatment becomes more pronounced with higher variability in the operation times. Another general conclusion is that the overall optimal storage allocation commonly follows a “storage bowl phenomenon” whereby the allocation of buffer storage space fits an inverted bowl pattern when the total storage space is also a decision variable     

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”.     

Tooling choices and product performance

One of the dilemmas that manufacturers face involves the tradeoff between the cost of maintaining a variety of production processes, and the cost of not having the ideal process for every product that they produce. This issue is continuing to become more of a problem as manufacturers are forced by market conditions to offer a wider selection of products. We study an instance of this problem in the manufacture of sheet metal parts. We model the problem of selecting and/or designing tools to punch holes in these parts. The cost of not having an “ideal process” is the cost of not having a tool that precisely matches a hole's design diameter. We consider both general “process deviation” costs as well as the Taguchi loss function. Solution procedures are provided for several versions of the problem.     

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.     

One-machine, N-product-type, continuous-time scheduling with a common due date: a polynomially solvable case

The paper analyzes a manufacturing system made up of one-machine which produces TV-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.     

An Empirical Evaluation of the “Entrapment” Procedure for Scheduling Jobs on Identical Machines

This work empirically evaluates the “entrapment” procedure used by Barnes and Brennan's branch-and-bound algorithm to minimize total cost of tardy jobs to be processed on identical machines. Using 25 problems taken from various known sources, it is shown that entrapment does not necessarily decrease computational time required to optimally solve such a problem.     

Economic Design And Control of Monitoring Mechanisms in Automated Production Systems

Monitoring production processes to assure product quality has been a major managerial and control problem. These processes are subject to shifts to “out-of-control” states, resulting in the production of defective items. Inspection as well as restoration capabilities are necessary to provide early detection and correction of these shifts in the process. This paper considers the costs of different policies for providing these detection and restoration capabilities. These policies amount to periodic or continuous inspection of the production process with perfect information, and continuous or periodic availability of maintenance facilities. The optimal operation of each policy is studied. Comparative analyses are conducted with different specifications of key parameters such as the rate of shift of the process and the cost of producing defective items. These analyses enable the derivation of the optimal policy when only ranges of the values of these parameters are known.     

On new types of non-crystalline metallic composite

The structure and mechanical properties of new types of non-crystalline metallic composites, namely “glass-quasi-crystal”, “glass-disclinated nanocrystal” and “quasi-crystal(-glass)-disclinated nanocrystal” composites are theoretically examined. In particular, a theoretical model is proposed which effectively describes the relationship between plastic deformation and the growth of the glassy phase in metallic “glass-quasi-crystal” composite materials. Here also basic features of both the structure and the mechanical properties of the “glass-disclinated nanocrystal” and “quasi-crystal(-glass)-disclinated nanocrystal” composites are theoretically examined. It is shown that such composites are characterized by a very high yield stress.     

Analysis of Excess Stock in Multiproduct Inventory Systems

A primary function of production management is the control of inventories. The typical manner of economic inventory control calls for a “pre-stocking” approach in which the focus is on the reorder quantities which should be put into inventory. A second manner of controlling inventories is what can be called a “post-stocking” analysis. Here the focus is on how much of the present inventory already in stock should be declared as surplus and disposed of. This paper describes the development and implementation of an analytical procedure for this second, excess inventory issue. The procedure is described in the context of an application to a General Motors carburetor assembly process in which product structure interactions play a significant role.     

The Single Period Stochastic Plant Layout Problem

In this paper we present an optimal solution procedure for the single period stochastic plant layout problem. The procedure only requires solving a “deterministic” from-to flow matrix. This “deterministic” matrix is a weighted-average of all from-to flow matrices. Since it may be difficult to estimate the probabilities of occurrence of the various states of nature, we developed a simulation model to test the robustness of our approach. For over 26,000 problems examined, the average error of using our approach was very small, only about one-sixth of one percent.     

Gamma Approximation for Preventive Maintenance Scheduling

This paper presents an approximation model for determining minimum cost preventive maintenance schedules where accurate failure data are not available except the “average” (mean) and the “typical” value (mode) of the component lifetime.     

A new analytical model about the relationship between nominal failure stresses and porosity for foamed metals under biaxial tension

Foamed metals have been widely used as various engineering materials, and their mechanical properties have also been drawing extensive attention. In the present paper, a new mechanical and analytical model is established for these materials with isotropic three-dimensional reticulated structure under biaxial tension, and the mathematical equation about biaxial nominal stresses is deduced for the biaxial tension at the beginning of failure of the porous body. With the relevant experiment, the relation formula is proved to be very effective. Different from the relevant theoretical system of Gibson and Ashby, the present mathematical relationship can be conveniently achieved from directly using the “beam theory” on this mechanical and analytical model. In addition, this relationship can be further expressed as the mathematical relationship among the nominal failure “deviatoric stress”, the nominal failure “average stress” and porosity, but the concepts of both the “deviatoric stress” and the “average stress” can appear just from the mathematical treatment.     

Combining cost-based and rule-based knowledge in complex resource allocation problems

A major challenge in the formulation of optimization models for large-scale, complex operational problems is that some data are impossible or uneconomical to collect, producing a cost model that suffers from incomplete information. As a result, even an optimal solution may be “wrong” in the sense that it is solving the wrong problem. In many operational settings, knowledgeable experts will already know, at least approximately, how a model should behave, and can express this knowledge in the form of low dimensional patterns: “high powered locomotives should pull intermodal trains” (because they need to move quickly) or “loaded C-141s should not be flown into Saudi Arabia” (for maintenance reasons). Unlike the literature on inverse optimization which uses observed actions to train the parameters of a cost model, we used exogenous patterns to guide the behavior of a model using a proximal point term that penalizes deviations from these patterns. Under the assumption that the patterns are derived from rational behaviors, we establish the conditions under which incorporating patterns will reduce actual costs rather than just the engineered costs. The effectiveness of the approach is demonstrated in a controlled, laboratory setting using data from a major railroad.     

A Flow-Through Dissolution Approach to In Vivo/In Vitro Correlation of Adinazolam Release from Sustained Release Formulations

A Copley^TM fraction collector and a Disotest^TM flow-through system were coupled to provide an automatic discrete sampling flow-through dissolution system for use both in the “open-loop” and “closed-loop” mode. The system was used to investigate the release characteristics of adinazolam in sustained release formulations using a pH 1.2 simulated gastric fluid (without enzymes) dissolution medium (USP XXI). These experimental formulations are designed to provide relatively slow to rapid drug release. The dissolution effluent was analysed off-line by reverse phase HPLC to determine the adinazolam concentration at programmed timed intervals. The differential dissolution profiles produced when the system is used in the “open-loop” configuration are more discriminating in describing the release characteristics of the formulations according to the relative release rates than the “closed-loop” cumulative profiles. Using the characteristic dissolution time parameter from the Weibull function, a better correlation with in vivo bioavailability data was achieved for the data from the system in the “open-loop” mode than when it was used in the “closed-loop” mode. In the “open-loop” mode the Weibull function characteristic dissolution time parameter yielded the best quantitative correlation with a correlation coefficient of 0.92 compared to a value of 0.85 for the “closed-loop” configuration     

A Markov Model for Quality Control Plan Selection

A Markov chain model is developed which provides a measure of the cost of using alternative plans to control the output quality of productive processes. Such a model provides a yardstick for selecting the “best” control plan structure for a given process. The model structure is explained by presenting the example of a two-state process controlled by a plan which executes corrective action on the first defective sampled.     

A New Approach to Aggregate Production Planning

This paper proposes a new framework for modelling aggregate production planning problems in which emphasis is placed upon offering the user the flexibility to specify (1) the production options to be employed, (2) the relationships among those options (some of which may be highly situation-specific), and (3) the relevant cost structure. The procedure offered for solving the problem embeds Bowmann's “transportation” approach to aggregate production planning into a large mixed integer programming framework.     

Microstructural investigations of reduced magnesium titanate spinels which have shown anomalous resistance behaviour

Samples from the reduced magnesium titanate spinel system (Mg_{1 + y}Ti_{2 − y}^x+O₄) have been examined using selected area electron diffraction (SAED) and high resolution electron microscopy (HREM) imaging. Unusual microstructural features are observed in samples in the region of the system (i.e., where x, the average Ti valency, lies between 3.26 < x < 3.33) where transitions to zero electrical resistance on cooling below 50 K are reported. These features do not occur in samples from outside this compositional range. Lamellar features with wavelengths up to 750 nm are observed, and associated electron diffraction patterns demonstrate streaking of diffraction spots around the direct beam. The presence of streaks, rather than divergent spots, indicates fanning of the structure across the lamellar boundaries and HREM images further indicate that interlamellar boundaries are coherent. Linear streaking parallel to 111 observed in some crystals may represent the same feature viewed perpendicular to a lamellar boundary. These observations are consistent with exsolution of a single high temperature phase to two co-existing spinels of slightly different compositions. The observation of coherent lamellar boundaries and streaking of electron diffraction spots are consistent with spinodal decomposition as the mechanism of exsolution.Fine-scale lamellar structures parallel to “111” are also observed, which are texturally distinct from those described above. Streaking of electron diffraction spots parallel to 110 may be associated with these features. These lamellae probably represent intimate spinel-spinelloid intergrowths, rather than ordering of cation vacancies or another process.

These microstructural features appear to relate to the critical resistivity transition, as they have only been observed in samples close to the compositions which have displayed such electrical behaviour. Similar studies on samples away from the region of interest fail to show these textures. A relationship between the solvus and the zero electrical resistance behaviour is inferred. In the simplest case, the zero electrical resistance material may represent a metastable homogeneous high temperature spinel from above the solvus; alternatively, the electrical behaviour may derive from the strained interlamellar boundaries. Fine-scale linear features parallel to “111”, often associated with the interlamellar boundaries, are interpreted as fine spinelloid domains; the electrical behaviour may also relate in some way to these features.

It should be noted that the presence of no single microstructural feature correlates directly with the occurrence of this behaviour, nor does the loss of any feature correlate with degradation; however, it is also clear that the microstructure is continually developing as the sample ages at room temperature. Different degradation rates in air and vacuum are explained in terms of the continuing exsolution being slowed by the development of spontaneous strain at interlamellar boundaries. Chemical attack by air releases interlamellar strain and allows exsolution to progress at full speed.