Optimal Production Levels Research Articles

Infinite Horizon Production Planning in Time-Varying Systems with Convex Production and Inventory Costs

We consider the planning of production over the infinite horizon in a system with time-varying convex production and inventory holding costs. This production lot size problem is frequently faced in industry where a forecast of future demand must be made and production is to be scheduled based on the forecast. Because forecasts of the future are costly and difficult to validate, a firm would like to minimize the number of periods into the future it needs to forecast in order to make an optimal production decision today. In this paper, we first prove that under very general conditions finite horizon versions of the problem exist that lead to an optimal production level at any decision epoch. In particular, we show it suffices for the first period infinite horizon production decision to solve for a horizon that exceeds the longest time interval over which it can prove profitable to carry inventory. We then develop a closed-form expression for computing such a horizon and provide a simple finite algorithm to recursively compute an infinite horizon optimal production schedule.

Design of multiproduct batch plants under demand uncertainty with staged capacity expansions

This paper addresses the staged capacity expansion of multiproduct batch plants operating in single product campaign (SPC) mode and in the presence of product demand uncertainty. This extends previous work by the authors on the design problem. Staged capacity expansions are modeled as additions of extra units of equal size at each stage at the end of each time period. The normality assumption is employed for the uncertain product demands. The problem formulation involves an inner stage which identifies the optimum production levels and an outer stage which establishes the design/capacity expansion decisions by maximizing the net present value (NPV) of the plant. This two-stage stochastic optimization problem for capacity expansion is equivalently recast as a deterministic mixed-integer nonlinear programming (MINLP) problem. Finally, the proposed formulation and solution strategy are illustrated with an example problem.

Canopy Dynamics, Light Interception, and Radiation Use Efficiency of Selected Loblolly Pine Families

Abstract Needlefall, aboveground net primary production (ANPP), canopy light interception and attenuation, and "radiation use efficiency" of five open-pollinated loblolly pine (Pinus taeda L.) families were investigated using 100-tree family block plots near Summerville, SC. Family variation in annual needlefall amounts was significant during the fourth (from 4796 to 6191 kg ha-1) and fifth growing seasons (from 4717 to 5721 kg ha-1); needlefall patterns for the poorest performing family were asynchronous from those of the others, with notably higher needlefall rates from April to July. Estimates of ANPP at age 4 yr varied by 16% (from 32.9 to 38.2 Mg ha-1) among families, and were generally commensurate with progeny test rankings based on height growth. The relationship between ANPP and leaf area index (LAI) was both significant and curvilinear, with an apparent optimum level of production (42.6 Mg ha-1) achieved at a LAI of about 13 (all-sided; February). The least productive families had the lowest mean LAI (e.g., 7.9), while the most productive families generally had higher levels of LAI (e.g., 13.6). Significant family differences in canopy light interception were present in every month sampled except June, when photosynthetically active radiation (PAR) interception exceeded 90% for all families. Light extinction coefficients (k) for February differed significantly among the five families, and ranged from 0.28 to 0.38; families with the largest LAIs generally had the lowest values of k and the highest levels of PAR interception. A strong linear relationship (r² = 0.74) was found between ANPP and intercepted PAR. Estimates of the dry matter:radiation quotient (ε "radiation use efficiency") differed significantly among families, and ranged from 1.33 g MJ-1 to 1.48 g MJ-1. Results of this study suggest that fundamental differences exist in production ecology among loblolly pine families, and that canopy-level characteristics such as LAI, PAR interception, and "radiation use efficiency" are important in conferring differential family performance. For. Sci. 44(1):64-72.

Regional Measures of Capacity Utilization in the 1980s

This paper presents a model to estimate the rate of capacity utilization (CU) in the manufacturing sector by state. Consistent measures of state-level CU rates have been unavailable since 1982. The lack of a capacity measure has hindered regional studies of capital formation, long-run output growth, and productivity growth. Our model employs a neoclassical approach to estimate CU. We estimate a model to determine the optimal level of production and compare it with the actual level in order to define our CU index. Our results show that states in the West North Central, South Atlantic, and Pacific census divisions tend to have a CU index consistently above the nation's average. On the other hand, states in the East North Central and West South Central census divisions tend to have a CU index below the nation's average.

Utilization of FecJ F gene in developing commercial sheep farming : Economic analysis

An increase of income per capita in Indonesia is not followed by an increase of numbers and quality of lambs stock. To meet he high demand both for domestic and international markets, sheep production should be elaborated commercially . The Research Institute for Animal Production, Bogor has been able to identify the segregation of FecJ F on Javanese sheep, which has large effect on ovulation rate and number of litters born. The study was purposed to analyse the economic value of using Fed gene and the crossing with St. Croix rams to obtain high number of lamb production as well as high pre-weaning growth rate . Sixty seven Garut ewes were used and classified into three classes of singles, twins and triplets or mom: lambs born . From each litter type, ewes were classified according to the breed of rams to be used . Gamt and St . Croix rams were used to represent small and large size of sires, respectively . The parameters observed were litter size, birth weight, sex, feed consumption, weaning weight and average daily gain . Lambs and ewes were weighed on biweekly and monthly basis, respectively. An increasing of input for single born ewes was not followed by dramatic increase in its body weight at weaning, which means that the optimum level of production was not achieved. This resulted a shortening of farmers income. However, for ewes having twins an increase of input was followed by significantly increased of production level . Therefore, the economic analysis model used for ewes that carry the Fed gene showed an increase of income of Rp.30,691 .50, and Rp.24,319.82, per ewe per period for St. Croix sires and Garut sires, respectively . Key words: Economic analysis, Fed gene, sheep

Antitumor effect induced by granulocyte/macrophage-colony-stimulating factor gene-modified tumor vaccination: comparison of adenovirus- and retrovirus-mediated genetic transduction.

Irradiated tumor cells genetically modified to secrete granulocyte/macrophage-colony-stimulating factor (GM-CSF tumor vaccine) are potent stimulators of systemic antitumor immunity. For the preparation of a GM-CSF gene-modified tumor vaccine, it is important to achieve efficient genetic transduction of tumor cells, leading to an appropriate expression of the induced gene. In this report, with a view to developing a protocol for an effective cancer vaccination therapy, we examined the vaccination efficacies of tumor cells secreting GM-CSF by either adenovirus- or retrovirus-mediated genetic transduction. By using an adenoviral vector, Adex1CAmGMCSF, a highly efficient gene delivery and a high-level expression of the GM-CSF gene were achieved. Unexpectedly, animal vaccination studies showed that the GM-CSF tumor vaccine transduced with the Adex1CAmGMCSF recombinant adenovirus (adenoviral GM-CSF tumor vaccine) was less efficacious than that transduced with the MFGmGMCSF recombinant retrovirus (retroviral GM-CSF tumor vaccine). The GM-CSF serum concentration attained by the adenoviral GM-CSF tumor vaccine was much higher than that obtained by the retroviral GM-CSF tumor vaccine. Our findings indicate that an optimal level of GM-CSF production is important for the tumor vaccine to elicit an adequate response in the host antitumor immunity.

Protein Expression in the Baculovirus System

AbstractInsect cell‐recombinant baculovirus co‐cultures offer a protein production system that complements microbial systems by providing recombinant proteins in soluble form and with most post‐translational modifications. Moreover, the large size of the viral genome enables cloning of large segments of DNA and consequent expression of complex protein aggregates. This unit describes methods associated with the large‐scale production of recombinant proteins in the baculovirus expression system. A method for large‐scale production of viral stocks is described and methods for titration of virus are provided (a plaque assay and an end‐point assay). Once viral stocks have been prepared and titered, a protocol for testing the virus in small‐scale cultures is provided to determine the kinetics of expression, which allows evaluation of various cell culture and infection conditions aimed at developing optimal levels of protein production (e.g., comparisons of different host cell lines, media, and environmental parameters). Support protocols provide instructions for preparing culture samples for protein analysis by SDS‐PAGE and discuss analytical methods for monitoring nutrient levels in cell culture fluids. Once optimal process parameters are identified, protocols describe production of the target protein on a large scale in fermentors using either regular batch production in bioreactors or a fed‐batch procedure of production in perfusion cultures. Techniques for harvesting cultures from bioreactors are also provided.

A multistage approach for production and workforce planning in long-cycle product environments

Abstract Aggregate production planning (APP) has been studied extensively for the past two decades. The APP problem, also called production and workforce scheduling, is to determine the optimal workforce and production level in each period of the planning horizon in order to satisfy demand forecasts for these periods. The advantages of the APP are low cost of data collection and computational cost of the running model; the accuracy of data; and, effective managerial understanding of the results. If the product of concern takes longer than one period, it is called a long-cycle product. Examples of long-cycle products are aircraft, ships, buildings and special machines. A detailed model incorporating dynamic productivity and long-cycle products considerations is presented to solve the problem of production and workforce planning. Using a multistage production system approach, a search technique is developed to solve this class of problems where the objective function is linear and some of the constraint coefficients are dynamically nonlinear. The model provides a better solution than an aggregate production planning model, often used to solve these problems.

A mechanism design approach to transfer pricing by the multinational firm

This paper is about how multinationals choose transfer prices and optimal production levels in the presence of differential corporate income tax rates and local ownership requirements. A key featrure of the model is that there is an asymmetric information problem between a parent and its foreign subsidiary. We examine the interaction between ownership structure, corporate taxes and bargaining power. Transfer prices induce underproduction compared to the full-information case when the parent has the bargaining ability. When bargaining is controlled by the subsidiary, overproduction obtains. The model is used to illustrate how governmental objectives can be accomplished without direct regulation of the transfer price.

A Production Decision Model for Time‐dependent Elastic Demand

The success of a manufacturing corporation mostly depends on its production decisions. The selection of production levels is a primary responsibility of management who should select production levels that maximize the discounted value of the cash‐flow stream (NPV) resulting from the production projects. As a result, the need to evaluate the cash‐flow stream for various production levels is becoming more frequent. Provides an explicit model for the economic evaluation of various attainable production levels. The model, developed in this study, under the condition of a time‐dependent elastic demand, for each year compares a series of gross incomes G, that results from the various attainable production amounts Q, with a corresponding series of minimum annual revenue requirements R. Based on these comparisons, it identifies the optimal production level and the unit selling price for a particular year where G‐R is a maximum and finally, based on the maximum G‐R values, it determines the NPV value. A computer program (written in PASCAL) is provided to implement the model on either a TI or IBM. The program is capable of displaying and printing the results. Because of the use of several levels of nesting, the top‐down programming technique is used in its design and implementation.

Production and work force planning in manufacturing systems for long-cycle products: A survey

Abstract The production and work force scheduling problem for long-cycle products is one of determining the optimal production and work force levels throughout the planning horizon for products requiring many months of effort prior to completion. If the product can be finished in the same period in which it is started, it is called a short-cycle product. Most repetitive manufacturing companies deal with short-cycle products. On the other hand, if it takes longer than one period to complete a product, it is called a long-cycle product. Examples of long-cycle products are aircraft, ships, buildings, and special machines. This paper presents a review of the studies on production planning for long-cycle products and points out the need for research incorporating the learning effect in this area.

An optimal investment and inventory policy

The relation between the optimal production level and the optimal investment in a flexible manufacturing machine will be the subject of this paper. The study concerns the production of N families of products on one production machine. The investment level in a particular production machine is assumed to depend on both the intra and inter family set-up times. The optimal production level will be shown to depend on the optimal investment choice made and as such on both the intra- and inter-family set-up times. The results show the necessity of coordination between several departments, as for instance the production planning department and financial department, of an organization. Moreover it will be argued that circumstances exist in which mathematical models can be used in a more qualitative level of analysis.

Ordering and Production Decisions with Supply Quality and Demand Uncertainty

In this paper, we solve a production planning problem that has a direct bearing on the cost to a facility of vendor quality and reliability. This solution is also an important first step in solving the multi-plant coordination problem. We consider a manufacturing facility with one critical raw material, and one or more products whose demand needs to be met. It is assumed that demand for finished goods and the arrival process for raw material are stochastic. We calculate simultaneously the optimal production level, and the raw material order quantity which minimize the total expected cost subject to capacity and release level constraints. The results obtained by our model (the integrated model) show that the production level should be no larger than the production level obtained by solving the traditional (nonintegrated) models, and that major savings are obtained by solving the integrated model. We are also able to characterize and evaluate the cost of reliable supplies of raw material. In addition we solve the above problem in the presence of capacity constraints. A procedure which allocates capacity to different products is presented.

Moral Hazard and Moral Imperative: Comment

In a recent article in this Journal, Wu and Colwell (1988) seek to describe how the optimal level of safety production chosen by an individual is determined. Their objective is to . . . handle questions of moral hazard, and moral imperative in a simpler and more heuristic manner than the previous literature (p. 101). The authors attempt to determine how the marginal benefit of safety production is impacted by various parameters for the cases of full and partial insurance coverage. The conditions under which the presence of insurance will lead to more safety production (moral imperative), and when it will lead to less safety production (moral hazard), are examined. While the questions explored by Wu and Colwell are of interest, many of their conclusions are incorrect, as several of their proofs contain a fundamental error. In particular, the discussion of partial insurance (section III of their paper) is fatally flawed, as the proofs of Propositions 1 and 2 are both invalid. Thus, the comparative statics results which follow (section IV of the paper) do not necessarily hold for the case of partial insurance coverage. Furthermore, a portion of their comparative statics results is also invalid for the case of full insurance coverage. The problem in their analysis occurs when equalities are incorrectly treated as identities. The mistake first appears in the proof of Proposition 1, which is contained in Appendix A (p. 116). The incorrect demonstration begins with equation A. 1, which is reproduced below using the authors' notation.

The contribution of efficient energy pricing to reducing carbon dioxide emissions

Carbon dioxide (CO 2) emissions from energy utilization are a major factor contributing to the greenhouse effect. Removing existing price distortions and imposing privately efficient energy pricing makes a substantial impact on energy demand. The estimated reduction in CO 2 emissions in the USA, China and India by adopting privately efficient electricity pricing is just less than the UK's total annual emissions of CO 2 from fossil fuel combustion. However, privately efficient pricing does not ensure the optimal social level of energy production that is necessary for averting the greenhouse effect. Further policy instruments and considerations need to be adhered to in order to attain this optimum level globally.

A demand-driven method for scheduling optimal smooth production levels

This paper is concerned with demand-driven production scheduling in a commercial environment where smoothed production plans generation over a rolling horizon is desirable as new observations of demand are received through time. Demands are assumed to be normally distributed and dependent on the previous observed levels. The method of chance constraint of Charnes and Cooper is extended to multi-product production planning with variable workforce, back-ordered inventory, and nonstationary stochastic demand process. Bayesian procedures for revising the chance constraints and several variants of linear-programming-based production planning models are presented. In all cases the proposed methodology ensures that demands are satisfied, at a given level of confidence, while achieving smooth production.

An efficient and simplified solution to the predesign problem of multiproduct plants

The operation of multiproduct batch plants at their optimal production capacity levels requires a careful selection among alternative feasible production lines, taking into account the specific characteristics of the plant itself and associated production constraints. This involves the proper design and sizing of equipment units at the predesign stage to obtain the final plant layout that allows the necessary flexibility to reach optimal production levels under most diverse conditions. An efficient optimization strategy based on gradient calculations has been devised which dramatically reduces the computing time required to achieve the solution, when compared with the best available heuristic procedures and deterministic nonlinear programming techniques. Test-cases are shown for different plant configurations, including both semicontinuous and batch equipment types, involving several products, where even some modifications on the production line are permissible. The retrofitting problem has also been contemplated. Test results corroborate the robustness of the proposed methodology and show relative greater efficiency when the number of products or equipment units increases considerably.

Application of time series analysis and modern control theory to the cement plant

Cement plant process is full of internal noise sources and feedback loops. Therefore, statistical approach is required to understand its dynamic characteristics. Time series analysis has been applied to some important subprocesses of a cement plant process. These are the vertical mill process, calcining process and clinker cooling process. Based on the AR models of these, a set of optimum controllers have been designed by modern control theory. Successful results of application are reported in this paper. A method of determining optimal production level is also discussed.

Does ideology matter?: Anecdotal experimental evidence on the voluntary provision of public goods

The paper reports the results of two controlled-market sessions in which voluntary contributions for the provision of a public good were solicited. The sessions were conducted in an environment comparable to the environment described by Isaac, McCue and Plott (1985) (hereafter, IMP). An important difference in one of the sessions was the use of participants believed a priori to be biased against free riding. Although the sessions do not precisely replicate the work of IMP, general tendencies found in IMP are obtained. When the production of public goods is required over a number of periods, the use of voluntary contributions as a mechanism for determining the level of production will not result in convergence to a socially optimal level of production. Individual rationality tends to dominate collective rationality. Free riding is an issue. The two sessions reported here, like the existing literature, also indicate that free riding is not complete. Finally, the results of one of the sessions are novel in that they are suggestive of the importance of ideology.

Moral Hazard and Moral Imperative

In a recent article in this Journal, Wu and Colwell 1988) seek to describe how the optimal level of safety production chosen by an individual is determined. Their objective is to . . . handle questions of moral hazard, and moral imperative in a simpler and more heuristic manner than the previous literature (p. 101). The authors attempt to determine how the marginal benefit of safety production is impacted by various parameters for the cases of full and partial insurance coverage. The conditions under which the presence of insurance will lead to more safety production (moral imperative), and when it will lead to less safety production (moral hazard), are examined. While the questions explored by Wu and Colwell are of interest, many of their conclusions are incorrect, as several of their proofs contain a fundamental error. In particular, the discussion of partial insurance (section Ill of their paper) is fatally flawed, as the proofs of Propositions 1 and 2 are both invalid. Thus, the comparative statics results which follow (section IV of the paper) do not necessarily hold for the case of partial insurance coverage. Furthermore, a portion of their comparative statics results is also invalid for the case of full insurance coverage. The problem in their analysis occurs when equalities are incorrectly treated as identities. The mistake first appears in the proof of Proposition 1, which is contained in Appendix A (p. 116). The incorrect demonstration begins with equation A.1, which is reproduced below using the authors' notation. p'(U[.sub.1] - U[.sub.o]) = [(1 - p)U[.sub.1]' + pUo'](1 - [alpha])L[pi]' The function U[.sub.o] represents utility in the event that a fixed loss (L) occurs, and thus can be expressed as U[.sub.o] = Uo[W - [alpha][pi](s)L - (1 - [alpha])L - C(s)], where W is initial wealth, a is the insurance coverage ratio, C(s) is the cost of safety production, 7r(s) is the price of insurance, and s is the amount of safety production. If a loss does not occur, utility is U[.sub.1] = U[.sub.1](W - [alpha][pi](s)L - C(s)). The probability of a loss (p) depends on the level of safety production, and is written as p = p(s). Wu and Colwell state that the above . . . equality implies that the derivatives of both sides of (A. 1) with respect to a are (p. I 1 6). Taking the derivative Wu and Colwell obtain equation A.2 (p. 116), which is repeated below. [Mathematical Expression Omitted] This equation is not correct. Both sides of equation A.1 depend on s, [alpha], L, and W, and for a particular vector (s, [alpha], L, W) the equality may hold. However, and this is the important point, equation A. I is not an identity, and it does not hold for all [alpha]. Therefore, it is wrong to claim that the derivative of the left-hand side with respect to a will be equal to the derivative of the right-hand side. …