Total Cost Function Research Articles

Energy, economy, and ecological (3E)‐based performance evaluation of a steam cycle power plant through optimization investigation

AbstractEnergy, economy, and ecological (3E)‐based analysis of steam cycle power plant evaluated through multiobjective investigation. The Montazer Ghaem steam‐based power plant situated in Iran is considered for investigation. Cycle efficiency, total cost, and ecological function of steam power cycle are treated as the 3E objective in the analysis. Simultaneous optimization of this performance parameter is executed through a heat transfer search algorithm. Fifteen operating variables of the steam power cycle, which includes different pressure, temperature, and isentropic efficiency are considered during the 3E‐based optimization investigation. The dryness fraction of the exhaust stream and condensing temperature are operating constraints considered in the present investigation. The results are presented in the form of Pareto solutions. The results of the Pareto solution indicate that a 6.73% variation in cycle efficiency, 44.67% variation in total cost rate, and 15.63% variation in ecological function (ECF) are observed between extreme values of 3E objectives. The obtained optimum condition is compared with the present actual operating condition of the steam power cycle. Comparative results reveal 5.27% higher cycle efficiency with 15.53% higher ECF as compared to the actual running case. For identical total cost rate of the system, 4.65% higher cycle efficiency with 1.21% rise in ECF was observed as compared to actual running case. Further, the uncertainty propagation of the Pareto points is obtained with different uncertainty levels to identify the robustness of the solutions. Finally, the important operating variables are identified and their effects on the 3E objectives are also investigated.

Synthesizing affective virtual reality multicharacter experiences

AbstractThis article presents a methodology for automatically synthesizing a virtual population (pedestrians placed in a virtual environment) that impacts a user with a specified affective experience. The pipeline began by developing a dataset of behaviors that could be assigned to virtual characters. Next, an annotation phase assigned affective responses of participants to each character's behavior. The design considerations of our affective multicharacter virtual reality experience were then encoded to cost terms and assigned to a total cost function. This method allowed the developer to control the priority and the targets of the cost terms, and given the user inputs, our application could optimize the multicharacter experience using a Markov chain Monte Carlo method known as simulated annealing. A user study was conducted to investigate whether our method could synthesize virtual reality multicharacter experiences that affect participants in an expected way. The results of our study showed that the three different synthesized multicharacter experiences (low, medium, and high negative affect) were perceived as expected by participants; therefore, we argue that we can indeed automatically synthesize virtual reality multicharacter experiences that impact participants' affect levels in an expected way. Limitations and future research directions are discussed.

Economics of Potato Production for Autumn Season 2015-2016 (Baghdad Governorate as A Practical Case)

The research aimed at estimating the production function and the total cost function, as well as measuring the efficiency of resource use, technical, economic, price and cost efficiency. The study was based primarily on a simple random sample of (155) farmers in Baghdad governorate for the autumn season (2015-2016), The double logarithmic formula was the most suitable for the production function. The results of the resource efficiency criteria indicated that potato farmers were efficient in using resources (seed, phosphate fertilizer, human labor) and were inefficient in using irrigation and pesticides. While the cubic formula was more suitable for the total cost function according to the statistical, econometrical and economical tests, and from it we showed that the optimum size of production and size that maximize profit are (119.069, 143.398) ton consequently. Technical, economic and price efficiencies were estimated at (34.25933, 34.25937, 73.521)% consequently, while cost efficiency was estimated at (0.454), and the net farm income that achieved over all the sample less about (10380.741) thousand dinars than that achieved at optimal size. The research concluded that the quantity of seeds had the greatest impact on potato production and that there was waste in using the available resources, which led to actual production being less than optimum production. The research recommends that the related institutions should work to provide a good quality potato seeds to cover the needs of local farmers, from good sources in a timely manner and at the right price to increase the production and productivity of this important crop and reduce production costs. As well as the protection of the local producer by adopting price policies that grant best income of farmers.

Virtual reality game level layout design for real environment constraints

This paper presents an optimization-based approach for designing virtual reality game level layouts, based on the layout of a real environment. Our method starts by asking the user to define the shape of the real environment and the obstacles (e.g., furniture) located in it. Then, by representing a game level as an assembly of chunks and defining the game level layout design decisions in cost terms (mapping, fitting, variations, and accessibility) in a total cost function, our system automatically synthesizes a game level layout that fulfills the real environment layout and its constraints as well as the user-defined design decisions. To evaluate the proposed method, a user study was conducted. The results indicated that the proposed method: (1) enhanced the levels of presence; (2) enhanced the levels of involvement of participants in the virtual environment; and (3) reduced the fear of collision with the real environment and its constraints. Limitations and future research directions are also discussed.

Minmax common flow-allowance problems with convex resource allocation and position-dependent workloads

We study minmax due-date based on common flow-allowance assignment and scheduling problems on a single machine, and extend known results in scheduling theory by considering convex resource allocation. The total cost function of a given job consists of its earliness, tardiness and flow-allowance cost components. Thus, the common flow-allowance and the actual jobs’ processing times are decision variables, implying that the due-dates and actual processing times can be controlled by allocating additional resource to the job operations. Consequently, our goal is to optimize a cost function by seeking the optimal job sequence, the optimal job-dependent due-dates along with the actual processing times. In all addressed problems we aim to minimize the maximal cost among all the jobs subject to a constraint on the resource consumption. We start by analyzing and solving the problem with position-independent workloads and then proceed to position-dependent workloads. Finally, the results are generalized to the method of common due-window. For all studied problems closed form solutions are provided, leading to polynomial time solutions.

An integrated reliable five-level closed-loop supply chain with multi-stage products under quality control and green policies: generalised outer approximation with exact penalty

In this paper, we design and optimise an integrated five-level Supply Chain (SC), which contains a supplier, a producer, a wholesaler, multiple retailers, and a collector. Accordingly, a Closed-loop Supply Chain (CLSC) with multi-stage products is designed with respect to the green production principles and Quality Control (QC) policy under back-logged and lost sale types of the shortage. Levels cooperate with each other to make an Integrated Supply Chain (ISC) so that the total cost function is minimised and the total reliability function is maximised, simultaneously. The model is constrained by real stochastic constraints. The total inventory cost includes the ordering costs, holding costs, shortage costs, setup costs, production costs, screening costs, reworking costs, disposal costs, tax cost of GHG emissions, collection costs, and disassembling costs. The final objective is to optimise the number and volume of the stockpiles of the products. The integrated CLSC model is a hyper-scale Mixed Integer Nonlinear Programming (MINLP) model. In this regards, a Generalised Outer Approximation with Exact Penalty (GOA/EP) is presented to optimise the MINLP model of research based on decomposition principles, Outer Approximation (OA), and relaxation techniques. Numerical analyses revealed the excellent performance of the presented method for solving the hyper-scale MINLPs.

Sustainable optimal ordering quantity for non-instantaneous deteriorating items under joint replenishment with substitution and carbon emission

PurposeCarbon emission is a significant issue for the current business market and global warming. Nowadays, most countries have focused to reduce the environmental impact of business with durable financial benefits. The purpose of this study is to optimize the entire cost functions with carbon emission and to find the sustainable optimal ordering quantity for retailers.Design/methodology/approachThis paper illustrates a sustainable inventory model having a set of two non-instantaneous substitutable deteriorating items under joint replenishment with carbon emission. In this model demand and deterioration rate are considered as deterministic, constant and triangular fuzzy numbers. The objective is to find the optimal ordering quantity for retailers and to minimize the total cost function per unit time with carbon emission. The model is then solved with the help of Maple software.FindingsThis paper presents a solution method and also develop an algorithm to determine the order quantities which optimize the total cost function. A numerical experiment illustrates the improvement in optimal total cost of the inventory model with substitution over without substitution. The graphical results show the convexity of the cost function. Finally, sensitivity analysis is given to get the impact of parameters and validity of the model.Originality/valueThis study considers a set of two non-instantaneous substitutable deteriorating items under joint replenishment with carbon emission. From the literature review, in the authors’ knowledge no researcher has undergone this kind of study.

A Comprehensive Study of EOQ (Economic Order Quantity) System for Spoilage Commodities with Stock–Sensitive Demand and Trade Credits

Prior EOQ models under trade credits generally assumed that the demand of the commodities was either stable or purely dependent on the selling price. This paper develops an economic order control model of deteriorating commodities with inventory associated demand under different conditions. It is assumed that the permissible delay period is permitted till specific threshold. The comparative study of order quantity with threshold quantity is also discussed. Optimal solutions are obtained with the help of differential calculus and optimality condition. Numerical examples and sensitive analyses are provided to validate the optimal solution. It is also shown that the total cost function is U-shaped.

Effective inventory management using postponement strategy with fuzzy cost

In this article, we consider a two level supply chain to evaluate the impact of postponement strategy on the retailer. Here the cost parameters are fuzzified. Signed distance method is used to defuzzify and to obtain the estimation of the total cost in the fuzzy sense. The common variable production cost, common fixed cost and the common unit holding cost per unit time are assumed to be fuzzy in nature. Inventory models are formulated for postponement system and independent system such that the total average inventory cost function per unit time is minimized. Algorithms are given to derive the optimal solutions of the proposed model. Theoretical analysis and the computational procedure helps to study the impact of deterioration rate on the optimal inventory policies. A comparative study between the postponement system and independent system considering fuzzy costs is also made.

A reverse logistics inventory model with multiple production and remanufacturing batches under fuzzy environment

In the last few years, inventory modeling with reverse logistics has received more attention from both the academic world and industries. Most of the existing works in the literature believed that newly produced products and remanufactured products have the same quality. However, in many industries, customers do not consider remanufactured products as good as new ones. Therefore, this study develops a reverse logistics inventory model with multiple production and remanufacturing batches (cycles) under the fuzzy environment where the remanufactured products are of subordinate quality as compared to the newly produced products. As the precise estimation of inventory cost parameters such as holding cost, setup cost, etc. becomes often difficult; so these cost parameters are represented as triangular fuzzy numbers. Used products are purchased, screened and then suitable products are remanufactured. The production and remanufacturing rates are demand dependent. The main goal of this study is to obtain the optimal production and remanufacturing policy that minimizes the total cost per unit time of the proposed inventory system. The signed distance method is employed to defuzzify the total cost function. A numerical example is presented to demonstrate the developed model. Finally, sensitivity analysis is executed to study the impact of key parameters on the optimal solution.

Enhanced total generalized variation method based on moreau envelope

Image restoration with total generalized variation (TGV) regularization has been proved to be a creditable method and used broadly, but this method is imperfect in retaining image details. This paper proposes a non-convex and non-separable regularization term based on TGV enhancement, which can maintain the strict convexity of the total cost function and avoid the underestimation of the TGV method. The new regularization is obtained by subtracting the Moreau envelope of TGV from the TGV term, in which the former is defined by infimal convolution. To minimize the cost function, the proximal forward-backward splitting (FBS) algorithm is applied, and the alternating direction method of multipliers with adaptive parameter estimation (APE-ADMM), which avoids the drawbacks of FBS algorithm, is proposed by applying the variable splitting and the augment Lagrangian method (ALM). This proposed algorithm can update the regularization parameter adaptively. Experiments varify that the proposed method is more accurate in solution estimation than the other promoted ones, and the new ADMM algorithm with new regularization shows improved effects of image restoration.

Computation of Optimal Spacing and Density of Bus Rapid Transit Stations Using Evolutionary Algorithms

In this research, a feasible mechanism is developed to determine the optimum number of bus rapid transit (BRT) stations as well as their respective locations along the service corridor. To accomplish this, a mathematical model is developed and optimized by using three different evolutionary algorithms, namely particle swarm optimization (PSO), genetic algorithm (GA), and differential evolution (DE), and the results are compared. The total cost function is composed of two main costs namely the operator’s cost, i.e., related to costs on service provider’s end, and the user’s cost, i.e., related to costs on commuters’ end. A functional numerical example with the commuters’ demand is worked out by minimizing the cost function, which demonstrates the applicability of the framework. In our case study, PSO outclassed GA and DE on the basis of convergence rate. Since our work has proved the robustness of PSO as compared to GA and DE, we conducted our sensitivity analysis keeping PSO as our benchmark algorithm to study the influence of various parameters on the optimal cost. The computational experiments reveal that the optimal cost is substantially affected by the variations in the commuters’ demand, commuters’ walking speed, and value of the users’ access and in-vehicle time. On the contrary, the acceleration/deceleration delays at a bus station, bus operating cost, and headway have an inconsiderable impact on the optimal cost.

Effects of using non-conventional feedstuffs on the productivity and costs of egg farms in Ibadan, Nigeria

This study examines effects of privately producing layers mash by including such non-conventional feedstuff as cassava, brewers dried grain, etc on the productivity, cost and profit of poultry (eggs) farms. Primary data was collected from three categories of farms -12 "conventional feedstuff users" (CFU), 24 "non-conventional feedstuff users" (NCFU) and 10 Animal Care concentrate users" (ACCU) found in a sample survey of 46 private feed using farms in Egbeda and Lagelu Local Government area of Ibadan. Estimates of their production, total variable cost and profit functions obtained by ordinary least squares as well as analyses of variance conducted on their production and cost statistics revealed that no sufficient evidence exists to suggest that productivity levels differ across the three categories of farms, but NCFU significantly lower average cost and more profits per trm of eggs produced than the CFU. No sufficient evidence, however, exists to suggest that ACCU had any significantly different cost or profit per tray of eggs produced from those of CFU.

Robust analysis for data-driven model predictive control

Here the idea of data driven is introduced in model predictive control to establish our proposed data-driven model predictive control. Considering one first-order discrete time nonlinear dynamical system, the main essence of data driven means the actual output value in cost function for model predictive control is identified through input–output observed data in case of unknown but bounded noise and martingale difference sequence. After substituting the identified actual output in cost function, the total cost function in model predictive control is reformulated as its standard form, i.e. one quadratic program problem with input and output constraints. Then semidefinite relaxation scheme is used to derive a lower bound for its optimal value, and the robust counterpart of an uncertain quadratic program is reduced to one conic quadratic problem. The above semidefinite relaxation scheme and conic quadratic problem correspond to the similar robust analysis based on convex optimization theory. Finally, one simulation example is used to prove the efficiency of our proposed theory.

Inventory system with price dependent consumption for deteriorating items with shortages under fuzzy environment

In the changing scenario of market, inventory system have become important for all researchers and fuzzy set theory mainly deals with quantitative analysis of uncertainty and imprecision. In this paper the inventory system for deteriorating items with price sensitive demand under fuzzy logic has been developed. This system is allowed shortage which is completely backlogged. Due to uncurtaining in the market fuzzy set theory is used to deal with the imprecise data. Therefore demand rate, deterioration rate and holdings cost taken as pentagonal fuzzy numbers and graded mean representation method (GMRM) has been used to defuzzify the total inventory cost (TC) function made from this model. The purpose of this work is to minimise the total inventory cost. We have illustrated the model by numerical example along with graphical illustration and sensitivity analysis is finally depicted to understand this model based on real life scenario.

Economic order quantity model for two generation consecutive technology products under permissible delay in payments

In this article, we discussed optimal replenishment policies for two succeeding generations' technology products under partial trade credit financing. It is often seen that in technology market, advanced generation product plays an important role in cannibalising the market of existing generation product. Thus, precise estimation of demand of technology generations' product is critical for taking any policy decisions. Demand estimation of technology products is a complex process, as the consumer buying behaviour of technology generational products is not only depends on marketing mix variables but also associated with the time-to-market phenomenon of new technologies. In technology market, interaction among users of different generational products controls the rate of substitution of older technology products with the new one. Therefore, due to the substitution nature of demand of multi-generation product, it is important to incorporate the interaction-substitution effect in replenishment policies for this kind of products. We used life cycle dynamics to project demand rates of technology generations. In this paper, we formulate the total cost function for five different situations depending upon the new generation introduction timing and length of the trade credit period. A detail sensitivity analysis is been performed to explore the efficacy of the model in a given situation.

The impact for retailer’s policy in supply chain system under trade credit and quantity discounts

This paper develops a powerful retailer inventory model under trade credit and quantity discounts in which the retailer’s order quantity is calculated for each setup and shipped in equal lots over multiple deliveries. Furthermore, the trade credit condition is that the retailer must make partial payments in cash for a given number of sub-shipments, with the remaining balance paid in trade credit time that expires after the inventory is depleted. This integrated powerful retailer supply chain model has not yet been discussed in previous supply chain coordination systems literature. We propose an annual total cost function and properties and develop theorems to illustrate that a unique optimal solution minimizes the relevant cost per year. We also develop an efficient algorithm to determine the optimal set of the replenishment time and the number of shipments. Numerical examples are provided to demonstrate the proposed model and algorithm. A sensitivity analysis is explored to examine the effects of four important parameters (i.e., setup cost, unit holding cost, interest rate, and receiving cost) on the optimal strategy. Finally, managerial insights are drawn.

Impact of cost of substitution and joint replenishment on inventory decisions for joint substitutable and complementary items under asymmetrical substitution

In this paper, impact of cost of substitution and joint replenishment on inventory decisions for joint substitutable and complementary items under asymmetrical substitution has been studied. The phenomenon of substitution is considered in a stock-out situation and when items become out of stock due to demand then unfulfilled demand is asymmetrically substituted by another item. We formulate the inventory model mathematically and derived optimal ordering quantities, optimal total costs and extreme value of substitution rate for all possible cases. Moreover, pseudo-convexity of the total inventory cost function is obtained and the solution procedure is provided. Numerical example and sensitivity analysis have been presented to validate the effectiveness of the inventory model and substantial improvement in total optimal inventory cost with substitution with respect to optimal total inventory cost without substitution is seen.

Optimization of the delivery route for community group-purchasing fresh products considering customer satisfaction

For this paper, the VRP model on the total cost minimization of fixed cost, transportation cost and penalty cost is developed under the constraint of the delivery time satisfaction function for the characteristics of community group purchasing. On the genetic algorithm optimization, an elite retention mechanism is added, a partial crossover rule is used to design the crossover operator, and the examples are tested. The results show that solving the total cost function can effectively reduce the cost, and the improved genetic algorithm has good computational speed and convergence. At the same time, good satisfaction was obtained, indicating that the company cannot neglect the customer satisfaction experience while pursuing the minimum total cost, which provides a decision reference for achieving the balance between the two.

Green design and product stewardship approach for two-warehouse inventory model

Background/Objectives: To trim down the recycling cost of any manufactured goods with the help of green design and product stewardship. Methods/Statistical analysis: For the planned EPQ (economic production quantity model) model, all costs are calculated to find total cost and this total cost is optimized with the help of the Hessian matrix. Sensitivity analysis is also carried w.r.t. different parameters, to illustrate the impact of these parameters on the proposed model. The convexity of the total cost function is also checked with the help of mathematical software Mathematica 9.0. Findings: Major finding of the proposed model are as follows: (i) Increase in the number of recycles results in the reduction of the total cost. (ii) Product stewardship parameter has a negative effect on total cost as the PS increases from 1 to 4 units, total cost decreases from 5926.00 to 5918.96 units (see Table 9 ) (similar findings can be written for numeric example 1 after correcting it). (iii) Green design costs have a positive effect on total cost, as the green design cost increases from 3 to 6 units, total cost also increases from 5918.49 to 5920.37 units (see Table 10 ). (iv) increase in the number of recycles results in the reduction of the total cost, as the number of recycles increases from 20 to 50 units total cost decreases from 5922.87 to 5919.12 units (see Table 11 ). Novelty/Applications: The Study of the effects of recycling by this green design and product stewardship approach makes the proposed model distinctive from the existing methods. The proposed model applies to eco-friendly manufacturing items with green design and product stewardship. Keywords: Green design; product stewardship; production model; own warehouse (OW); rented warehouse (RW); shortage; deterioration