Profit Objective Function Research Articles

Optimizing customized bus services for multi‐trip urban passengers: A bi‐objective approach

AbstractCustomized bus services typically focus on single‐trip requests, which often struggle to accommodate the growing needs for varied multiple trips in urban daily travel. This paper addresses the customized bus routing problem for passengers with multiple trips. A bi‐objective mathematical model is established for maximizing the operational profit and minimizing the travel costs by considering the characteristics of the multi‐trip requests and time‐dependent travel time. Besides, a novel profit objective function is proposed considering the service's completion status and the starting price. Since the proposed mixed integer linear programming model is an NP‐hard problem, a non‐dominated sorting genetic algorithm II‐based method is proposed to handle different sizes of instances. Finally, the instances with multi‐trip requests are carried out to test the accuracy of the model and the effectiveness of our method compared with Gurobi and the local search‐based multi‐objective algorithm approach.

Forecast Horizon of Dynamic Lot Sizing Problem with Perishable Inventory and Multiple Chain Stores: Shipping and Stockout Cost

Perishable products are very common, but managing inventory of perishable products can be very challenging for firms, especially in distribution systems, including multiple chain stores. In this environment, we consider a dynamic lot-sizing problem faced by a distribution center that dis-patches a single perishable product to multiple chain stores. Demand cannot be backlogged, but it does not have to be satisfied; unsatisfied demand means stockout (lost sale). The first step is to transform the total profit function into a special total cost function. Our next step is to explore the properties of the optimal solution and use them to formulate a dynamic programming algorithm to solve the problem. Furthermore, we establish forecast and decision horizon results, which help the operation manager to decide the precise forecast horizon in a rolling decision-making process. Based on the model setting and the methods of dynamic programming, we obtained two interesting findings: (1) the maximized profit objective function is equivalent to the minimized cost objective function, and (2) the famous zero inventory property conditionally holds in the inventory management of perishable products. On an extensive test bed, useful insights were obtained on the impact of the lifetime of the product and cost parameters on the total cost and length of the forecast horizon. Thus, the contributions of this study are as follows: (1) we explore two structure policies in an optimal solution to devise efficient algorithms to reduce computational complexity; (2) we provide a sufficient condition for forecasting and decision horizons; and (3) we determine that, for a given fixed cost, the median forecast horizon first increases with the lifetime of the product and stockout cost and then remains invariable when it reaches a certain level.

Research on Active Pricing and Replenishment Decision Making of Vegetable Commodities Based on Particle Swarm Algorithm

With economic development, people's eating habits are becoming more green and healthy, which provides a wide market for the sale of vegetable products. Due to the short shelf life and easily damaged characteristics of vegetable products, most of them cannot be sold the next day. As a result, supermarkets need to replenish their stock on a daily basis based on historical sales data. To help supermarkets formulate pricing and replenishment strategies to maximise sales, this paper takes two approaches based on domestic and international studies. First, this paper draws a scatter plot of total sales and markup rate and fits the functional relationship and concludes that the correlation between the two is not strong; it adopts a time series forecasting model to determine the cost price of each vegetable category for the next seven days, and solves the total daily replenishment and pricing for the next seven days using particle swarm algorithm through the establishment of a profit objective function. Second, considering the limited selling space of supermarkets and satisfying the market demand as much as possible, this paper introduces the constraint that the sellable single product categories are within 20, and solves for the replenishment and pricing of single products on 1 July 2023 in supermarkets. This paper provides workable ideas for pricing and replenishment decisions for vegetable products in supermarkets.

Evaluation of energy saving and emission reduction effect of distributed energy system

The conventional evaluation methods of energy conservation and emission reduction lack the discussion of quantification index of energy conservation and emission reduction potential, and the evaluation effect is poor. Therefore, an evaluation method for energy conservation and emission reduction of distributed energy systems is proposed, which considers system dynamics and demand response. According to the requirements of system dynamics analysis, the relational variables in the system dynamics model are determined. The input-output relationship of energy saving, and emission reduction effect evaluation is described by system dynamics equation, and the input-output relationship of energy saving, and emission reduction effect evaluation is determined. Based on the maximum profit objective function and the minimum cost objective function of the user, the continuum equation of the medium transmission process in the distributed energy system is obtained. The evaluation indexes of energy saving, and emission reduction effect are selected from the three aspects of power consumption side, power generation side and the system itself to realize the evaluation of energy saving and emission reduction effect. The experimental results show that the evaluation curve obtained by this method is basically consistent with the actual curve, and the evaluation accuracy is high.

Two-level differential burn-in policy for spatially heterogeneous defect units in semiconductor manufacturing

Burn-in (BI) is an effective technique in semiconductor manufacturing to weed out defective devices. BI has been generally conducted on all of packaged devices for the same duration. Realizing that devices in the BI population usually have different reliability at various production levels, this study proposes a new two-level differential BI policy and two BI optimization models to determine the cost-optimal and profit-optimal BI decisions, respectively. The BI tests are conducted at two production levels: wafer-level (WL) and package-level (PL). After a common wafer-level BI for all devices, survival devices are subject to three different decisions: rejection without PLBI, acceptance without PLBI, and test with PLBI. The cost objective function consists of the BI test costs, BI failure costs, and warranty failure cost, while the profit objective function considers the manufacturing costs, BI test costs, warranty failure cost, revenue, and yield loss. Spatially varying yield and probability with reliability defects are computed via spatial regression modeling of clustered defect counts. Two numerical examples are used to illustrate the proposed BI policy and models based on the spatial defects modeling. Analytical results demonstrate that the two-level differential BI policy can be a cost- and profit-effective alternative over the conventional single PLBI policy.

Интеллектуальный поиск точных решений задачи планирования открытых горных работ

A method of intelligent search for accurate solutions to the planning of open-pit mining has been developed. The method is implemented within the framework of the Constraint Programming Paradigm that allows us to process heterogeneous qualitative and quantitative constraints (in particular, economic, technological, etc.) simultaneously, as well as to maintain the model of subject domain being developed which is open to adding new constraints or deleting existing constraints. Various constraints can be added to the model, including those for which it is difficult to find a suitable analytical expression. In contrast to existing methods of local search the proposed method systematically explores the search space. The method allows us to find a global optimum in large dimensional spaces that describe practically significant problems arising in production. Currently, to solve this problem, the methods of integer linear programming are widely used. But its fundamental disadvantage is the need to represent all the constraints in the form of linear equalities and inequalities. However, in practice, some combinatorial optimization problems cannot be linearized and solved using traditional methods of mathematical programming. The developed method is illustrated by the example of a three-dimensional problem of finding the position of an intermediate pit wall by the processing periods taking into account the specified performance for mineral and overburden rocks and the objective profit function taking into account discounting. The types of constraints necessary for modeling the problem under consideration are identified. The possibility of applying the existing inference procedures on constraints is considered for these types. The method proposed makes it possible to obtain accurate solutions due to the intellectualization of the solution process by using highly efficient algorithms of reducing the search space for each type of constraints and specialized heuristics for pruning unpromising alternatives in the search tree.

Risk-constrained optimal bidding and scheduling for load aggregators jointly considering customer responsiveness and PV output uncertainty

Recent years have witnessed a growing trend in the participation of renewable energy on the generation side and relatively high peak loads on the demand side, which makes it gradually challenging for traditional methods concentrating separately on the generation side to maintain system balance. Load resources, with potentialities to provide faster and more economical responses to balance signals, are able to make contributions to system balance through demand response(DR) programs in addition. With the reformation and development of the electricity market, load aggregators(LAs) pear as representatives of small-scale customers and generations to meet response limitations and participate in DR programs. The LA in this paper, which aggregates residential customers and a PV system with battery energy storage(BES) units, balances the power by optimal scheduling and bidding in Day-ahead(DA) and real-time(RT) markets based on real-time electricity price(RTP). And the objective of this paper is to maximize the profits of LA. A majority of papers use deterministic methods for the modeling of renewable generations and residential loads. However, influenced by multiple factors, the actual renewable outputs and residential responsive loads towards real-time electricity prices are unavoidably uncertain. These uncertainties bring risks to LA’s scheduling and bidding strategies, which results in the reduction of LA’s profits. A stochastic model based on the scenario generation method is adopted to reflect the uncertainties of customers’ responsive loads and the PV system’s outputs. The objective profit function turns out to be a risk function influenced by uncertain factors and the risk control method conditional risk at value(CVaR) is integrated to obtain optimal solutions for this maximization problem. Case studies have verified the effectiveness of the proposed strategy.

Automated taxis’ dial-a-ride problem with ride-sharing considering congestion-based dynamic travel times

In this paper, we study the dial-a-ride problem of ride-sharing automated taxis (ATs) in an urban road network, considering the traffic congestion caused by the ATs. This shared automated mobility system is expected to provide a seamless door-to-door service for urban travellers, much like what the existing transportation network companies (TNC) do, but with decreased labour cost and more flexible relocation operations due to the vehicles’ automation. We propose an integer non-linear programming (INLP) model that optimizes the routing of the ATs to maximize the system profit, depending on dynamic travel times, which are a non-linear function of the ATs’ flows. It is important to involve traffic congestion in such a routing problem since for a growing number of ATs circulating in the city their number will lead to delays. The model is embedded within a rolling horizon framework, which divides a typical day into several horizons to deal with the real-time travel demand. In each horizon, the routing model is solved with the demand at that interval and assuring the continuity of the trips between horizons. Nevertheless, each horizon model is hard to solve given its number of constraints and decision variables. Therefore, we propose a solution approach based on a customized Lagrangian relaxation algorithm, which allows identifying a near-optimal solution for this difficult problem. Numerical experiments for the city of Delft, The Netherlands, are used to demonstrate the solution quality of the proposed algorithm as well as obtaining insights about the AT system performance. Results show that the solution algorithm can solve the proposed model for hard instances. Ride-sharing makes the AT system more capable to provide better service regarding delay time and the number of requests that can be attended by the system. The delay penalty on the profit objective function is an effective control parameter on guaranteeing the service quality while maintaining system profitability.

Multi-Period Configuration of Forward and Reverse Integrated Supply Chain Networks with the Choice of Transport Mode

Today’s competitive business environment has resulted in increasing attention to social responsibilities and customer’s attitudes. Buying and returning have become a common practice for different reasons, including incompleteness or immature failure of the product or its failure to meet the customer’s satisfaction. Before the buying and returning cycle can be handled appropriately, companies need a proper logistics network designed following a proper design strategic. In the present research, a forward and reverse logistics network is proposed for product distribution and collection. The contribution of this paper to the literature is the proposal of a multi-period, multi-echelon, integrated forward and reverse supply chain network design problem with transportation mode selection considered. Different kinds of decisions including the determination of optimum number and locations of facilities, facilities opening time and transportation mode selection among different facilities have been considered in this paper. Due to multi-period nature of the problem, the problem is flexible for future periods. A new mixed integer nonlinear programming model was proposed for the introduced problem considering different levels of facility capacities with the maximum profit objective function. As another contribution, a genetic algorithm was developed to cope with problem’s complexity when the problem size goes large.

ANALYSIS AND OPTIMIZATION OF BLOOD-TESTING PROCEDURES

This paper is devoted to the performance analysis and optimization of blood testing procedures. We present a queueing model of two queues in series, representing the two stages of a blood-testing procedure. Service (testing) in stage 1 is performed in batches, whereas it is done individually in stage 2. Since particular elements of blood can only be stored and used within a finite time window, the sojourn time of blood units in the system of two queues in series is an important performance measure, which we study in detail. We also introduce a profit objective function, taking into account blood acquisition and screening costs as well as profits for blood units, which were found uncontaminated and were tested fast enough. We optimize that profit objective function w.r.t. the batch size and the length of the time window.

Economic design of variable-parameter X-Shewhart control chart used to monitor continuous production

Control charts are a quantitative management tool used in statistical process control to monitor product quality in production processes. This study proposes a new economic design of the variable-parameter (Vp) -Shewhart control chart for monitoring a continuous production process. In this design, the mean monitoring quality may exhibit an upward or downward shift due to two types of assignable causes. In certain continuous production settings, product quality directly affects production profit; the mean shift in monitoring quality influences lost cost, unit income and product yield. Thus, for modelling continuous production, using a maximum profit objective function for the optimization algorithm of this economic model is more appropriate than using minimum cost. Therefore, the Vp -Shewhart control chart uses an economic criterion for optimum parameter design to maximize the anticipated quality-related profit. The assignable cause occurrence is assumed to be an exponentially distributed random variable; Markov chain theory with a 9 × 9 transition probability matrix is used to subdivide the process operation into three actual states and three necessary actions. A numerical investigation is used to demonstrate the superiority of the proposed profit model compared to existing models. The proposed Vp -Shewhart control chart is applied to an example case to show its feasibility and practical application.

Mining rate optimization considering the stockpiling: A theoretical economics and real option model

In the extraction of metal from a mine, the intermediate ore between the economic and the breakeven cutoff grade is usually stockpiled for future processing once the mine is depleted. This research establishes a theoretical two-stage economic model to derive the value of this stockpile and how it affects optimal mining rate. By deriving the optimal condition for objective profit function and parameterized analysis, this research finds the stockpiling option can significantly boost a mine's profit. Processing the stockpiled material affects the optimal mining rate and cutoff grade strategy significantly compared to the case that it is not processed. The research also investigates the optimal mining rate's sensitivity to input variables such as commodity price, discounting rate, capital cost, and processing capacity, etc. In addition, the intrinsic advantages of this approach compared to the broadly used Lane's model (1988) are discussed.

Optimizing the cut off grade in Sarcheshmeh copper mine using Lane Quartet Model

Lane Algorithm is used to determine optimum cut off grade for a mining operation. There may be three parts in each operation: mining, concentration and refining. In Sarcheshmeh Copper Mine the concentrate coming from the stock has the average grade in addition to the production rate and cost. Therefore, the grade distribution is affected by production rate and cost parameters. The calculation of the cut off grade is done using a modified Lane Algorithm. Therefore, a mix of blending stock received from outside and the concentrate from the mine was considered in the Lane Algorithm. Initially, the profit objective function was taken into account with the addition of the stock limitations; then, the Lane Quartet Model was used and the cut off grade determined. The model uses the technical and economical data of different parts to determine the cut off grade. The result of the model was a cut off grade of (0.1408%), which brings about an increase of848051645 US dollars as profit, in comparison to the cut off grade (0.1617%) that was obtained by the Lane tripartite model.

A recursive approach for lot sentencing problem in the presence of inspection errors

ABSTRACTIn this paper, a new sequential acceptance sampling plans in the presence of inspection errors is developed. A suitable profit objective function is employed for optimizing the lot sentencing problem. A backward recursive approach is applied for obtaining the profit of different decisions in each stage of sampling. Required probabilities are obtained using Bayesian rule. A case study is solved for illustrating the application of proposed models and sensitivity analysis are carried out on the parameters of the proposed methodologies and the behaviour of models by changing the parameters are investigated.

Profit-based conventional resource scheduling with renewable energy penetration

Technological breakthroughs in renewable energy technologies (RETs) enabled them to attain grid parity thereby making them potential contenders for existing conventional resources. To examine the market participation of RETs, this paper formulates a scheduling problem accommodating energy market participation of wind- and solar-independent power producers (IPPs) treating both conventional and RETs as identical entities. Furthermore, constraints pertaining to penetration and curtailments of RETs are restructured. Additionally, an appropriate objective function for profit incurred by conventional resource IPPs through reserve market participation as a function of renewable energy curtailment is also proposed. The proposed concept is simulated with a test system comprising 10 conventional generation units in conjunction with solar photovoltaic (SPV) and wind energy generators (WEG). The simulation results indicate that renewable energy integration and its curtailment limits influence the market participation or scheduling strategies of conventional resources in both energy and reserve markets. Furthermore, load and reliability parameters are also affected.

A synergic economic order quantity model with trade credit, shortages, imperfect quality and inspection errors

This paper develops a synergic economic order quantity (EOQ) model, in which trade credit, shortages, imperfect quality and inspection errors are taken into consideration simultaneously. We prove that the objective function of annual profit is strictly concave and show the closed-form optimal solution to the model. In special cases, some related EOQ models can be derived from our model, which we illustrate with numerical examples. Managerial implications are also proposed.

An Interactive Method for Two-plants Production Inventory Control with Two-Warehouse Facility under Imprecise Environment

This paper develops an integrated production inventory model with an aim to minimize the cost of production per unit of the product and maximization of profit without compromising the quality of the product. In this model we consider two plants, two secondary warehouses (SWs) and two showrooms (SRs) those are adjacent to the respective plants. For the purpose, we assume to be erected by a firm two plants: Plant-I and Plant-II. Plant-I is situated in an urban area with a lower production capacity in comparison to its product demand where the demand meets through SR-I. On the other hand, Plant-II is situated in a rural area with higher production capacity in comparison to its product demand where the demand meets through SR-II. The excess production in Plant-II meets the current market demand in the area of Plant-I. Here, demand is assumed to be stock dependent in both the showrooms (SR-I and SR-II). Average profit in the integrated model is calculated and global optimum is obtained through a descriptive-cum-analytical review. The inventory parameters are taken as fuzzy numbers. The fuzzy numbers are first transformed into corresponding interval numbers and then follow the interval mathematics, the objective function for average profit is converted into respective multi-objective functions. Furthermore, the objective functions are being maximized and solved for a Pareto-optimum solution by interactive fuzzy decision-making procedure. The model also illustrates graphically and numerically.

Portfolio Determination of a Zero-Interest Financial System Entity

Beginning in the 1930s and increasing significantly post-colonialism, some Muslims scholars have wondered about the divine edict of interest-free nominal sector and how to realize it in the context of modern mass deposit institution and wide, concentrated financing demand for trade, entrepreneurship and consumption ends. This undertaking has faced challenges posed by the interest-based nominal sector. Evidence has mounted about the limitations of interest-free banks in the way they are organized and, of late, the largely a theoretical way they do business and their business and political operative environment. For explaining the phenomenon and predicting events, a risk-discounted, expected profit objective function produces rules for inter and intra-sectoral allocation of funds. The nonhomogeneity of mark-up and profit-loss-sharing products leads to adopting the average sizes of outlays in the two sectors as the choice variables. Identifying allocation rules for resources will benefit empirical analysis, banking policy and the central bank’s monitoring effort.

Optimal Control of the Extractive Distillation for the Production of Fuel-Grade Ethanol

Laboratoire de Thermique, Energetique et Proce de s (LaTEP), E cole Nationale Supe rieure en Ge nie de Technologies Industrielles(ENSGTI), Universitedes Pays de l’Adour (UPPA), Rue Jules Ferry, BP 7511, 64 075 PAU Cedex, FranceABSTRACT: The extractive distillation of ethanol using glycerol as the entrainer was studied to determine its optimal controlprofiles when the azeotropic feed was subjected to composition disturbances. The process was modeled by a differential-algebraicequation (DAE) system that represents the dynamics of the equilibrium stages in the extraction column. The model equationswere solved by discretizing the time domain using orthogonal collocation on finite elements. Initially, the effects of feeddisturbances on the product flow rate and quality were analyzed. Subsequently, a profit objective function was formulated, andthe optimal profiles of the manipulated variables (reflux ratio and reboiler duty) were determined, subject to quality constraints.The solution was obtained by solving the nonlinear programming (NLP) problem that resulted from the discretization. Theproblem was solved in GAMS using IPOPT as the nonlinear solver, testing two different linear solvers, the Harwell subroutinesMA57 and MA86. The optimal control strategy was compared to a simple PI control scheme.

Inventory model with fuzzy lead-time and dynamic demand over finite time horizon using a multi-objective genetic algorithm

The real-world inventory control problems are normally imprecisely defined and human interventions are often required in solving these decision-making problems. In this paper, a realistic inventory problem with an infinite rate of replenishment over a prescribed finite but imprecise time horizon is formulated considering time dependent ramp type demand, which increases with time. Lead time is also assumed as fuzzy in nature. Shortages are allowed and backlogged partially. Two models are considered depending upon the ordering policies of the decision maker (DM). The imprecise parameters are first transformed to corresponding nearest interval numbers depending upon some distance metric on fuzzy numbers and then following the interval mathematics, the objective function for total profit from the planning horizon is obtained (which is an interval function). Then interval objective decision making problem is reduced to multi-objective problems using different approaches. Finally a fast and elitist multi-objective genetic algorithm (FEMOGA) is used for solving these multi-objective models to find pareto-optimal decisions for the DM. The models are illustrated numerically. As a particular case, the results due to linear trended and constant demands have been presented.