Finite Production Rate Research Articles

Economic production quantity for a decaying item with stochastic demand and positive lead time

This paper considers a single-item, single-location production-inventory system subject to decay and random demand. Production occurs on a single machine at a constant and finite production rate. Shortages are allowed and partially backordered, while the other fraction of unmet demand is lost. A continuous review, lot size-reorder point policy is implemented to determine the size and the timing of production orders. The typical zero-lead time assumption made in existing economic production quantity models for a decaying inventory with random demand is relaxed here: when a production order is issued, a positive lead time is required before production starts. The long-run expected total cost per time unit is derived characterizing the stock dynamics as an Itō diffusion. Several properties concerning the inventory dynamics and the cost function are demonstrated, and an optimization procedure that finds the optimal solution for the developed cost function is presented. Numerical experiments are carried out with a twofold objective: (i) to validate the inventory model through simulation, and (ii) to evaluate the model sensitivity with respect to variations in parameter values.

Understanding the open string pair production of the Dp/D0 system

Consider a system consisting of Dp and Dp′, placed parallel at a separation and with p − p′ = 2n (assuming p ≥ p′, the integer n ≥ 0 and p′ > 0). When either Dp or Dp′ carries a worldvolume electric flux, one in general expects a non-vanishing open string pair production due to the pair of virtual open string/anti open string connecting the two D branes under the action of the applied flux. However, this will not be true for p′ = 0 and p = 2, 4, 6 when the Dp carries a pure electric flux. In this note, we will explore the case for which a finite non-vanishing open string pair production rate can indeed be produced when a certain worldvolume flux is applied to the Dp brane and understand the physics behind.

Optimizing Supplier Selection and Order Lot-Sizing Decisions in a Two-Stage Supply Chain

This paper analyzes different lot-sizing policies for the supplier selection and order allocation problem in a two-stage supply chain. The supply chain consists of multiple candidate suppliers and a single buyer. In this system, selected suppliers produce a product in batches at finite production rates, ship it to the buyer, and the buyer sells it to the market at a constant demand rate. Our goal is to evaluate two lot-sizing policies and select the one that optimizes the supply chain by minimizing the total cost and maximizing supplier efficiency. A bi-objective mixed-integer nonlinear programming (BOMINLP) model is proposed. The first objective consists of the development of a coordination mechanism for supplier selection and order allocation that minimizes the entire supply chain cost, and the second objective comprises a data envelopment analysis (DEA) approach to evaluate the overall performance of suppliers to optimize supplier efficiency. Then, the lot-for-lot and order frequency policies are applied to the BOMINLP model separately to determine the set of selected suppliers as well as the corresponding order quantities and number of orders allocated to each selected supplier per replenishment cycle. Numerical examples that illustrate the solution approach and compare the two lot-sizing policies are provided.

Replenishment-shipment decision for a multiproduct producer-client coordinated FPR model with postponement, rework and subcontracting

This research constructs a mathematical scheme to explore replenishment-shipment decisions for a multiproduct producer-client coordinated finite production rate (FPR) model with the postponement, rework, and subcontracting plan. The considered multiple goods have a common component, and a batch FPR fabrication with postponement is planned to meet the annual multiproduct requirements. The first fabricating phase makes only the standard components needed for a batch and subcontracts a proportion of them (with additional cost) to expedite the process. In contrast, the second fabricating phase produces the finished multiple merchandise in sequence. The in-house rework processes with extra expense help retain the desirable quality. Each merchandise’s finished batch is transported to the clients in equal-sized numerous shipments. This study derives the optimal batch cycle length and transporting frequency by minimizing the overall fabricating-shipment expenses (including clients’ holding costs). This work offers a numerical example demonstrating various crucial system features influenced by the factors of subcontracting, postponement, rework, and transportation policies to facilitate managerial decision making in industries.

Manufacturing inventory model with random demand and finite production rate under two levels of trade credit finance

Manufacturing inventory model with random demand and finite production rate under two levels of trade credit finance

Manufacturing inventory model with random demand and finite production rate under two level of trade credit finance

Manufacturing inventory model with random demand and finite production rate under two level of trade credit finance

Optimizing an FPR-based supplier-retailer integrated problem with an outsourcer, rework, expedited rate, and probabilistic breakdown

Internal supply chains exist in many global enterprises, where manufacturing tasks and sales jobs operate separately, but the management needs to integrate their financial performance reports. In addition, the fabrication planning must meet specific operational goals, such as meeting external clients’ requirements on quality and short order due dates, avoiding internal fabricating interruptions due to inevitable equipment breakdowns, and minimizing overall manufacturing and stock holding costs. Motivated by helping multinational corporations deal with the issues mentioned earlier, this study aims to optimize a finite production rate (FPR)-based supplier-retailer cooperative problem with multi-shipment, rework, subcontracting, probabilistic failure, and expedited rate. Wherein using an outsourcer and expedited-rate help shorten the needed batch producing time significantly; the rework of defects and corrective action on unanticipated breakdown assist in up-keeping the quality and avoiding fabricating delay. We develop an FPR-based model to cautiously represent the considered manufacturing features and activities involved in transporting end products and retailers’ stock holding. Model’s formulating and investigating assists us in gaining the function of operating costs. In addition, optimization procedures with a proposed algorithm help us verify its convexity and decide the model’s best fabricating runtime solution. Finally, we validate how this study works and what important information our model can disclose using a numerical example to facilitate management’s decision-making to end our work.

Optimisation of finite economic production quantity model under cloudy normalised triangular fuzzy number

This study introduced an economic production quantity (EPQ) model with a finite production rate established for cloudy normalised triangular fuzzy number (CNTFN). In real-life situations, the goals and inventory parameters are not precise. Such type of uncertainty may be characterised by fuzzy numbers. The main objective of this research effort is to develop a mathematical model and optimise EPQ with different environment-like crisp, general fuzzy and cloudy fuzzy situations. A novel defuzzification methodology has been used for EPQ by Yager's ranking index method. Here, the constraint goal and the inventory cost parameters are assumed to be triangular-shaped fuzzy numbers with different types of left and right membership functions. The cost functions associated to these models are verified to be convex, and optimal criteria are established in all three situations. The models are numerical, graphically demonstrated and sensitivity analysis shows a decent explanation. The paper also discusses the applications and future scope of the CNTFN model in realistic situations such as when items are not easy to replenish due to some transport problem and some problems in geographically hilly regions.

Scaling advantage of chaotic amplitude control for high-performance combinatorial optimization

The development of physical simulators, called Ising machines, that sample from low energy states of the Ising Hamiltonian has the potential to transform our ability to understand and control complex systems. However, most of the physical implementations of such machines have been based on a similar concept that is closely related to relaxational dynamics such as in simulated, mean-field, chaotic, and quantum annealing. Here we show that dynamics that includes a nonrelaxational component and is associated with a finite positive Gibbs entropy production rate can accelerate the sampling of low energy states compared to that of conventional methods. By implementing such dynamics on field programmable gate array, we show that the addition of nonrelaxational dynamics that we propose, called chaotic amplitude control, exhibits exponents of the scaling with problem size of the time to find optimal solutions and its variance that are smaller than those of relaxational schemes recently implemented on Ising machines.

An Inventory Production Model for Deteriorating Items Allowing Price Discount with Permissible Delay in Payments

The present Paper deals with an inventory production policy for a ramp type deteriorating item over a finite planning horizon with constant demand, finite production rate and shortages are not allowed. The optimal number of production cycles that minimizes the average system cost is determined. The model permits inventory shortage in each cycle, which is completely backlogged within the cycle itself. Every cycle starts with zero stock and production. As production continues, the inventory begins to accumulate after meeting current demands. The excess inventory accumulated during the production period is used to account for demand and deterioration in the no-production period. Numerical examples, tables, and final concluding remarks are discussed in the subsequent sections. Numerical example solved by using Mathematica software.

A coordination mechanism for supplier selection and order quantity allocation with price-sensitive demand and finite production rates

We study a supplier selection and order quantity allocation problem in a two-stage supply chain, which is composed of a set of potential suppliers and a single buyer/retailer trading one product. The demand at the buyer's stage is price-sensitive and suppliers have finite production rates. Within this framework, the optimization of the supply chain is evaluated by considering the performance of both stages and guaranteeing their profitability through a coordination mechanism based on profit-sharing. Two mixed integer nonlinear programming models are presented under different lot-sizing policies to determine the optimal set of selected suppliers, retail price, and order quantity and number of orders per order cycle for each selected supplier. The structure of the models' solutions is examined by deriving properties of the optimal supplier selection and order quantity allocation scheme. Numerical examples are also provided to illustrate the applicability of the proposed models.

An optimal setup cost reduction and lot size for economic production quantity model with imperfect quality and quantity discounts

<p style='text-indent:20px;'>The purpose of this paper concentrates on an economic production quantity model with the factors of imperfect quality and quantity discounts, in which the inspection action occurs during the production stage. There is specific consideration of there being a finite production rate, and the quantity discounts offered by the supplier serves the purpose of stimulating buying greater quantities. This is in contrast to EPQ models that do not take these added factors into consideration. The objective of this paper is to determine the setup cost reduction, which is a function of capital investment, and inventory lot size. An alternative solution procedure was developed that does not employ the Hessian Matrix concavity in the expected total profit. We develop an algorithm to determine the optimal solution for this model. Theoretical results are discussed and a numerical example is proposed. Managerial insights are also examined.

Quantum features of entropy production in driven-dissipative transitions

The physics of driven-dissipative transitions is currently a topic of great interest, particularly in quantum optical systems. These transitions occur in systems kept out of equilibrium and are therefore characterized by a finite entropy production rate. However, very little is known about how the entropy production behaves around criticality and all of it is restricted to classical systems. Using quantum phase-space methods, we put forth a framework that allows for the complete characterization of the entropy production in driven-dissipative transitions. Our framework is tailored specifically to describe photon loss dissipation, which is effectively a zero temperature process for which the standard theory of entropy production breaks down. As an application, we study the open Dicke and Kerr models, which present continuous and discontinuous transitions, respectively.We find that the entropy production naturally splits into two contributions. One matches the behavior observed in classical systems. The other diverges at the critical point.

A hybrid finite production rate system featuring random breakdown and rework

To reduce the order response time or achieve optimal utilization, manufacturers often include an outsourcing alternative in their production plans. Further, undesirable machine breakdowns and nonconforming items produced during the in-house processes must also be effectively managed/corrected to adhere to the fabrication schedules and meet the desired quality level. This study addresses the aforementioned concerns by examining a hybrid finite production rate (FPR) system featuring: breakdown that follows the Poisson distribution, and rework/repair of all the nonconforming goods produced. A portion of the batch size is outsourced to an external supplier, who guarantees quality but at a higher unit cost than that incurred in-house. A mathematical model is explicitly built to represent the features of the proposed hybrid FPR system. We use the optimization approach and an algorithm to determine the optimal replenishing runtime that minimizes total costs; results are demonstrated through a numerical example and sensitivity analyses. Diverse crucial system information available to assist manufacturers in production planning includes the individual and joint influence of rework, outsourcing, and breakdown on: (a) variable rework cost; (b) the optimal runtime; (c) total system cost; (d) utilization; (e) detail of system's cost elements; and (f) other important system parameters.

Combining the delayed differentiation policy and common parts' partial outsourcing strategy into a multi-item FPR-based system

This study investigates a multi-item finite production rate(FPR-) based system incorporating a delayed product differentiation policy and common parts' outsourcing strategy. A two-stage fabrication scheme is proposed, wherein, in stage one, all common parts of the end products (assuming they have a known completion rate as compared with the finished products) are partially produced in-house and partially supplied by an outside contractor with an extra unit outsourcing; in stage two, all end products are finished in sequence, under a rotation fabrication cycle time discipline. An explicit model is developed to clearly represent the proposed problem. Through the optimization technique, the optimal rotation cycle decision is obtained. Thus, diverse characteristics of this particular multi-item, FPR-based system with postponement and outsourcing strategies can now be revealed. As demonstrated by numerical illustrations, these characteristics include the (i) convexity of the system cost function, (ii) impact of common parts' outsourcing strategy on the utilization, (iii) breakup of system cost components, (iv) combined impact of the outsourcing ratio and common parts' completion rate on the system cost function, and (v) effect of the outsourcing ratio on optimal rotation cycle decision. Our decision-support-type system can facilitate production managers in achieving their goals of reducing orders' response times and minimizing the overall system cost.

Price and profit structuring for single manufacturer multi-buyer integrated inventory supply chain under price-sensitive demand condition

This paper undertakes the study of an integrated production-inventory and pricing decision problem for a single manufacturer-multiple buyers supply chain where each buyer faces price-dependent demand. The item manufactured at a finite production rate is shipped to the buyers in multiple equal-sized shipments. Earlier researchers have not studied this problem for maximizing the overall supply chain profit and its allocation among the chain partners. For the allocation of the maximized profit, four different schemes are being proposed, each for a different level of understanding and faith among the partners. Demand, taken as price-sensitive, affects the costs to the manufacturer as the same is dependent upon the sales volume. Since the manufacturer fixes its sales price depending upon the sales volume affected cost, the volume will affect the buyer in terms of its unit purchase cost, and the holding cost which is charged as a percentage of the unit cost. This reality is attempted in this paper in addition to maximization of the chain profit and its allocation among the chain partners for integrated inventory management. Associated problems, formulated as mixed-integer non-linear programming problems, are computationally very hard, and thus evolutionary heuristics as Genetic Algorithm and Teaching-Learning Based Optimization are proposed. The strength of various proposed schemes for profit distributions has been analyzed using numerical experimentation. It is found that a forward contract between manufacturer and buyers will help to generate the maximum profit. It has also been shown that the distribution of profit based on Shapley function values is most fair and logical.

Wigner entropy production and heat transport in linear quantum lattices

When a quantum system is coupled to several heat baths at different temperatures, it eventually reaches a non-equilibrium steady state featuring stationary internal heat currents. These currents imply that entropy is continually being produced in the system at a constant rate. In this paper we apply phase-space techniques to the calculation of the Wigner entropy production on general linear networks of harmonic nodes. Working in the ubiquitous limit of weak internal coupling and weak dissipation, we obtain simple closed-form expressions for the entropic contribution of each individual quasi-probability current. Our analysis highlights the essential role played by the internal unitary interactions (node-node couplings) in maintaining a non-equilibrium steady-state and hence a finite entropy production rate. We also apply this formalism to the paradigmatic problem of energy transfer through a chain of oscillators subject to self-consistent internal baths that can be used to tune the transport from ballistic to diffusive. We find that the entropy production scales with different power law behaviors in the ballistic and diffusive regimes, hence allowing us to quantify what is the "entropic cost of diffusivity."

On the Optimality of Inventory and Shipment Decisions in a Joint Three Echelon Inventory Model with Finite Production Rate under Stock Dependent Demand

Abstract This paper develops a mathematical model for a joint three-level supply chain with a single manufacturer (may be a supplier) supplying a single kind of product to a single distributor (may be a wholesaler) and then to a single retailer (may be a buyer). The model is developed for finite production rate and the product demand is expressed in terms stock level. In the proposed work, ordering/setup costs, carrying costs and transportation costs are considered for model development. Optimal inventory and shipment decisions are treated as decision variables. The objective of the proposed model is to demonstrate the optimality of decision variables under the novel idea of stock dependent demand. Also aimed at studying the optimal annual net revenue and total relevant costs of the respective entities and the supply chain. Computer programme is written in MATLAB with respect to the optimality criteria derived and the model is solved with the help of case study data. Also the sensitivity analysis is carried out to show the variation in optimality of decision variables and objective function with respect to model parameters. Finally few managerial implications are discussed from the research findings.

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Joint two-echelon inventory model for optimality of cycle time and inventory decisions with finite production rate under credit period

In the universal competition of business environment, to face the global challenges around the business, it has turn into more traditional of giving trade credit by the vendor to the buyer as part of improving the sales revenue. The buyer need not to pay the vendor immediately whenever buyer received the goods, if a vendor offers credit period to the buyer. In this scenario focusing on the entire supply chain (SC) performance in terms of cycle time, inventory levels, number of shipment and the overall variable cost of the entire SC is essential. Mathematical models are developed for the joint two-echelon inventory system by assuming that production rate is finite. The present work aims to illustrate the optimality of cycle time, levels of inventory, number of shipments and the overall variable cost of the SC under the phenomena of credit period. Finally, numerical examples are solved to illustrate the theoretical results and also the sensitivity analysis is carried out.