Deterministic Demand Research Articles

Scheduling Splitable Jobs on Identical Parallel Machines to Minimize Makespan using Mixed Integer Linear

The scheduling of parallel machines with and without a job-splitting property, deterministic demand,and sequence-independent setup time with the goal of minimizing makespan is examined in this work.For simultaneous processing by multiple machines, single-stage splitable jobs are broken into random(job) sections. When a job starts to be processed on a machine, an operator has to setup the machinefor an hour. By creating two Mixed Integer Linear Programming models, this work proposes amathematical programming strategy (MILP). A MILP model takes the job-splitting property intoaccount. Another model, however, does not include the job-splitting property. This study investigatesthe performance of the proposed models using Gurobi solver. These programs' numerical calculationsare based on actual problems in the Indonesian city of Bandung's plastics industry. On four identicalparallel injection molding machines, 318 jobs must be finished in 22 periods. The real schedulingmethod is contrasted with these two MILP models. The maximum workload imbalance, the maximumrelative percentage of imbalance, and the makespan of these three scheduling systems are used toevaluate their effectiveness. Without the job-splitting property, MILP can handle the real issue ofscheduling identical parallel machines on injection molding machines to reduce makespan, resultingin a 36% average decrease. The MILP model's job-splitting property can reduce makespan by anadditional 2.40%. The order of relative ranking is MILP with job-splitting property, MILP withoutjob-splitting property, and actual scheduling based on the makespan minimization, workloadimbalance, and relative percentage of imbalance.

Last mile delivery with drones: A carbon emissions comparison

The development and potential adoption of drones or unmanned aerial vehicles as delivery vehicles creates incredible opportunities and unique challenges for last mile delivery. This research first presents a last mile delivery fleet model with drones that can be further modified and expanded over time. The model shows the optimal number of drones needed based on deterministic or stochastic demand using both traditional charging and battery swapping. The research then compares the carbon emissions of four delivery modes: traditional internal combustion delivery vehicles, all-electric vehicles, plug-in hybrids, and drones within the context of last mile delivery. Findings reveal that the breakdown of carbon emissions by delivery modality depends on parameter assumptions, ambient temperature, delivery radius, electric grid pollution rate, and number of customers.

Coordinated replenishment policies for a single-supplier multi-retailer cold chain for fresh produce

Purpose The single-supplier multi-retailer cold chain is a widely adopted type of supply chain in the real-world food industry. This paper aims to consider the problem of effectively designing and managing a single-supplier multi-retailer cold chain for fresh produce with deterministic demand to minimize the total cost, which includes cooling, loss of value and carbon emission costs. Design/methodology/approach The global stability index (GSI) method and the non-Arrhenius model are integrated to describe the behavior of food quality degradation. The power-of-two (PoT) policy is adopted in determining the coordinated replenishment policies for the suppliers and retailers, and an appropriate wholesale price structure that can achieve the coordination of the chain is presented. Findings The properties of the cold chain are uncovered, and an appropriate wholesale price scheme that achieves chain coordination with the optimal PoT decision is provided. In the numerical examples, different scenarios are investigated, and it is found that the cold chain parameters influence the optimal decisions in certain ways. Originality/value The PoT policy – an efficient policy to determine the replenishment strategy – has not been adopted in finding the solution of a single-supplier multi-retailer cold chain in the literature. Also, no study has compared the uncoordinated and coordinated cold chain. Moreover, in the existing literature, the wholesale price is usually a constant rather than having a coordinated scheme. This research aims to fill these research gaps.

A novel fuzzy finite-horizon economic lot and delivery scheduling model with sequence-dependent setups

This paper addresses the economic lot and delivery scheduling problem (ELDSP) within three-echelon supply chains, focusing on the complexities of demand uncertainty, limited shelf-life of products, and sequence-dependency of setups. We develop a novel mixed-integer non-linear programming (MINLP) model for a supply chain comprising one supplier, multiple manufacturers with flexible flow shop (FFS) production systems, and multiple retailers, all operating over a finite planning horizon. The common cycle (CC) strategy is adopted as the synchronization policy. Our model employs fuzzy set theory, particularly the “Me measure,” to effectively handle the retailers’ demand uncertainty. Our findings indicate that total supply chain costs escalate with an increase in demand, final components’ holding costs, and sequence-dependent setup costs, but decrease with increasing production rates. Furthermore, while total costs are significantly sensitive to changes in demand, they are relatively insensitive to fluctuations in sequence-dependent setup times. The models developed offer valuable managerial insights for optimizing costs in synchronized multi-stage supply chains, aiding managers in making informed decisions about production lot sizes and delivery schedules under both deterministic and fuzzy demand scenarios. Additionally, the proposed models bridge key research gaps and provide robust decision-making tools for cost optimization, enhancing supply chain synchronization in practical settings.

Pricing strategy based on a stochastic problem with barter exchange under variable promotional effort for a retail channel

Barter exchange platform gains popularity as an effective trade exchange strategy to minimize the vast use of paper money. In retail management, the application of the barter platform is growing because of cashless trade. It allows a retail enterprise to trade unused products in exchange for other assets purchased by reducing the actual purchase of assets. In this context, the study analyzes a stochastic model of a barter exchange problem under a retail channel. It investigates the barter exchange policy in three different models: conventional newsvendor model without barter exchange, with barter exchange, and with barter exchange with promotional effort and emissions level. The market demand for products is considered random and random with deterministic variables for three types of models. Stochastic models are solved in two different ways: with and without probability distribution functions of the random market demand. For maximization of the retailer's profit, the proposed framework obtains optimal decisions on ordered quantity, retail price, promotional effort, and emissions level. Five examples are tested and numerical results show that the barter exchange policy is more profitable than a traditional newsvendor model. A combination of stochastic and deterministic variable demand provides 34.31% more profit than a stochastic demand. Sensitivity analysis, discussions, and managerial insights are provided in detail on optimal decisions.

Chemical reaction inspired approach for routing problems with hard time constraints

ABSTRACT One of the most common issues in logistics and transportation planning is the vehicle routing problem. The objective is to find minimum cost-vehicle routes for serving a set of dispersed customers with deterministic demands while satisfying some constraints. In this paper, we focus on two main constraints, which are vehicle capacity and time windows for customers. We propose to tackle this NP-hard problem with a bio-inspired approach based on a hybridization of Chemical Reaction Optimization and local search method. The solving process of our approach mimics the chemical reactions between molecules to attain their stability with lowest energy. For more diversification of the search space, we involved in the initialization stage a local search method based on greedy adaptive procedure. The performances of our hybrid approach are assessed on the base of various benchmark instances. Simulation results show the good performances and the efficiency of the proposed approach.

Innovative decision support tools for perishable food supply chain management

PurposeWe introduce decision support tools aimed at optimizing perishable food supply chain management, effectively balancing conflicting objectives such as the exporter’s product collection cost and the importer’s profit. This involves considering factors like perishability, selling price, discount rate, and order quantity to achieve optimal outcomes.Design/methodology/approachThis study considered a three-echelon supply chain comprising farmers, a single exporter, and a single importer providing a single, random-lifetime, perishable product under deterministic customer demand. The proposed mathematical model derived the optimal order quantity, selling price, and discount rate for the entire supply chain. This integrated optimization model treats both demand and supply sides as a multi-objective problem, employing a nonlinear program and a two-stage capacitated vehicle routing problem formulation. Numerical examples and a case study focusing on Thailand durian supply chain were conducted to illustrate the approach of the proposed model.FindingsTaking into account both the importer’s profit and the exporter’s product collection cost, the proposed integrated supply chain model and tools maximize profitability, minimizes waste, and meets demand by optimizing perishable product collection costs and proposing a discount system for selling prices.Research limitations/implicationsLimited to a single perishable product in a three-echelon international food supply chain. Future research can explore different products and supply chain contexts.Practical implicationsThe tools enhance decision-making for supply chain managers, improving efficiency, reducing costs, and enhancing customer satisfaction in the perishable food industry.Social implicationsThe proposed model aids in local workforce management by forecasting required manpower for upcoming seasons. By factoring in product quality and pricing, it ensures customers receive fresh products at fair prices. Furthermore, the near-zero waste concept enhances storage conditions at importers' facilities, contributing to improved environmental hygiene.Originality/valueThe integrated model and decision support tools offer a novel approach to address complexities and conflicting objectives in perishable food supply chains, providing practical insights for researchers and practitioners.

Creating a sustainable closed-loop supply chain: An incentive-based contract with third-party E-waste collector

This paper proposes a closed-loop supply chain model to study the impact of product returns and awareness program on e-waste supply chain. The study focuses on the sustainability aspects of e-waste management and the effects such initiatives bring about to the environment at large. Reusing and recycling of collected products in manufacturing will improve the supply of scarce resources and reduce reliance on virgin raw materials. Engaging in CLSC can enhance brand reputation and competitiveness through sustainability while reducing the health risks to informal recycling workers by formalizing practices. The proposed model consists of a manufacturer, retailer, and third-party collector (TPC) under wholesale price and incentive contracts with deterministic demand. From the analysis it is observed that integrating a third-party collector with higher recycling rate boosts the total profit of the decentralized setting with a TPC. The centralized model, with a single decision maker, results in lower retail prices and higher collection rates compared to the decentralized models thereby commanding a higher overall profit.

Uncertain Commuters Assignment Through Genetic Programming Hyper-Heuristic

Traffic assignment problem (TAP) is of great significance for promoting the development of smart city and society. It usually focuses on the deterministic or predictable traffic demand and the vehicle traffic assignment. However, in the real world, traffic demand is usually unpredictable, especially the foot traffic assignment inside buildings such as shopping malls and subway stations. In this work, we consider the dynamic version of TAP, where uncertain commuters keep entering the traffic network constantly. These dynamically arriving commuters bring new challenges to this problem where planning paths for each commuter in advance is incompetent. To address this problem, we propose a genetic programming (GP) hyper-heuristic method to assign uncertain commuters in real-time. Specifically, a low-level heuristic rule called reactive assignment strategy (RAS) is proposed and is evolved by the proposed method. All commuters obey the same strategy to route themselves based on their local observations in a traffic network. Through training based on a designed heuristic template, all commuters will have the ability to find their appropriate paths in real-time to maximize the throughput of the traffic network. This decentralized control mechanism can address dynamically arriving commuters more efficiently than centralized control mechanisms. The experimental results show that our method significantly outperforms the state-of-the-art methods and the evolved RAS has a certain generalization ability.

Inland port and waterway capacity expansion model under demand uncertainty

We address the inland port and waterway capacity expansion (IPWCE) problem under demand uncertainty, the purpose of which is to determine the capacity expansion scales and timings for inland ports and waterways. To achieve this goal, we first build an inland waterway multimodal network (IWMN) that consists of physical and operational multimodal networks. Second, by viewing the IPWCE problem under deterministic demand as a subproblem of the IPWCE problem under uncertain demand, we develop a model for IPWCE under deterministic demand (IPWCEDD) based on bilevel programming and a model for IPWCE under uncertain demand (IPWCEUD) based on network real options theory. Third, we propose a sensitivity analysis-based descent search (SADS) algorithm to solve the IPWCEDD model. Moreover, in accordance with the optimal solutions of the IPWCEDD model, we then develop a least squares Monte Carlo simulation (LSM) method to solve the IPWCEUD model. Finally, we verify the effectiveness, efficiency, and applicability of the proposed models as well as the solution algorithm and methods through experiments of two different scales. The results of the small-scale experiment indicate that the proposed SADS algorithm and LSM method can solve the models optimally within the time limit. The large-scale experiment, which is conducted on the Yangtze River IWMN of mainland China, shows that capacity expansions at Chongqing Port, Nanjing Port, and Wuhan Port and on the waterway links connecting these ports can yield the maximum increased option values for the IPWCE problem under demand uncertainty. Moreover, the corresponding optimal expansion timing for implementing the capacity expansion plan is in the second year. Our research outcomes can help to guide IPWCE under demand uncertainty and further establish a high-quality inland river transport system.

Modeling of effective management of logistics supply of an industrial enterprise

Introduction. The economy and industry, which show a tendency to grow even in wartime, will require improved logistics and improved infrastructure. The implementation of such measures is based on scientifically based solutions in the effective management of high-tech (HT) production within the logistics management of integrated supply chains. The purpose of the paper is to determine an effective approach to inventory management at a high-tech industrial enterprise within the framework of developing a scientifically based inventory management strategy using the analysis of existing models. Results. The paper presents an analysis of the main models of operational inventory management of a high-tech enterprise: a single-product statistical model with deterministic demand, a model in the case of accounting for unsatisfied requirements, a model of inventory management based on random demand, a model in the case of loss of unsatisfied requirements, a model of a production system with periodic checks in case of random demand. It is emphasized that inventory management consists in establishing the moments and volumes of the order for their occupancy and distribution along the chains of the supply subsystem within the framework of strategic management. There is an orientation towards cost minimization. The whole inventory management process is imagined as a component of the supply-production-marketing system, which is managed on the basis of a complex logistics approach.Accounting for the features of each subsystem - supply, production, sales, as well as optimal management of resources, is based on cost minimization and leads to high-quality satisfaction of demand for ready-made innovative products with sufficient economic effect. Conclusion. Inventory management consists in establishing the moments and volumes of the order for their filling and distribution among the links of the supply subsystem. The listed inventory management models are intended for practical use, others are of interest because they allow you to understand the essence and identify the main properties of the inventory management system. Accounting for the specifics of each subsystem (supply, production, sales), as well as competent management of their resources, flows (financial, material, information), based on cost minimization, ultimately leads to the main goal of the IT of an industrial enterprise - high-quality satisfaction of demand for finished products with maximum economic effect.

Textile and apparel supply chain coordination under ESG related cost-sharing contract based on stochastic demand

In recent years, heightened attention has been given to the challenges of sustainable development precipitated by environmental pollution in the Textile and Apparel (TA) industry. The burgeoning demand for fast fashion, often reliant on cheap and environmentally unsustainable textiles, exacerbates this environmental degradation. To facilitate a harmonized and sustainable progression of the entire TA industry, this study employs the Stackelberg game model to investigate the prerequisites for establishing Environmental, Social, and Governance (ESG) related cost-sharing contracts and their consequential effects on supply chain coordination. Specifically, the paper compares four distinct supply chain models under two conditions: whether market demand is stochastic or deterministic. Through this comparative analysis, the study finds that the ESG related cost-sharing contracts bring more profit to the textile and apparel supply chain (TASC) in deterministic and stochastic demand, which effectively mitigates the risks associated with unpredictable demand. Numerical results indicate that the ESG cost-sharing contract significantly improves TASC's ESG performance with customers' sustainable awareness increasing. Furthermore, such contracts are instrumental in enhancing the aggregate ESG environmental performance of the Textile and Apparel Supply Chain (TASC), elevating profits for both manufacturers and retailers and alleviating the impact of fluctuating demand on supply chain participants.

Multi-layered perceptron network for short-term load forecasting

The use of the multi-layer perceptron (MLP) network for short-term load forecasting is performed. Through weather and load data from the Hydro-Quebec database, capabilities, advantages, and limitations of this artificial intelligence method in load forecasting are investigated. Current management tools for energy systems are based on deterministic optimization methods, where supply, demand, and production are assumed to be known. Changes in electricity supply and demand have made their adjustment more complex. It is no longer a question of adjusting centralized production to demand, but rather of adjusting centralized production, decentralized production, and production from decentralized storage facilities. Our approach will be based on a predictive optimization method adapted to energy systems. An artificial neural network is applied to forecast load for Mascouche in Quebec, Canada. It is about a part of the Hydro-Quebec’s grid where the maximum capacity is 140 megawatts.

Burst-Aware Time-Triggered Flow Scheduling With Enhanced Multi-CQF in Time-Sensitive Networks

Deterministic transmission guarantee in time-sensitive networks (TSN) relies on queue models (such as CQF, TAS, ATS) and resource scheduling algorithms. Thanks to its ease of use, the CQF queue model has been widely adopted. However, the existing resource scheduling algorithms of CQF model only focus on periodic time-triggered (TT) flows without consideration of bursting flows. Considering that the bursting flows often carry high-priority data in real systems, in this paper we investigate the mixed-flow (i.e., TT and bursting flows) scheduling problem in CQF-based TSN aiming to maximize the number of schedulable flows and system load balance while satisfying the deterministic demands of delay, jitter, and reliability for both TT and bursting flows. Unfortunately, it is challenging to schedule the mixed flows with the original CQF model because of the huge difference between TT and bursting flows. To resolve this problem, we firstly design an enhanced Multi-CQF model to satisfy the basic demands of bursting flows sent at any time without affecting the deterministic transmission of TT flows. Given the complexity of mixed-flow scheduling and the proposed queue model, it is difficult for traditional algorithms to fully utilize network resources. Thus, we further propose a time-correlated DRL resource scheduling (TimeDRS) algorithm to optimize the resource allocation. TimeDRS can be extended to other time-related resource scheduling scenarios, such as TDMA-based scheduling. Experimental results demonstrate that our proposed approaches can greatly reduce frame loss and end-to-end latency for bursting flows, and well balance runtime and schedulability compared with state-of-the-art benchmarks.

Optimal Core Acquisition and Remanufacturing Decisions With Discrete Core Quality Grades

The acquisition of used products (cores) is essential for leveraging the advantages of remanufacturing. Due to limited historical information about cores, it is difficult for the remanufacturers to accurately assess the quality of cores before disassembly and inspection. In this article, we investigate the joint acquisition and remanufacturing problem with a discrete empirical distribution. Under both deterministic and stochastic demands, two integer programming models are developed to obtain operational rules for making optimal decisions. Since the discrete empirical distribution is assumed to be the nominal distribution or asymptotic distribution of the true quality, the error caused by the difference between the estimated discrete empirical distribution and the true distribution cannot be neglected. Thus, we evaluate the error using the Phi-divergence measure, and the corresponding effects of this difference on the resultant acquisition and remanufacturing rules are analyzed. Through numerical examples, we observe that optimal acquisition and remanufacturing decisions are negatively affected by the difference between the estimated distribution and the true distribution, even if the estimated distribution can pass a hypothesis test. Furthermore, to overcome suboptimal outcomes, a multisource information fusion approach is proposed, which can utilize quality information collected from multiple sources to make accurate acquisition and remanufacturing decisions.

Optimal capacity allocation for high-speed railway express delivery

This study investigates the potential of implementing express delivery services within specified time windows on the high-speed railway (HSR) and optimizes the train capacity allocation scheme for HSR express delivery (HSReD). We first propose an integer linear programming (ILP) model for the deterministic demand case to maximize the profit of the HSReD operation (revenue minus transportation cost, loading/unloading costs, and the penalty incurred due to schedule delays). Then, a two-stage stochastic programming model is developed to account for the stochastic demand case, with the objective of maximizing the expected profit. To facilitate the solution process, the two-stage stochastic programming model is transformed into an equivalent nonlinear model, which is further reformulated into an equivalent integer linear programming (EILP) model that can be solved by commercial solvers. Finally, the proposed method is applied on a small toy network, Nanjing-Hangzhou HSR network and Beijing-Shanghai HSR network to illustrate its efficacy.

Incorporating product decay during transportation and storage into a sustainable inventory model

With the increased attention to global warming, governments set new policies for companies to control greenhouse gas (GHG) emissions. Therefore, supply chain decision-making should consider both costs and emissions of main logistics activities such as production, storage, and transportation. It is especially important for perishable goods, as the decay of products brings additional economic and environmental challenges for production, storage, and distribution operations. Most research on inventory models for perishable products focuses on minimizing the total cost and ignores emissions. There are a few papers that consider both costs and emissions. However, since they ignore product decay during transportation, they do not fully support real-life decision-making on perishable products. This paper presents a sustainable inventory model for a perishable product with deterministic demand. Our model is the first to consider product decay during transportation explicitly. Therefore, it can assess different transportation alternatives with different costs, emissions, and lead times to select the most sustainable and cost-efficient option. It is also the first to integrate the emissions of production, inventory holding, transportation, and disposal in making transportation mode selection and inventory control decisions. The model is solved analytically, and numerical experiments show that taking product decay during transportation into account leads to different optimal solutions than those proposed by existing models, which neglect product decay during transportation. Finally, we perform sensitivity analyses to show the impact of key parameters on the improvement potential of incorporating product decay during transportation.

The predictive management in campus heating system based on deep reinforcement learning and probabilistic heat demands forecasting

As a promising technology for replacing the rule-based decision-making in region heating systems (RHS), deep reinforcement learning (DRL) is a practical solution to identify the optimal control for heating equipment. However, as residential customers perform more casual energy-consumption behaviors, the intermittency and volatility of heat demands make managing heat supply and storage much harder for DRL agents. This study proposes a novel predictive management method for campus heating systems (CHS) with air-source heat pumps (AHP) and thermostatic water tanks. The novelty of the proposed method lies in the combination of the heat demands forecasting model and DRL-based adaptively controlling for heat supply equipment, which is firstly proposed to improve the heating supply reliability and reduce the storage dependence for CHS. Specifically, an enhanced rule, namely minimum length hamming encoding, and an input array constructing method is introduced to deal with discrete feature data and then improve the accuracy of deterministic heat demands forecasting based on long-short term memory (LSTM), and the Kernel density estimation (KDE) are employed to obtain the prediction intervals (PIs) from H-step ahead heat demands forecasting series. Followed by these, the twin delayed deep deterministic policy gradient, a model-free DRL control algorithm, is adopted for adaptively adjusting the output flow rate of AHP and then the storage of the hot water tank. To demonstrate the validity of the proposed method, a case study is presented where a campus heat demands forecasting achieves a maximum accuracy gain of 4.52%, and an optimal AHP operating controlling determined from PIs achieves a better cost reduction and supply reliability, which is superior over the conventional method using real-time heat demands or deterministic forecasting results as input.

Multi-item dynamic lot sizing with multiple transportation modes and item fragmentation

This paper addresses a tactical joint inventory and transportation planning problem for multiple items with deterministic and time-varying demand, considering different transportation modes and item fragmentation. The latter corresponds to the splitting of the same item ordered quantity between several trucks or containers. On the one hand, fragmenting the items potentially reduces the number of containers used. On the other hand, loading the item lot fragments on several containers may negatively impact the handling and shipping operations. This new problem is proposed as a way to tackle such conflict. Several Mixed Integer Linear Programming models are proposed for the problem, which rely on two multi-item lot-sizing models with mode selection and two bin-packing models with item fragmentation. A relax-and-fix heuristic is also proposed. Using realistic instances, computational experiments are first conducted to identify the most efficient model in terms of computational time, to study the impact of key parameters on the computational complexity and to analyze the efficiency of the heuristic. Then, managerial insights are derived through additional computational experiments, in particular, to identify contexts requiring joint optimization of lot-sizing and bin-packing decisions, as well as the impact of item fragmentation constraints. Directions for future research are finally proposed.

Managing supply chain risks with dual sourcing: Bayesian learning of censored supply capacity

Dual sourcing is a common strategy for mitigating supply chain risks, with supply capacity uncertainty being one of the most significant risks. However, firms often have limited knowledge about uncertain supply capacity, and can only observe it when the delivered quantity is less than the ordered amount. This leads to censored supply capacity observations. To investigate how supply capacity learning affects dual-sourcing decisions, we propose a model of a firm sourcing non-storable substitute products from an expensive reliable supplier and an inexpensive unreliable supplier to meet a deterministic time-varying demand over a finite horizon. The unreliable supplier has a random capacity with an unknown parameter. The firm updates its belief about this parameter using Bayesian learning and adapts its sourcing decisions to balance the tradeoff between maximizing current profits based on its current belief (exploitation) and increasing the precision of its belief for future periods (exploration). We use Bayesian dynamic programming to determine the firm’s myopic sourcing policy and partially characterize its optimal sourcing policy. We apply a state space reduction technique to Weibull distributed capacity, resulting in an inductively solvable optimization problem. The optimal sourcing policy can be obtained under a condition that ensures splitting the demand between the suppliers is optimal. For exponentially distributed capacity, the optimization problem has a recursive closed-form solution, and the optimal sourcing policy is such that the optimal order quantity from the reliable (unreliable) supplier is smaller (greater) than the myopic quantity. We complement our analytical results with numerical examples and discuss extensions to random demand and inventory carryover.