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Robust optimization has come out to be a potent approach to study mathematical problems with data uncertainty. We use robust optimization to study a nonsmooth nonconvex mathematical program over cones with data uncertainty containing generalized convex functions. We study sufficient optimality conditions for the problem. Then we construct its robust dual problem and provide appropriate duality theorems which show the relation between uncertainty problems and their corresponding robust dual problems.

In this paper, we introduce inertial Tseng’s extragradient algorithms combined with normal-S iteration process for solving variational inequality problems involving pseudo-monotone and Lipschitz continuous operators. Under mild conditions, we establish the weak convergence results in Hilbert spaces. Numerical examples are also presented to show that faster behaviour of the proposed method.

In this paper, a deterministic heuristic method is developed for obtaining an initial solution to an extremely large-scale capacitated vehicle routing problem (CVRP) having thousands of customers. The heuristic has three main objectives. First, it should be able to withstand the computational and memory problems normally associated with extremely large-scale CVRP. Secondly, the outputs should be reasonably accurate and should have a minimum number of vehicles. Finally, it should be able to produce the results within a short duration of time. The new method, based on the sweep algorithm, minimizes the number of vehicles by loading the vehicles nearly to their full capacity by skipping some of the customers as and when necessary. To minimize the total traveled distance, before the sweeping starts the customers are ordered based on both the polar angle and the distance of the customer from the depot. This method is tested on 10 sets of standard benchmark instances found in the literature. The results are compared with the results of the CW100 method by Arnold et al. [Comput. Oper. Res. 107 (2019) 32–42]. The results indicate that the new modified sweep algorithm produces an initial solution with a minimum number of vehicles and with reasonable accuracy. The deviation of the output from the best-known solution (BKS) is reasonable for all the test instances. When compared with the CW100 the modified sweep provides a better initial solution than CW100 whenever the capacity of the vehicle is more and the depot is located eccentrically. The heuristic does not face any memory problems normally associated with the solving of an extremely large-scale CVRP.

This paper addresses the Multi-Skill Resource-Constrained Project Scheduling Problem with Transfer Times (MSRCPSP-TT). A new model has been developed that incorporates the presence of transfer times within the multi-skill RCPSP. The proposed model aims to minimize project’s duration and cost, concurrently. The MSRCPSP-TT is an NP-hard problem; therefore, a Multi-Objective Multi-Agent Optimization Algorithm (MOMAOA) is proposed to acquire feasible schedules. In the proposed algorithm, each agent represents a feasible solution that works with other agents in a grouped environment. The agents evolve due to their social, autonomous, and self-learning behaviors. Moreover, the adjustment of environment helps the evolution of agents as well. Since the MSRCPSP-TT is a multi-objective optimization problem, the Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS) is used in different procedures of the MOMAOA. Another novelty of this paper is the application of TOPSIS in different procedures of the MOMAOA. These procedures are utilized for: (1) detecting the leader agent in each group, (2) detecting the global best leader agent, and (3) the global social behavior of the MOMAOA. The performance of the MOMAOA has been analyzed by solving several benchmark problems. The results of the MOMAOA have been validated through comparisons with three other meta-heuristics. The parameters of algorithms are determined by the Response Surface Methodology (RSM). The Kruskal–Wallis test is implemented to statistically analyze the efficiency of methods. Computational results reveal that the MOMAOA can beat the other three methods according to several testing metrics. Furthermore, the impact of transfer times on project’s duration and cost has been assessed. The investigations indicate that resource transfer times have significant impact on both objectives of the proposed model.

Let ℋ be a family of graphs. An ℋ-packing of a graph G is a set {G1, G2,…,Gk} of disjoint subgraphs of G such that each Gj is isomorphic to some element of ℋ. An ℋ-packing of a graph G that covers the maximum number of vertices of G is called a maximum ℋ-packing of G. The ℋ-packing problem seeks to find a maximum ℋ-packing of a graph. Let i be a positive integer. An i-star is a complete bipartite graph K1,i. This paper investigates the ℋ-packing problem with H being a family of stars. For an arbitrary family 𝒮 of stars, we design a linear-time algorithm for the 𝒮-packing problem in trees. Let t be a positive integer. An ℋ-packing is called a t+-star packing if ℋ consists of i-stars with i ≥ t. We show that the t+-star packing problem for t ≥ 2 is NP-hard in bipartite graphs. As a consequence, the 2+-star packing problem is NP-hard even in bipartite graphs with maximum degree at most 4. Let T and t be two positive integers with T > t. An ℋ-packing is called a T\t-star packing if ℋ={K1,1,K1,2,…,K1,T}\{K1,t}. For t ≥ 2, we present a t/t+1-approximation algorithm for the T\t-star packing problem that runs in 𝒪(mn1/2) time, where n is the number of vertices and m the number of edges of the input graph. We also design a 1/2-approximation algorithm for the 2+-star packing problem that runs in 𝒪(m) time, where m is the number of edges of the input graph. As a consequence, every connected graph with at least 3 vertices has a 2+-star packing that covers at least half of its vertices.

A Golomb Ruler (GR) is a set of integer marks along an imaginary ruler such that all the distances of the marks are different. Computing a GR of minimum length is associated to many applications (from astronomy to information theory). Although not yet demonstrated to be NP-hard, the problem is computationally very challenging. This brief note proposes a new continuous optimization model for the problem and, based on a given theoretical result and some computational experiments, we conjecture that an optimal solution of this model is also a solution to an associated GR of minimum length.

In automobile and household appliances, the manufacturer’s decision to offer retailer rebates to retailers or delayed incentives directly to end customers is very important. Under game theoretic environment, we show that delayed incentive is an important tool not only for price discrimination but it also provides more flexibility to the manufacturer. We differentiate the impact of delayed incentives and retailer rebates. We draw implications for optimal rebate strategies for both retailer rebates and delayed incentives. We also discuss delayed incentives in the form coupons that give more control to the manufacturer, whereas retailer rebates require retailer’s participation. Analysis and numerical insights show that the manufacturer prefers better observance of retail price. We provide a decision rule to the manufacturer on how to select the rebate type based on customer heterogeneity.

With the continuous deterioration of the environment and the improvement of consumer green awareness, more and more producers began to launch green products. For example, many automobile companies began to produce new energy vehicles. However, whether a new product can be successfully introduced to the market depends not only on the product’s quality improvement, but also on its sales channels. In this paper, we model a supply chain composed of a manufacturer and two asymmetric retailers to analyze how the retailers’ strategic decisions affect the introduction of a newer green product. Backward induction is adopted to survey the dynamic decisions of the supply chain members. Given the leading retailer’s product choice, the follower-up retailer’s product choices and decision optimums are defined by specific thresholds of consumer green valuation and production costs. Results show that the follower-up retailer would make completely different responses within a same threshold range when the leading retailer takes different product decisions. In other words, even if the leading retailer chooses green new products, the follower will not necessarily imitate the choice of green products, and it could be more advantageous to choose the old generation products (for price competition). Furthermore, results show that green product introduction does not necessarily bring Pareto improvement to both the two retailers. Finally, we derive the specific intervals in which green products can be successfully introduced into the market. Our modelling work and results provide instructive managerial insights on green product introduction in a retailer led supply chain.

In this paper, the uniform price and discriminative price methods are compared in the carbon auction market using multi-agent Q-learning. The government and different firms are considered as agents. The government as auctioneer allocates initial permits in the carbon auction market, and the firms as bidders compete with each other to obtain a larger share of the auction. The carbon trading market, penalty, reserve price, and bidding volume limitation are considered. The simulation analysis demonstrates that bidders have different behavior in two pricing methods under different amounts of carbon permits. In the uniform price, the value of bidding volume, firms’ profit, and the trading volume for low permits and the value of the government revenue, clearing price, the trading price, and auction efficiency for high permits are greater than ones in the discriminative price method. Bidding prices have a higher dispersion in the uniform price than the discriminative price method for different amounts of carbon permits.

Discrete-time queueing models find a large number of applications as they are used in modeling queueing systems arising in digital platforms like telecommunication systems and computer networks. In this paper, we analyze an infinite-buffer queueing model with discrete Markovian arrival process. The units on arrival are served in batches by a single server according to the general bulk-service rule, and the service time follows general distribution with service rate depending on the size of the batch being served. We mathematically formulate the model using the supplementary variable technique and obtain the vector generating function at the departure epoch. The generating function is in turn used to extract the joint distribution of queue and server content in terms of the roots of the characteristic equation. Further, we develop the relationship between the distribution at the departure epoch and the distribution at arbitrary, pre-arrival and outside observer’s epochs, where the first is used to obtain the latter ones. We evaluate some essential performance measures of the system and also discuss the computing process extensively which is demonstrated by some numerical examples.

Data Envelopment Analysis (DEA) is a popular non-parametric technique for the assessment of efficiency of a set of homogeneous decision making units (DMUs) with the same set of inputs and outputs. In the conventional DEA models, it is assumed that all variables are fully controllable. However, in the real-world applications of DEA, some of the variables are completely uncontrollable or partially controllable. In this paper, we are concerned about partially controllable variables which are called semi-discretionary variables. In DEA models, in the presence of semi-discretionary variables, decision makers have partial control on these variables and the proportional changes are possible to some extent. Previous DEA models with semi-discretionary variables consider a certain level of control on the variables which is fixed and it is given by decision makers or a higher authority. Since this level is usually given by experts, it is possible that in some cases all experts may not come up with an agreement, so in this paper we consider variable instead of fixed level of control on each semi-discretionary variable. In the presence of semi-discretionary variables, the proportional changes in inputs and out-puts may not be feasible and as a result the obtained target value by conventional DEA models is not achievable for an inefficient DMU. Thus, we propose a bi-objective model to evaluate DMUs when modifying a variable to its target value should be managed by decision makers in a voting system. One of the advantages of the proposed model is including decision making conditions directly into a DEA model.

We study multitasking scheduling and due-window assignment problems in a single machine, which can be found in various application domains. In multitasking environment, unfinished job always interrupts in-processing job. In common due window assignment, the aim is to find optimal due window to minimise the value of the earliness and tardiness penalty. In this paper, we study two problems, where the objective of the first problem is minimise the earliness, tardiness, due-window starting time, and due-window size costs, the objective of the second problem is minmax common due-date with completion time penalty, then we obtain some analytical properties and provide polynomial time solutions. Finally, the experimental results show that the proposed methods are effective.

Made available in DSpace on 2022-04-28T19:41:03Z (GMT). No. of bitstreams: 0 Previous issue date: 2021-05-01 The purpose of this paper is to propose mathematical models to represent a lot sizing and scheduling problem on multiple production lines that share scarce resources and to investigate the computational performance of the proposed models. The main feature that differentiates this problem from others in the literature is that the decision on which lines to organize should be taken considering the availability of the necessary resources. The optimization criterion is the minimization of the costs incurred in the production process (inventory, backlogging, organization of production lines, and sequence-dependent setup costs). Nine mixed integer optimization models to represent the problem are given and, also, the results of an extensive computational study carried out using a set of instances from the literature. The computational study indicates that an efficient formulation, able to provide high quality solutions for large sized instances, can be obtained from a classical model by making the binary production variables explicit, using the facility location reformulation as well as the single commodity flow constraints to eliminate subsequences. Moreover, from the results, it is also clear that the consideration of scarce resources makes the problem significantly more difficult than the traditional one. Instituto de Matemática Ufms - Universidade Federal de Mato Grosso Do sul Instituto de Ciâncias Matemáticas e de Computação Usp - Universidade de São Paulo Departamento de Matemática Unesp - Universidade Estadual Paulista Departamento de Matemática Unesp - Universidade Estadual Paulista

This paper investigates the effects of investment and inspection policies on an integrated production–inventory model involving defective items and upstream advance-cash-credit payment provided by the supplier. In this model, retailers offer customers a downstream credit period. Furthermore, the defective rate of the item can be improved through capital co-investment by the supplier and retailer. The objective of this study was to determine the optimal shipping quantity, order quantity, and investment alternatives for maximizing the supply chain’s joint total profit per unit time. An algorithm was developed to obtain the optimal solution for the proposed problem. Several numerical examples are used to demonstrate the proposed model and analyze the effects of parameters changes on the optimal solutions. Finally, management implications for relevant decision makers are obtained from the numerical examples.

In the integrated uncapacitated lot sizing and bin packing problem, we have to couple lot sizing decisions of replenishment from single product suppliers with bin packing decisions in the delivery of client orders. A client order is composed of quantities of each product, and the quantities of such an order must be delivered all together no later than a given period. The quantities of an order must all be packed in the same bin, and may be delivered in advance if it is advantageous in terms of costs. We assume a large enough set of homogeneous bins available at each period. The costs involved are setup and inventory holding costs and the cost to use a bin as well. All costs are variable in the planning horizon, and the objective is to minimize the total cost incurred. We propose mixed integer linear programming formulations and a combinatorial relaxation where it is no longer necessary to keep track of the specific bin where each order is packed. An aggregate delivering capacity is computed instead. We also propose heuristics using different strategies to couple the lot sizing and the bin packing subproblems. Computational experiments on instances with different configurations showed that the proposed methods are efficient ways to obtain small optimality gaps in reduced computational times.

Motivated by the practices that many small and middle-sized enterprises (SME) retailers have financial constraints due to their limited budget and financing access, this paper studies the manufacturer’s financial strategy (i.e., trade credit versus vertical merger with a capital-constrained retailer) in a supply chain with two financial asymmetric retailers. We first compare the equilibrium profits under different financing modes and find that if manufacturer’s capital cost under trade credit or administrative cost under vertical merger is below a certain threshold, the manufacturer should finance instead of deselect the capital-constrained retailer even though the competition is intensified. Furthermore, manufacturer can choose a financing strategy based on the tradeoff between financing value and cost from trade credit or vertical merger. Under trade credit, the increased horizontal competition intensity is against the capital-constrained retailer while with vertical merger the competition intensity is harmful to the capital-abundant retailer. In addition, through investigating the impact of different financial modes on the equilibrium profits of the supply chain players, we find that whether trade credit can outperform vertical merger for both the manufacturer and the capital-constrained retailer depends on horizontal competition intensity, profit-sharing proportion and administrative cost of vertical merger. Moreover, the capital-abundant retailer will get the lowest profit when other participators act like an alliance. Our study provides a roadmap for the manufacturer to make a financing policy for capital-constrained retailer who competes with a funded retailer.

As of 21st century, the terms of efficiency and productivity have become notions which dwells on both business and academic world more frequently compared to past. It is known that it is hard to increase the efficiency and productivity of both production and service systems. In this study, the efficiency analysis of the branches of a bank was conducted. Furthermore, a Weighted Stochastic Imprecise Data Envelopment Analysis (WSIDEA), which is a new approach developed based on Data Envelopment Analysis (DEA), was proposed. Efficiency levels and results of decision-making units were examined according to the proposed new method. Additionally, six different DEA model results are obtained. The results of the six different DEA model and the proposed “WSIDEA” model were compared in terms of efficiency level of decision-making units, and the differences between them were examined. Sensitivity of the inefficient units were also examined. On the other hand, unrealistic efficiency levels created by traditional methods for branches were also analyzed. Apart from all these sensitivity analyses, the sensitivity of the data set used in the analysis is scrutinized.

In this paper, we consider a class of interval-valued variational optimization problem. We extend the definition of B-(p, r)-invexity which was originally defined for scalar optimization problem to the interval-valued variational problem. The necessary and sufficient optimality conditions for the problem have been established under B-(p, r)-invexity assumptions. An application, showing utility of the sufficiency theorem in real-world problem, has also been provided. In addition to this, for the interval-optimization problem Mond–Weir and Wolfe type duals are presented and related duality theorems have been proved. Non-trivial examples verifying the results have also been presented throughout the paper.

The distance spectral radius of a connected graph is the largest eigenvalue of its distance matrix. In this paper, we give several less restricted graft transformations that decrease the distance spectral radius, and determine the unique graph with minimum distance spectral radius among home-omorphically irreducible unicylic graphs on n ≥ 6 vertices, and the unique tree with minimum distance spectral radius among trees on n vertices with given number of vertices of degree two, respectively.

Data envelopment analysis (DEA) measures the efficiency score of a set of homogeneous decision-making units (DMUs) based on observed input and output. Considering input-oriented, the inverse DEA models find the required input level for producing a given amount of production in the current efficiency level. This article proposes a new form of the inverse DEA model considering income (for planning) and budget (for finance and budgeting) constraints. In contrast with the classical inverse model, both input and output levels are variable in proposed models to meet income (or budget) constraints. Proposed models help decision-makers (DMs) to find the required value of each input and each output’s income share to meet the income or budget constraint. We apply the proposed model in the efficiency analysis of 58 supermarkets belonging to the same chain. However, these methods are general and can be used in the budgeting and planning process of any production system, including business sectors and firms that provide services.

This paper presents a Greedy Randomized Adaptive Search Procedure (GRASP) for the Prize-Collecting Covering Tour Problem (PCCTP), which is the problem of finding a route for traveling teams that provide services to communities geographically distant from large urban locations. We devised a novel hybrid heuristic by combining a reactive extension of the GRASP with Random Variable Neighborhood Search (VND) meta-heuristic for the purpose of solving the PCCTP. Computational experiments were conducted on a PCCTP benchmark from the literature, and the results demonstrate our approach provides a significant improvement in solving PCCTP and comparable with the state-of-the-art, mainly regarding the computational processing time.

The present paper proposes an integrated production–distribution planning approach for a textile and apparel supply chain. Tactical and operational decisions are considered in the proposed multi-product and multi-period planning problem. Using a rolling horizon, the approach aims at defining optimal quantities to produce, to store and to deliver. The integration consists in coordinating informational flows between producer and retailer. Information sharing will allow the producer to estimate more accurately the future replenishment orders that may happen at the operational level and adjust production capacity requirements accordingly. For this purpose, a two-stage planning approach is devised; the first stage deals with the tactical level while the second stage deals with the operational level. The monthly decisions taken at the tactical planning level are accounted for in the operational planning considering a variable rolling horizon. Moreover, accurate forecasts of future replenishment orders are established based on information sharing and introduced in the operational planning to determine the weekly decisions. Linear programming models are used to build production and distribution plans at the tactical and operational levels. Using real-life data from a textile and apparel Tunisian firm, we show that producer-retailer coordination based on the sharing of current sales information, yields significant cost savings reaching up to 20% of the supply chain cost. These findings can only motivate the partnership between producer and retailer through reliable information sharing in joint tactical-operational and production–distribution planning.

Consumers’ strategic purchasing behavior has a great influence on the pricing and sales of new products. In order to study the impact of strategic consumers on the sales of 5G mobile phones, we establish a two-period pricing model. The supply chain contains two manufacturers, a communications operator and a mobile phone retailer. Cases where two manufacturers have the same or different pricing rights are researched by using the Stackelberg game and the Nash game model. Our research results are as follows: (1) We obtain the optimal 5G communication fees in two periods and find out how they change with the proportion of consumers changing. (2) We figure out the profits of the supply chain in two periods and analyze them. We find that the communication operator earns more than the others most of the time. (3) We investigate how the proportion of strategic consumer impact on supply chain profits and conclude that the optimal price and demand in a period will decrease as the proportion of consumers who only purchase products in the other period increases

This paper considers a dual-channel closed-loop supply chain consisting of a manufacturer, a retailer and a collector in which the retailer possesses private demand information and determines whether to share his private information with other chain members. Specifically, we develop four information sharing models, namely no information sharing (Model C–R), the retailer sharing information with the manufacturer (Model C–R–M), the retailer revealing information to the collector (Model C–R–C), and the retailer disclosing information to both the manufacturer and the collector (Model C–R–T). We adopt the Stackelberg game to acquire the equilibrium strategies and examine the value of information sharing on chain members’ decisions. We find that, chain members will set the largest wholesale price, retail prices of direct and indirect channels when the retailer only shares information with the manufacturer and the highest return rate can be obtained in the case of the retailer only revealing information to the collector. We can also find that, information sharing is profitable to the manufacturer and the collector, while is detrimental to the retailer. The manufacturer, the collector and the retailer can reach the largest profits in Model C–R–T, Model C–R–C and Model C–R–M, respectively.

Nowadays many industry consider an interval time as a due date instead of precise points in time. In this study, the hybrid flow shop scheduling problem with basic blocking constraint is tackled. Where jobs, if done within a due window, are deemed on time. Therefore, the criterion is to minimize the sum of weighted earliness and tardiness. This variant of the hybrid flowshop problem is not investigated to the best of our knowledge. we introduced a new metaheuristic centered on the iterated greedy approach. to evaluate the proposed method we start by the re-implementation and the comparison of seven well-selected procedures that treat the hybrid flowshop problem. In order to prove the robustness of our method, we evaluated it using a new benchmark of more than 1000 instances. The experimental results demonstrated that the proposed algorithm is effective and produces a very high solution.

The topic of collecting public donations has always attracted the attention of charity Non-Governmental Organizations as their basic policy; nevertheless, despite its importance, not much scientific research has been conducted on the issue. The optimal location of electronic charity boxes is effective in optimizing the obtained benefits. In this paper, for the first time in the literature, a location problem is defined with the aim of maximizing people’s motivation for money donation. We propose a new model to find the optimal location of e-charity boxes across the city with an aim to maximize the total amount of received benefits, as well as the total amount of donation motivation. To reach this aim, the effective criteria on the amount of gathered donation in each district and in each location type are investigated separately. Then, considering some constraints of the problem, a new mathematical model is proposed in order to determine the optimal location of e-charity boxes. We solve the model using LP-Metric, SAW, and TOPSIS methods, as a combination of Multi-Objective and Multi-Attributes Decision Making methods. Besides, we run the model in a real case study and 80 final locations are specified as the optimal locations in the studied city.

In this paper, we analyze the optimal order-quantity decisions in a supply chain with mass customization (MC) manufacturer and overconfident retailers. First, we consider a newsvendor model in which an unbiased retailer sells mass customized products. The retailer needs to make order quantity decisions before the selling season. Meanwhile, the supplier is a mass customization manufacturer and implements modular production. The supply process is uncertain, as the real quantity the retailer received is the order quantity multiplied by a random yield rate. Second, two overconfident models are considered and theorems are proposed. In the first model, the behavioral bias of overconfidence only affects the retailer’s judgment of variance of market demand. In the second model, the behavior bias of overconfidence affects not only the retailer’s cognition of the variance of market demand, but also his cognition of the expectation of market demand. In addition, the relationship between the optimal decisions and the modularity level is obtained. Finally, we provide managerial insights for the decision makers of the retailers and the manufacturers on order quantity and modularity level, respectively.

In the article, a semi-infinite fractional optimization model having multiple objectives is first formulated. Due to the presence of support functions in each numerator and denominator with constraints, the model so constructed is also non-smooth. Further, three different types of dual models viz Mond-Weir, Wolfe and Schaible are presented and then usual duality results are proved using higher-order (K × Q) − (ℱ, α, ρ, d)-type I convexity assumptions. To show the existence of such generalized convex functions, a nontrivial example has also been exemplified. Moreover, numerical examples have been illustrated at suitable places to justify various results presented in the paper. The formulation and duality results discussed also generalize the well known results appeared in the literature.

Aiming at the attitude solution accuracy and robustness for small UAVs in complex flight conditions, this paper proposes a dynamic adaptive attitude and heading systems(AHRS) estimator with singular value decomposition Cubature Kalman filter(SVDCKF). Considering the problem of random bias for the low-cost attitude sensor, this paper designs a method that the sensor random bias is used as the state vector to eliminate the effect of the sensor random bias. Due to the non-linearity of small UAVs AHRS model and the non-positive definite phenomenon of the covariance matrix, a nonlinear AHRS filter combined with the Cubature Kalman filter and singular value decomposition is designed to improve the attitude solution accuracy. In addition, when the UAV flies in the different flight conditions, the three-axis acceleration of the attitude sensor will affect the attitude solution. Thus, a dynamic adaptive factor based on adaptive filtering is used to adjust continuously the acceleration noise variance to improve the robustness of the AHRS. The experimental results show that the method and algorithm proposed not only improve the attitude solution accuracy, and satisfy the flight requirements of small UAVs, but also eliminate the influence of the attitude sensor random bias and three-axis acceleration for the attitude solution to improve the proposed algorithm robustness and anti-interference.

The longest induced path problem consists in finding a maximum subset of vertices of a graph such that it induces a simple path. We propose a new exact enumerative algorithm that solves problems with up to 138 vertices and 493 edges and a heuristic for larger problems. Detailed computational experiments compare the results obtained by the new algorithms with other approaches in the literature and investigate the characteristics of the optimal solutions.

This paper investigates the quality and pricing decisions in a supply chain consists of one retailer and two manufacturers. The retailer updates the trust value to manufacturers based on the historical information of product quality to determine the actual order quantity. We propose four game models by considering two situations, i.e., manufacturer-dominant scenario and retailer-dominant scenario. Based on theoretical and numerical analysis, we obtain a series of valuable management insights. For example, when a manufacturer with unreliable product quality is the leader and competes with another reliable manufacturer, the retailer’s profit would eventually surpass that of two stronger manufacturers. When the retailer is the leader, the retailer’s profit is often greater when two manufacturers engage in the Stackelberg game rather than that in Bertrand game, and the manufacturer with unreliable product quality can make profit no less than that of another manufacturer with reliable quality.

Due to the hugely populated world, recycling of the used products has become the most significant perspective in e-commerce. The scientists have been exploring how increases the degree of recyclability and the green innovation level. This paper considers a supply chain with a manufacturer, a retailer, a supplier, and a collector. The manufacturer can increase or decrease the level of green innovation by changing the quality of raw materials. He sells them through his direct channel as well as the retailer’s traditional channel. The retailer enforces the strategy promotional effort for enlarging his market demand. After formulating the problem, the strategies in collector-led, supplier-led, collector–supplier Nash, and collector–supplier–retailer Nash game are studied under manufacturer Stackelberg games along with the centralized policy. The parameters’ sensitivity has been analyzed to the profits and decision variables and then draw significant managerial insights. The model declares the optimal strategies for each player as well as the chain. It is achieved that the higher level of green innovation and promotional effort always increases all the profit. The optimal pricing decisions be lowest under the Collector–Supplier Nash game.

To determine the optimal warehouse location, it is usually assumed that the collected data are uncontaminated. However, this assumption can be easily violated due to the uncertain environment and human error in disaster response, which results in the biased estimation of the optimal warehouse location. In this study, we investigate this possibility by examining these estimation effects on the warehouse location determination. Considering different distances, we propose the corresponding estimation methods for remedying the difficulties associated with data contamination to determine the warehouse location. Although data can be contaminated in the event of a disaster, the findings of the study is much broader and applicable to any situation where the outliers exist. Through the simulations and illustrative examples, we show that solving the problem with center of gravity lead to biased solutions even if only one outlier exists in the data. Compared with the center of gravity, the proposed methods are quite efficient and outperform the existing methods when the data contamination is involved.

This study introduces an inventory system with a non-instantaneous deteriorating product with credit facility and variable demand depending on the selling price. Two different selling prices are considered in the deterioration and non-deterioration periods. Shortages are partially backlogged and dependent on the length of the customers’ waiting time upto the arrival of fresh lot. Alternative trade-credit policy is applied herein, and several cases, sub-cases and situations are investigated. The corresponding optimization problems of different cases, sub-cases and situations are solved using an interval-oriented multi-section technique with the help of interval mathematics and interval order relations. A numerical example with three different credit periods is studied and solved to validate the said problem. Also, two different case studies are investigated. Then to investigate the effect of changes of several system parameters on the optimal policy, post optimality analyses are performed.

We propose a generalized second-order asymptotic contingent epiderivative of a set-valued mapping, study its properties, as well as relations to some second-order contingent epiderivatives, and sufficient conditions for its existence. Then, using these epiderivatives, we investigate set-valued optimization problems with generalized inequality constraints. Both second-order necessary conditions and sufficient conditions for optimality of the Karush–Kuhn–Tucker type are established under the second-order constraint qualification. An application to Mond–Weir and Wolfe duality schemes is also presented. Some remarks and examples are provided to illustrate our results.

We consider a capital-constrained contract-farming supply chain with a risk-averse farmer and a risk-neutral agro-dealer, where the farmer faces some yield uncertainty that can be covered by insurance. Using the Stackelberg model, we derive the optimal strategies on the insured level, production and wholesale price. The result shows that farmers with low risk aversion tend not to be insured, while those with high risk aversion tend to insure. Further analysis indicates that, as the degree of the farmer’s risk aversion increases, the farm size decreases, but the yield per unit area and the wholesale price of the agricultural product increases. In addition, yield insurance and premium subsidies can lead to a decrease of the yield per unit area. However, the expansion of the farm size can compensate for the inhibitory effect of the decrease of yield per unit area on the total yield, and thus the total yield increases. We also find that when the premium subsidy rate is low, the yield insurance’s value to farmers is negative. Moreover, the yield insurance’s value to farmers increases with respect to the bank’s interest rate.

In this article, an imperfect production inventory model consisting of a manufacturer and a retailer with quality improvement effort and the promotional effort sensitive demand pattern is investigated under a two-tier credit policy. We study the model for deteriorating items where the deterioration occurs at different rates in the manufacturer’s and the retailer’s level considering a fixed lifetime of the product. Discussing the six possible cases of credit policy analytically, we analyze the behavior of the model under an integrated system concerning production lot-size, quality effort and promotional effort such that the integrated average profit is maximum. To obtain the optimal solutions of the model, we design an operative solution algorithm. A numerical example is provided to test feasibility of the model, and the effect of the variation of the key parameters is also studied. The outcomes of this proposed model show that the manufacturer and the retailer have to be more careful about their offered credit periods in aspect of the profit. It is observed that the integrated profit is maximum when both credit periods provided by the manufacturer and the retailer belong to the manufacturer’s cycle. Moreover, we identify that the extended product lifetime does not meet with higher profit all times. This study directs that quality effort and promotional effort stimulate the market demand while it is not always economically profitable for the supply chain.

This note studies a unrelated parallel-machine scheduling problem with controllable processing times and job-dependent learning effects, where the objective function is to minimize the weighted sum of total completion time, total load, and total compression cost. We show that the problem can be solved in O(nm+2) time, where m and n are the numbers of machines and jobs. We also show how to apply the technique to several single-machine scheduling problems with total criteria.

A multistage stochastic capacitated discrete procurement problem with lead times, cancellation and postponement is addressed. The problem determines the procurement of a product under uncertain demand at minimal expected cost during a time horizon. The supply of the product is made through the purchase of optional distinguishable orders of fixed size with delivery time. Due to the unveiling of uncertainty over time it is possible to make cancellation and postponement corrective decisions on order procurement. These decisions involve costs and times of implementation. A model of the problem is formulated as an extension of a discrete capacitated lot-sizing problem under uncertain demand and lead times through a multi-stage stochastic mixed-integer linear optimization approach. Valid inequalities are generated, based on a conventional inequalities approach, to tighten the model formulation. Experiments are performed for several problem instances with different uncertainty information structure. Their results allow to conclude that the incorporation of a subset of the generated inequalities favor the model solution.

In the Business to Consumer (B2C) environment, it is important to alleviate the mismatch between delivery capacity and demand in the express delivery supply chain. To do this, we propose three contracts to improve supply chain performance: the advanced payment contract, penalty contract, and time insurance contract. To assess these contracts, we considered the supply chain of one e-retailer and one express delivery provider. We discussed which contract is better for the supply chain partners when the three contracts can coordinate the supply chain. We found that when its unit cost of delayed orders is lower, the e-retailer will choose the advance payment contract among three contracts. When its unit cost of delayed orders is medium, the e-retailer will opt for the time insurance contract. When its unit cost of delayed orders is high, the e-retailer will not choose the advanced payment contract. In this case, whether the e-retailer chooses the time insurance contract and penalty contract depends on the value of wholesale price.

The production and transportation of chemicals is a risky process with high-cost operations for members of the supply chain, where some of the materials deteriorate over time and deal with value-reduction challenges. This paper studies a two-stage hazardous chemicals supply chain with a supplier and a manufacturer in a finite time horizon with a constant deterioration rate for both sides. To prevent potential hazards and improve product quality, the manufacturer invests in risk reduction and quality improvement technologies that can also attract more market demand. Owing to the importance of time in the storage and production of chemical products, this study focuses on a novel lead-time based discount contract to coordinate the channel members. The contract seeks to maximize the total profit of the chain by determining the optimal lead-time and manufacturer’s technology level. By doing so, the supplier provides high-quality products and the manufacturer’s unit supplying cost reduces and can buy more chemicals from the supplier. On the other hand, the supplier will have more time to supply the product and its initial cost will be reduced. As a result, the profit of both sides increases simultaneously. Some numerical examples are applied to examine the applicability of the proposed models. Finally, several sensitivity analyses on the main parameters are conducted to extract some in-depth managerial implications.

This study contributes to the periodic review inventory system literature by: (1) investigating customer service level (CSL) as a social responsibility in pharmaceutical supply chains (PSCs) and (2) proposing supply chain contracting to achieve win–win coordination and guarantee a satisfied CSL. Specifically, considering the demand uncertainty as one of the main challenges faced by pharmacies, we analyze how applying contracts to coordinate the inventory policy of a pharmacy with that of its supplier can affect their profits and the CSL offered to society. Having shown the advantages of the centralization compared to the decentralization, we design a coordination scheme based on the quantity discount contract to encourage the players move towards centralization. Under the proposed scheme, we first obtain the minimum and maximum acceptable amounts of discount from each actor’s viewpoint. Then, we propose a benefit-sharing strategy in order to make the plan interesting to both sides. The proposed discount contract and benefit-sharing strategy distribute the extra profits equitably between the two participants according to their bargaining power, which can make a win–win condition for two actors. Our results suggest that coordinating review period and order-up-to-level of the retailer and replenishment multiplier of the supplier will be of benefit in terms of both economic profitability and social responsibility.

The nurse rostering problem refers to the assignment of nurses to daily shifts according to the required demand of each shift and day, with consideration for the operational requirements and nurses’ preferences. This problem is known to be an NP-hard problem, difficult to be solved using the known exact solution methods especially for large size instances. Mostly, this problem is modeled with soft and hard constraint, and the objective is set to minimize the violations for the soft constraints. In this paper, a new two-stage variable neighborhood search algorithm is proposed for solving the nurse rostering problem. The first stage aims at minimizing the violations of the soft constraints with the higher penalty weights in the objective function. While the second stage considers minimizing the total solution penalty taking into account all the soft constraint. The proposed algorithm was tested on the 24 benchmark instances of Curtois and Qu (Technical Report, ASAP Research Group, School of Computer Science, University of Nottingham (2014)). The test results revealed that the proposed algorithm is able to compete with the results of a recent heuristic approach from literature for most of the tested instances.

The role of medicines in health systems is increasing day by day. The medicine supply chain is a part of the health system that if not properly addressed, the concept of health in that community is unlikely to experience significant growth. To fill gaps and available challenging in the medicine supply chain network (MSCN), in the present paper, efforts have been made to propose a location-production-distribution-transportation-inventory holding problem for a multi-echelon multi-product multi-period bi-objective MSCN network under production technology policy. To design the network, a mixed-integer linear programming (MILP) model capable of minimizing the total costs of the network and the total time the transportation is developed. As the developed model was NP-hard, several meta-heuristic algorithms are used and two heuristic algorithms, namely, Improved Ant Colony Optimization (IACO) and Improved Harmony Search (IHS) algorithms are developed to solve the MSCN model in different problems. Then, some experiments were designed and solved by an optimization solver called GAMS (CPLEX) and the presented algorithms to validate the model and effectiveness of the presented algorithms. Comparison of the provided results by the presented algorithms and the exact solution is indicative of the high-quality efficiency and performance of the proposed algorithm to find a near-optimal solution within reasonable computational time. Hence, the results are compared with commercial solvers (GAMS) with the suggested algorithms in the small-sized problems and then the results of the proposed meta-heuristic algorithms with the heuristic methods are compared with each other in the large-sized problems. To tune and control the parameters of the proposed algorithms, the Taguchi method is utilized. To validate the proposed algorithms and the MSCN model, assessment metrics are used and a few sensitivity analyses are stated, respectively. The results demonstrate the high quality of the proposed IACO algorithm.

This paper studies a dual-channel supply chain composed of a retailer and a supplier, and discusses the optimal decisions of supply chain participants under decentralized decision-making without and with demand disruption, respectively. By comparing the optimal decisions in the two scenarios, we find that the optimal decision after demand disruption is a linear function of the demand disruption plus optimal decision before demand disruption. Additionally, when the demand disruption is in interval (−ψu2, ψu1), the optimal total production of the supply chain is equal before and after demand disruption. Moreover, the profits of the supply chain members and the value of their recognizing demand disruption are largely affected by the scale of demand disruption. Finally, the results show that the improved revenue-sharing contract can effectively improve the supply chain performance.

Conventional DEA models tend to allocate the fixed resources to multiple decision-making units (DMUs) and treat the allocated resource as an extra input for every single DMU. However, the existing DEA resource allocation (DEA-RA) methods are applicable exclusively to the DMUs with exact values of inputs and outputs. A lack of precision for the input or output data of DMUs, such as the interval data, would cause a failure of the existing methods to allocate resources to DMUs. In order to resolve this problem, three DEA-RA models are proposed in this paper for different scenarios of decision-making. All of the proposed DEA-RA models are based on a set of common weights. Finally, the proposed models are empirically tested and validated through three examples. As revealed by the results, our proposed models are capable of providing a more fair and practical initial allocation scheme for decision makers.

By constructing a dual-channel fresh agricultural product (FAP) supply chain consisting of a retailer and a supplier, this paper considers the effect of fresh-keeping level on the freshness of perishable products and constructs a time-varying demand function based on freshness. The operating cost of the internet channel to the supplier has also been considered in the model. Optimal pricing strategy and profits of supply chain members under dual channels are investigated respectively in this paper. Comparing the optimal profit under traditional single-channel and dual-channel supply chain, we obtain the condition that the internet operating cost should satisfy. Given the situation where the supplier obtains profit while the retailer loses after the supplier introduced the internet channel, this paper proposes a revenue-sharing contract to make up for the loss of the retailer and achieves a win–win situation. Research shows that in the numerical analysis the supplier’s and the retailer’s profit can only be improved when the operating cost of the internet channel c0 and revenue-sharing ratio ψ are within a certain range. When ψ ≥ 0.4 and $ 0\le {c}_0\le \sqrt{\frac{2.34{\psi }^2+1.25\psi +7.39}{8.43{\psi }^3+4.62{\psi }^2+5.72\psi +9.05}}+8.64$, Pareto improvement will be attained on both sides in the supply chain.

In this paper, a supply chain model between a manufacturing firm and a group of retailers has been developed. Manufacturing firm produces simultaneously both perfect and imperfect items which are separated by screening process. Then the perfect items are transferred to the retailers’ showroom/warehouse located in different places and a part of imperfect items are repaired by rework process. Retailers receive the products from the manufacturer with paying partial pre-payment to ensure the replenishment of order. On the other hand, the manufacturer provides partial free transportation facility to the retailers due to pre-payment. The corresponding problem has been formulated mathematically as a profit maximization problem and then solved it analytically. As an illustration of this supply chain model, three numerical examples have been considered and solved. Finally, post optimality analyses have been carried out to investigate the effects of changes of different parameters on the optimal policy.

We discuss some basic concepts and present a numerical procedure for finding the minimum-norm solution of convex quadratic programs (QPs) subject to linear equality and inequality constraints. Our approach is based on a theorem of alternatives and on a convenient characterization of the solution set of convex QPs. We show that this problem can be reduced to a simple constrained minimization problem with a once-differentiable convex objective function. We use finite termination of an appropriate Newton’s method to solve this problem. Numerical results show that the proposed method is efficient.

The fluctuations in the business environment and seasonal variations characteristic of food supply chains contribute greatly to the increasing complexity of the entire Supply Chain planning. In the present paper, quantitative models are applied to support the decision-making purchasing management department of a retail company. Specifically, a multiperiod mathematical model was developed with the aim of optimizing decision-making of the purchasing managers. The developed model consists of a multiperiod Mixed Integer Nonlinear Programming model, with the objective to minimize the ratio between how much is costing the company to move the products along the Supply Chain and the products’ costs. It is discussed how to order the product, what is the most advantageous storage mode and whether it is preferable to order once or twice a week. Real instances, provided by a Portuguese retail company, regarding the demand for one year are tested for two scenarii, which are used currently by the company. The results show that the proposed model can reduce, on both scenarios, the ratio between operational costs and merchandise costs, for almost all products, and therefore it can be an important tool for supporting decision-making of the purchasing manager.