Search

The Dynamic lot sizing (DLS) model is widely used in production planning, to minimize inventory levels, which basically will minimize production costs. The DLS model tries to eliminate the assumption of a fixed demand level throughout the period used in the Economic Order Quantity (EOQ) model. The characteristics of business processes in online retailers are the basis of this research to develop DLS models. This research develops a DLS model for retailers with multi-supplier cases, quantity discounts, and capacity constraints that consider Advanced Demand Information (ADI). Based on the numerical test results, it appears that ADI has an effect on reducing total production costs in the DLS model. The results of the numerical tests also showed that the model was able to solve the problems of the production planning process for SMEs and retailers who considered ADI.

The Dynamic lot sizing (DLS) model is widely used in production planning, to minimize inventory levels, which basically will minimize production costs. The DLS model tries to eliminate the assumption of a fixed demand level throughout the period used in the Economic Order Quantity (EOQ) model. The characteristics of business processes in online retailers are the basis of this research to develop DLS models. This research develops a DLS model for retailers with multi-supplier cases, quantity discounts, and capacity constraints that consider Advanced Demand Information (ADI). Based on the numerical test results, it appears that ADI has an effect on reducing total production costs in the DLS model. The results of the numerical tests also showed that the model was able to solve the problems of the production planning process for SMEs and retailers who considered ADI. [ABSTRACT FROM AUTHOR]

Lot sizing is a prevalent issue within manufacturing companies, where determining the optimal procurement and production lot sizes is crucial for maximizing profits. This problem has become more complex, given that numerous suppliers can provide the same raw materials with different prices and quantity discount schemes. A company should also determine optimal carriers to deliver materials to the company’s warehouse. In a manufacturing process, the company should determine the optimal production lot size and its schedules. In this paper, a model was developed to solve simultaneously procurement and production lot sizing, as well as production scheduling problems. The model encompasses multiple suppliers offering quantity discounts, aiming to maximize company profit by accounting for various costs, including procurement, production, inventory, and quality costs. A case study is taken from a company producing noodles and its related derivative products to illustrate the application of the model. Based on the optimization results, the company obtained a total profit of IDR. 14,656,550,000 or $950,921.30 (the exchange rate of $1 at IDR. 15,413). The sensitivity analysis results show that the objective function is sensitive to changes in the purchase cost, sale revenue, and discount rate parameters. The decision variables for accepted product demand, product quantity, and the starting and completion time of product family are only sensitive to changes in certain parameters. Meanwhile, the decision variables for product inventory, product backlog, raw material inventory, and purchased raw material quantity are sensitive to the changes in all the analyzed parameters.

A hedonic regression framework is proposed for evaluating the determinants of beer prices and consumer ratings. This study specifically addresses the endogeneity problem associated with the impact of consumer ratings on beer prices using a set of beer sensory and chemical characteristics as instrumental variables in the estimation procedure. The results suggest that beer prices tend to be influenced by consumer ratings and the objective characteristics of beers, while consumer ratings tend to be influenced by the sensory and chemical characteristics of beers. Also, limited evidence is found for the use of quantity discounts by beer producers. [ABSTRACT FROM AUTHOR]

Quantity discount is a frequently adopted scheme that has not been explicitly investigated in logistics service procurement auctions. This paper focuses on a revised winner determination problem under quantity discounts and demand uncertainty for a fourth-party logistics (4PL) provider in a combinatorial reverse auction. To characterize our research problem, a two-stage stochastic nonlinear programming model is constructed. Inspired by the idea of sample average approximation (SAA), the nonlinear model is reformulated as a deterministic mixed integer linear programming model by using a linearization technique with superior expressions. Since the reformulation has a large number of decision variables and constraints, we integrate SAA with a dual decomposition Lagrangian relaxation technique (DDLR) to develop a solution method called SAA-DDLR. Numerical experiments are conducted to illustrate the effectiveness and applicability of our model and method. Sensitivity analysis reveals that both the 4PL and 3PLs can benefit from the quantity discount scheme. Managerial insights are drawn for the 4PL to run a cost-effective logistics system in the presence of quantity discounts. [ABSTRACT FROM AUTHOR]

In the context of inventory management, this review presentation offers a thorough overview of several Economic Order Quantity (EOQ) models and their real-world uses. It explores the fundamental EOQ model and broadens to incorporate models that account for perishable items, quantity discounts, and scarcity prices. The talk also looks at the many sectors in which these models are used to optimize order amounts, save costs, and improve operational efficiency. Businesses may improve their inventory control strategies, realize considerable cost savings, and increase performance by making educated decisions based on a thorough grasp of the various EOQ models and their practical implementations. [ABSTRACT FROM AUTHOR]

Efforts to incorporate inventory management (IM) strategies in small and medium‐sized enterprises (SMEs) are very limited due to the lack of cost‐effective and easy‐to‐use techniques. This research article suggests an effective and proven IM strategy that can improve the productivity and competitiveness of SMEs. The purpose of this research article is twofold: first, to develop an integrated IM strategy for SMEs to reduce inventory carrying costs; second, to design individual replenishment policies for each product. This article discusses an integrated approach considering rank order clustering (ROC) technique, a forward version of the Wagner–Whitin (W–W) lot‐sizing algorithm, and quantity discounts. First ROC is used to form clusters of different assemblies consisting of common components for aggregating the demand. The W–W algorithm is tested next over 1 year of time horizon followed by quantity discounts. Insights derived from a case study proved that the proposed integrated IM approach could save a substantial amount of total cost compared to the existing purchase policy. In addition, this approach can be a promising approach to determine appropriate replenishment quantities for each planning period. In addition, stock‐out situations can be minimized. The novelty of this study is that it proposes a practical, simple‐to‐implement, and proven IM technique for increasing productivity and achieving sustainable development of SMEs, which are working in growing economies like India. [ABSTRACT FROM AUTHOR]

In this paper, we formulate a mathematical inventory model for deteriorating items with a constant rate of deterioration. The supplier offers the retailer successive discount on purchase of goods if the order size crosses predefined quantity levels. Retailer uses preservation techniques to reduce the deterioration rate. In order to increase the sales, retailer implements promotional strategies. Market demand of the product is influenced by promotional efforts, stock level and selling price of the product. The objective is to find optimum order quantity, cycle time, promotional cost, preservation cost and selling price in order to maximize total profit for the retailer. A numerical example is given to validate the mathematical model. Sensitivity analysis has been carried out to analyze the effect of change of other inventory parameters on decision variables and total profit. Results indicate that due to preservation technology we can see remarkable decrease in the deterioration rate hence cycle time increases and retailer can set a cheaper selling price to increase sales. Promotional efforts help the retailer to enhance sales of the product. Moreover, depending upon the product demand and order size, quantity discounts help retailer to reduce the purchase cost and hence overall profit of retailer increases. [ABSTRACT FROM AUTHOR]

I analyse the relationship between price discrimination, with respect to the package size of the product, and market concentration in the liquid laundry detergent market. Specifically, I study how quantity discounts change with market concentration. I estimate a fixed effects model and find that this relationship is non‐monotonic and I provide evidence that it is U‐shaped. These results suggest that firms offer more quantity discounts in less and more concentrated markets, while they offer less quantity discounts in moderately concentrated markets. [ABSTRACT FROM AUTHOR]

This study investigates pricing and return policies under various supply contracts in a closed-loop supply chain in which a supplier has more bargaining power than a retailer. We develop integrated supply contract models based on the principal–agent paradigm. Specifically, the supplier with more bargaining power devises a supply contract, acting as a Stackelberg leader. Then, given the contract offer, the retailer decides on pricing and return policies which affect consumers’ demand and return behaviours. We look into three commonly used supply contracts, i.e. wholesale price, buy-back and quantity discount contracts. The main purpose of this study is to explore how each supply contract affects the retailer’s decision on pricing and return policies, which in turn influence the profits of the entire supply chain and of its members. In doing so, we focus on investigating which contract coordinates the supply chain involving the retailer’s moral hazard. Through analytic comparison of contracts and extensive numerical analyses, we present numerous propositions to enrich the body of knowledge in the closed-loop supply chain and to provide meaningful decision guidelines to the practice. [ABSTRACT FROM PUBLISHER]

In this paper, we have considered a vendor-managed inventory (VMI) arrangement in a supply chain (SC), where the buyer imposes a penalty for shipments exceeding an upper limit. We have shown as how the industry practice of VMI under penalty can be used as a SC coordination mechanism. The vendor can influence the buyer to increase the batch size without making the buyer worse off. We also discuss how such a penalty scheme may be derived. Further, we have established the equivalence of VMI under deterministic demand with that of quantity discount models, thus highlighting the need to incorporate both cooperation and coordination perspectives while analysing SC collaboration mechanisms. [ABSTRACT FROM PUBLISHER]

In this study, we have proposed a supplier selection problem with the goals of minimizing the net cost, minimizing the net rejections, minimizing the net late deliveries, and minimizing the net green house gas emission subject to realistic constraints like suppliers’ capacity, buyer’s demand etc. Due to uncertainty, the buyer’s demand is fuzzy in nature and can be represented as a triangular neutrosophic number. We have also considered that quantity discounts are provided by the suppliers. The weights for different criteria are calculated using neutrosophic analytical hierarchy process. The neutrosophic goal programming approach has been applied in this article for solving the proposed supplier selection problem. An illustration has been given with comparison between fuzzy goal programming approach to demonstrate the effectiveness of the proposed model.

Copyright of Control Theory & Applications / Kongzhi Lilun Yu Yinyong is the property of Editorial Department of Control Theory & Applications and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

This paper proposes to solve a supply chain planning problem with realistic features. The problem consists of planning productions, transportations and storage activities in a supply chain at a tactical level on a finite horizon. The main features considered are decentralised decision making and iteration of the planning process on a rolling horizon basis. In each planning process, the actors optimise their local planning and coordinate to achieve a good overall planning. A multi-agent system is used to model such supply chain behaviour. The study is conducted in a divergent two-echelon supply chain with one manufacturer and multiple independent retailers. Coordination is achieved using a standard contract in practice, known as the ‘quantity discount’ contract. The planning framework on the supply chain structure is detailed. Lot-sizing models integrating the quantity discount are presented for the local planning problems. Experimental tests are conducted with three major parameters: quantity discount price, quantity discount breakpoint and rolling horizon length. They are used to determine the quantity discount parameters in achieving the best supply chain profit, and to analyse the increasing profit of the actors. A decision-making tool which is able to consider realistic features of supply chain planning is therefore resulted. [ABSTRACT FROM PUBLISHER]

It was usually observed in typical EOQ inventory models that the holding cost, the purchasing cost and the demand rate are constant and the purchasing cost is irrespective of the order size. But practically, the demand rate is based on various factors including sale price, seasonality and availability. Due to the lengthening of shortage periods, the holding cost per unit item increases. Also with the inclusion of quantity discounts, the unit purchasing cost is usually decreased for higher order sizes. This article addresses jointly with the inconsistency of the rate of demand, unit purchasing cost and unit holding cost for deteriorating items. This paper proposes a model based on an inventory problem including selling price of products and stock-dependent market demand rate, holding cost based on storage time and purchasing cost is influenced by order size by offering all units quantity discounts. An algorithm for estimating the optimum solution of decision variables by maximizing total profit and minimizing the overall cost of the model is developed in this paper. Validation of the developed model is confirmed with the help of a numerical example along with the sensitivity-analysis of decision variables by varying various inventory parameters.

Producers of consumer packaged goods often offer several package sizes of the same product and charge a lower unit price for a larger size. In this article, the authors investigate the 'quantity-discount effect,' or the phenomenon that consumers derive transaction utility from the unit price difference between a small and a large package size of the same product. The authors propose a modeling framework composed of a demand-side model and a supply-side model. The empirical results suggest that quantity-discount-induced gains or losses have a significant impact on consumer buying behavior. The authors also find a substantial amount of structural heterogeneity; that is, some consumers perceive quantity discounts as gains, whereas others perceive quantity discounts as losses. Conversely, the supply-side analysis suggests that manufacturers in the empirical application do not consider quantity-discount effects when setting prices. Through a series of policy experiments, the authors show that by accounting for quantity-discount-dependent consumer preferences, manufacturers can design more effective nonlinear pricing schemes and obtain greater profits. [ABSTRACT FROM AUTHOR]

We study the supply chain (SC) returning strategy and quantity discount coordination under the condition of product quality defects. We assume that the demand is a triangular fuzzy number (TFN), considering the SC coordination problem consisting of a manufacturer and a retailer. The decentralized SC coordination model and the integrated SC coordination model under a fuzzy environment are established respectively. The fuzzy set theory is used to study the manufacturer’s quantity discount and the retailer’s coordination of return policy. The signed distance is used as the ranking method to find the optimal order quantity in SC, and the optimization theory is used to maximize the participants’ profits. We first demonstrate that the retailer’s profit will be reduced in a typical integrated channel, and then we propose a quantitative discount return policy to coordinate the profits of the manufacturer and the retailer. Finally, the coordination steps are designed, and the manufacturer’s return policy is given. Meanwhile, some illustrative cases are provided to illustrate the feasibility of the proposed model.

Biomass is an abundant energy source, particularly in Canada, as an alternative or primary source for electricity generation. However, low economy of scale could cause a loss of efficiency for bioenergy adoption in small remote communities. In this sense, coordination among the players could promote the efficiency and profitability of bioenergy supply chains for these communities. There are different coordination strategies with varying impacts on supply chain players’ profit or cost. Therefore, analyzing and comparing them could provide insights on how to decide about the choice of coordination strategy. In doing so, this study considers the coordination strategies of quantity discounts and cost-sharing. The study adopts a system dynamics approach for simulating these coordination scenarios, obtaining their corresponding optimal supply chain decisions, followed by a comparative analysis. For a case study, the study considers multiple suppliers providing biomass for electricity generation in three communities in northern Quebec.

In this study, we have proposed a supplier selection problem with the goals of minimizing the net cost, minimizing the net rejections, minimizing the net late deliveries, and minimizing the net green house gas emission subject to realistic constraints like suppliers' capacity, buyer's demand etc. Due to uncertainty, the buyer's demand is fuzzy in nature and can be represented as a triangular neutrosophic number. We have also considered that quantity discounts are provided by the suppliers. The weights for different criteria are calculated using neutrosophic analytical hierarchy process. The neutrosophic goal programming approach has been applied in this article for solving the proposed supplier selection problem. An illustration has been given with comparison between fuzzy goal programming approach to demonstrate the effectiveness of the proposed model. [ABSTRACT FROM AUTHOR]

In today's competitive business markets, a revenue optimization method is always one of the most crucial issues ahead of commercial supply chains so that it is utilized by the managers to improve their profitability. On the other hand, enhancing coordination and collaboration between the chains' members has taken a vital role in increasing their efficiency and profitability. Thus, managers tend to employ/design marketing and coordinating incentive mechanisms using the revenue optimization method, as the most influential tools, to motivate the purchasers to order more and subsequently increase their market share. Here, this issue is studied in a two‐echelon supply chain by designing incentive contracts in order to evaluate the profit of organizations and enterprises and assess the best contract, which causes the highest profit, as the main goal of the businesses. In this study, a pricing‐inventory model is developed for a single‐item two‐echelon supply chain consisting of a manufacturer and a retailer in the presence of three different scenarios. In the first scenario, a credit payment (delay‐in‐payment) contract is considered between the chain members. In the second scenario, we studied a market segmentation policy in which the market demand is divided into price and quality oriented customers' demand while a quantity discount contract is assumed as the third one. The profit of supply chain under these new conditions is computed by some numerical examples and then the effects of cost parameters on the decision variables and the profit are analyzed. [ABSTRACT FROM AUTHOR]

Consumers often stockpile goods to store for future consumption. The existing theoretical literature has focussed on a price-based explanation where stockpiling arises due to temporary price reductions. In contrast, this paper explores a transaction-cost-based explanation where consumers stockpile to avoid the need to incur future transaction costs. It shows how transaction costs lead to positive consumer stockpiling in an oligopoly equilibrium even when future prices are expected to fall. Relative to a no-stockpiling benchmark, such stockpiling lowers profits, but improves consumer and total welfare. Our results extend to the case of quantity discounts where stockpiling consumers pay relatively lower per-unit prices than non-stockpiling consumers, when purchasing multi-unit bundles. [ABSTRACT FROM AUTHOR]

Highlights • We model a new quantity discounts supply chain planning problem. • The model is very hard to solve using leading commercial solvers. • We develop MIP-based local search algorithms for our problem. • We apply our model to a realistic food supply chain. • We show the efficiency of our algorithms in getting high quality solutions quickly. Abstract Supplier selection with quantity discounts has been an active research problem in the literature. In this paper, we focus on a new real-world quantity discounts scheme, where suppliers are selected in the beginning of a strategic planning period (e.g., 5 years). Monthly orders are placed from the selected suppliers, but the quantity discounts are based on the aggregated annual order quantities. We incorporate this type of cost structure in a multi-period, multi-product, multi-echelon supply chain planning problem, and develop a mixed integer linear programming (MIP) model for it. Our model is highly intractable; leading commercial solvers cannot construct high quality feasible solutions for realistic instances even after multiple hours of solution time. We develop an algorithm that constructs an initial feasible solution and a large neighborhood search method that combines two customized iterative algorithms based on MIP-based local search and improves such solution. We report numerical results for a food supply chain application and show the efficiency of using our methodology in getting very high quality primal solutions quickly. [ABSTRACT FROM AUTHOR]

We propose an alternative approach to identify unobserved consumer types and assess whether firms price discriminate. Unlike other screening schemes that rely on quantity discounts or product differentiation, in our finite mixture structure individuals have unit demands and the product is homogeneous. We implement the model using an original U.S. airlines data set. The results support the existence of two demand types. The high‐type "business" traveler is less price sensitive, has a higher valuation, and pays a higher price than the low type "tourist." The proportion of high types also increases as the departure date nears. [ABSTRACT FROM AUTHOR]

Purpose: Diverted prescription opioids are significant contributors to drug overdose mortality. Street price has been suggested as an economic metric of the diverted prescription opioid black market. This study examined variables that may influence the street price of diverted oxycodone and oxymorphone. Methods: A cross‐sectional study was conducted utilizing data from the previously validated, crowdsourcing website StreetRx. Street price reports of selected oxycodone and oxymorphone products, between August 22, 2014 and June 30, 2016, were considered for analysis. Geometric means and 95% confidence intervals were calculated comparing prices per milligram of drug in US dollars. Univariate and multivariable regressions were used to examine the influence of dosage strength, drug formulation, and bulk purchasing on street price. Results: A total of 5611 oxycodone and 1420 oxymorphone reports were analyzed. Across various dosages and formulations, geometric mean prices per milligram ranged between $0.12 and $1.07 for oxycodone and $0.73 and $2.90 for oxymorphone. For a 2‐fold increase in dosage strength, there is a 24.0% (95% CI: −28.1%, −19.6%, P < 0.001) and a 22.5% (95% CI: −24.2%, −20.8%, P < 0.001) decrease on average in price per milligram for oxycodone and oxymorphone, respectively. Lower potency, high dosage strength, crush‐resistant opioids, and those purchased in bulk were significantly cheaper. Conclusion: Street prices for diverted oxycodone and oxymorphone are influenced by multiple factors including potency, dosage, formulation, and bulk purchasing. Buyers who purchase large quantities of low potency, large dosage, crush‐resistant formulation prescription opioids can expect to achieve the lowest price. [ABSTRACT FROM AUTHOR]

How do consumers decide how many units to buy? Whereas prior research on individual consumers' purchases has focused primarily on purchase incidence and brand choice, the authors focus on the psychological process behind the purchase quantity decision. The authors propose that a simple anchoring and adjustment model describes how consumers make purchase quantity decisions and suggests how point-of-purchase promotions can increase sales. Two field experiments and two lab studies show that anchor-based promotions presented as multiple-unit prices, purchase quantity limits, and suggestive selling--can increase purchase quantities. The final study shows that consumers who retrieve internal anchors can counter these anchor-based promotions effectively. Firms might receive net benefits from anchor-based promotions depending on whether increases in unit sales reflect increased category consumption, brand switching, variety switching, store switching, or stockpiling. [ABSTRACT FROM AUTHOR]

This paper investigates the production technology facing computerized credit unions in Canada. A full system of translog cost equations is estimated in order to test for economies of scale, economies of scope, and other production characteristics in a multiproduct context. The regression results indicate that most of the credit unions in our sample experience significant increasing returns to scale as they expand their level of output. There is also evidence of cost complementarity or economies of scope in their mortgage and other lending activities. As a result, legislation which limits the ability of credit unions to grow and diversify will likely raise the operating costs of this important group of financial institutions. Additional structural tests of the most general translog specification suggest that none of the restrictive production conditions commonly imposed by other researchers using Cobb-Douglas and CES specifications provide a valid representation of credit union technology. The results of many earlier studies are therefore open to question. [ABSTRACT FROM AUTHOR]

This paper addresses a new robust multi-objective multi-period model for supply chain planning under uncertainty considering quantity discounts. The proposed model maximizes the current profit of the distributor by making a balance between the total costs of the supply chain and the distributor company’s revenues of selling products and also maximizes the company’s expected profit by introducing brands and taking the risk of loss on it. Considering uncertainty in the purchasing cost, selling fees, and demand fluctuations, the new robust multi-objective mixed-integer programming model is solved as a single-objective mixed-integer programming model by utilizing the LP-metrics method. By settling regulatory penalty parameters and considering different economic scenarios, the robustness and effectiveness of the developed model are verified with the data from BEH PAKHSH Company, a commodities distributor in Iran. The outcomes show that the proposed model is a promising approach to run an efficient supply chain. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to investigate the role of trade credit and quantity discount in supply chain coordination when the sales effort effect on market demand is considered. In this paper, we consider a two-echelon supply chain consisting of a single retailer ordering a single product from a single manufacturer. Market demand is stochastic and is influenced by retailer sales effort. We formulate an analytical model based on a single trade credit and find that the single trade credit cannot achieve the perfect coordination of the supply chain. Then, we develop a hybrid quantitative analytical model for supply chain coordination by coherently integrating incentives of trade credit and quantity discount with sales effort effects. The results demonstrate that, providing that the discount rate satisfies certain conditions, the proposed hybrid model combining trade credit and quantity discount will be able to effectively coordinate the supply chain by motivating retailers to exert their sales effort and increase product order quantity. Furthermore, the hybrid quantitative analytical model can provide great flexibility in coordinating the supply chain to achieve an optimal situation through the adjustment of relevant parameters to resolve conflict of interests from different supply chain members. Numerical examples are provided to demonstrate the effectiveness of the hybrid model. [ABSTRACT FROM AUTHOR]

Quantity commitment discounts (QCDs) are vertical agreements in which a seller conditions price discounts on the specified quantity or share of a product line that the buyer commits to purchase from the seller. QCDs are a natural outcome of sales-promoting competition among differentiated sellers and would be commonly used absent any possibility of excluding rivals. Both economic theory and the law recognize that in some cases pricing and business practices of sellers may harm or weaken rivals and might also reduce social welfare. Absent clear standards defining the bounds of illegal conduct, the mere threat of antitrust liability may dampen rivalry among firms, with resulting harm to the competitive process and, ultimately, consumers. Existing tests for exclusionary effects are unreliable and biased in favor of finding anticompetitive harm. [ABSTRACT FROM AUTHOR]

[Display omitted] The selection of potential suppliers has recently become a big challenge for the manufacturing industries due to the rapid spread of covid-19 and the escalating frequency of natural calamities such as earthquakes and floods. When decision-makers (DMs) consider quantity discounts from multiple sources, things get much more complicated. Although previous studies have looked at selecting suitable suppliers from economic and environmental aspects, no one has considered foreign transportation risks while evaluating the textile industry's global green suppliers. In this regard, for the first time, this study combines economic and environmental factors with the foreign transportation risk criterion to develop a holistic model for global green supplier selection and order allocation (SS&OA) in the textile industry under all-unit quantity discounts. Initially, the fuzzy analytical hierarchy process (FAHP) method is used to calculate the relative weights of the criteria. Second, a multi-objective linear programming (MOLP) model is developed to reduce the total procurement cost, quality rejection rate, delivery lateness rate, greenhouse gas emissions from product procurement, and foreign transportation risks. Subsequently, the developed MOLP model is transformed into a fuzzy compromise programming (FCP) model to obtain order allocation quantities among selected suppliers with their offered quantity discount rates. A real-life case study of the Pakistani textile industry is presented to validate the proposed methodology's applicability by determining the optimal order allocation quantities among multiple suppliers based on two decision-making attitudes of DMs (neutral and risk-averse). Finally, sensitivity and comparative analyses are carried out to guarantee that the proposed technique produces accurate and optimal solutions. The final results of the proposed methodology show that it can effectively manage data uncertainties during SS&OA compared to other existing approaches. The suggested integrated methodology's outcomes can assist the supplier organization in overcoming its current shortcomings and developing a long-term relationship with the buyer organization. [ABSTRACT FROM AUTHOR]

In this article, we consider and investigate the cases when the retailer's capitals are restricted and when the supplier offers another kind of 2-level trade credit. This means that the supplier offers 2-level trade credit for the retailer to settle the account and the retailer's capitals are restricted, so the retailer decides to pay off the unpaid balance as follows: Firstly, the retailer decides to pay off the unpaid balance at the end of the first credit period if the retailer can pay off all accounts and, in addition, the retailer can use the sales revenue to earn interest throughout the replenishment cycle time. Secondly, the retailer decides to pay off all accounts either after the end of the first credit period, but before the second credit period, or after the second credit period if the retailer cannot pay off the unpaid balance at the end of the first credit period. Additionally, the delay will incur interest charges on the unpaid and overdue balance due to the difference between the interest earned and the interest charged. Consequently, the main purpose of this article is to characterize the optimal solution processes and (in accordance with the functional behavior of the cost function) to search for the optimal replenishment cycle time. Finally, numerical examples are given to illustrate the theoretical results which are proven in this article by means of mathematical solution procedures. [ABSTRACT FROM AUTHOR]

This article argues that as the distribution of a firm's buyers becomes more heterogeneous, the firm's profit-maximizing quantity-discount schedule becomes less steep. First, we note that one measure of heterogeneity is the slope of the hazard function, expressed in terms of a simple crossing condition. We then show that marginal price schedules, for distributions of buyers which are more heterogeneous by this measure, are less negatively sloped in that they cross schedules for more homogeneous distributions from below. Intuitively, quantity discounts are a response to an individual buyer's declining marginal utilities, and buyer heterogeneity interferes with this response. [ABSTRACT FROM AUTHOR]

This article studies a multi-item auction characterized by asymmetric bidders and quantity discounts. We report a practical application of this type of auction in the procurement of Internet services to the 709 public schools of Buenos Aires. The asymmetry in this application is due to firms' existing technology infrastructures, which affect their ability to provide the service in certain areas of the city. A single round first-price sealed-bid auction, it required each participating firm to bid a supply curve specifying a price on predetermined graduated quantity intervals and to identify the individual schools it would supply. The maximal intersections of the sets of schools each participant has bid on define regions we call competition units. A single unit price must be quoted for all schools supplied within the same quantity interval, so that firms cannot bid a high price where competition is weak and a lower one where it is strong. Quantity discounts are allowed so that the bids can reflect returns-to-scale of the suppliers and the auctioneer may benefit of awarding bundles of units instead of separate units. The winner determination problem in this auction poses a challenge to the auctioneer. We present an exponential formulation and a polynomial formulation for this problem, both based on integer linear programming. The polynomial formulation proves to find the optimal set of bids in a matter of seconds. Results of the real-world implementation are reported. [ABSTRACT FROM AUTHOR]

Applying traditional integer programming techniques in order to solve real logistic problems can be an important challenge. To ensure tractability, real instances are often either simplified in scope or limited in size, given rise to solutions that may not address realistic issues. In this paper we present a novel approach to solve a multicommodity capacitated network flow problem with concave routing costs, considering also outsourcing, overload and underutilization facility costs. It is derived from a real NP production and transportation problem concerning to the processing of biological samples in a large health-care network, with consideration of volume-based price incentives-i.e. economies of scale-on the shipping costs. It is a tactical level model providing the global view of network layout and the coordinating policy among facilities with realistic assessment of long-term operations costs. The goal is to find an efficient resolution procedure in order to integrate it into a Decision Support System used by planners. With this aim, we analyse three alternative methods of linearizing the involved modified all-units discount cost function. Performance of the different modelling techniques is shown through extensive computations. [ABSTRACT FROM AUTHOR]

This paper develops a new inventory model with carbon tax policy and imperfect quality items in which the buyer exerts power over its supplier. It employs an order overlapping scheme to avoid shortages, overcomes some flaws in the literature, and develops two efficient solution algorithms. It also investigates different carbon tax systems on the performance of the model. Numerical results are discussed to bring some managerial insights. [ABSTRACT FROM AUTHOR]

We study a microprocessor company selling short-life-cycle products to a set of buyers that includes large consumer electronic goods manufacturers. The seller has a limited capacity for each product and negotiates with each buyer for the price. Our analysis of their sales data reveals that larger purchases do not always result in bigger discounts. Instead, the discount curve is like an 'N.' While existing theories cannot explain this nonmonotonic pattern, we develop an analytical model and show that the nonmonotonicity is rooted in how sellers value capacity when negotiating with a buyer. Large buyers accelerate the selling process and small buyers are helpful in consuming the residual capacity. However, satisfying midsized buyers may be costly because supplying these buyers can make it difficult to utilize the remaining capacity, which is often too much for small buyers but not enough for large buyers. We briefly discuss the implications for capacity rationing and posted pricing as well as potential applications to other industries. This paper was accepted by Serguei Netessine, operations management. [ABSTRACT FROM AUTHOR]

The practice of diverting genuine products to unauthorized gray markets continues to challenge companies in various industries and creates intense competition for authorized channels. Recent industry surveys report that the abuse of channel incentives is a primary reason for the growth of gray market activities. Therefore, it is crucial that companies take the presence of gray markets into consideration when they design contracts to distribute products through authorized retailers. This issue has received little attention in the extensive literature on contracting and supply chain coordination. In this study, we analyze the impacts of gray markets on two classic contracts, wholesale price and quantity discount, in a supply chain with one manufacturer and one retailer when the retailer has the opportunity to sell to a domestic gray market. Our analysis provides interesting and counterintuitive results. First, a classic quantity-discount contract that normally coordinates the supply chain can perform so poorly in the presence of a gray market that the supply chain would be better off using a wholesale price contract instead. Second, the presence of gray market can also degrade the performance of the wholesale price contract; therefore, a more sophisticated contract is needed for coordinating the supply chain. We show that contracts that solely depend on retailer's order quantity cannot coordinate the supply chain, and provide the conditions for coordinating the supply chain with price-dependent quantity discount contracts. We also provide comparative statics and show that when there is a gray market, coordinating the supply chain enhances total consumer welfare. [ABSTRACT FROM AUTHOR]

In this paper, the problem of lot sizing for the case of a single item is considered along with supplier selection in a two-stage supply chain. The suppliers are able to offer quantity discounts, which can be either all-unit or incremental discount policies. A mathematical modeling formulation for the proposed problem is presented and a dynamic programming methodology is provided to solve it. Computational experiments are performed in order to examine the accuracy and the performance of the proposed method in terms of running time. The preliminary results indicate that the proposed algorithm is capable of providing optimal solutions within low computational times, high accuracy solutions.