Quantity Discounts Research Articles

Strategic decisions to join group purchasing organizations

Group purchasing organizations (GPOs) aim to aggregate the purchasing requirements of many buyers and utilize economies of scale to save costs and obtain quantity discounts from suppliers. This paper extends the application of GPOs to the chain stores industry. A new retailer is going to enter the market and faces decisions on joining chain stores (as a GPO) or independently working with a supplier, product pricing, and serving different segments of the market (i.e., informed and uninformed customers). When joining the GPO, a membership fee must be paid to the GPO. The supplier offers a quantity discount schedule that depends on the contract administration fee paid to the GPO. Using nonlinear programming, the optimal decision-making policy is established in a closed-form format. The results show that all decisions are significantly affected by the proportion of informed customers in the market. Accordingly, when the proportion of the informed customers is less than a threshold, not joining the GPO is a great choice for the retailer. When this proportion is growing, the retailer is advised to join the GPO as soon as possible. Our findings indicate that, in the presence of rapid growth of information technologies which leads to an increase in people’s awareness of the market, GPOs play a strategic role in the chain stores industry nowadays. We demonstrate that GPOs not only provide many benefits for customers and retailers but also other players in the group purchasing chain would also profit.

Nonlinear Pricing with Average-Price Bias

Empirical evidence suggests that consumers facing complex nonlinear prices often make choices based on average (not marginal) prices. Given such behavior, we characterize a monopolist’s optimal nonlinear price schedule. In contrast to the textbook setting, nonlinear prices designed for “ average-price bias” distort consumption downward for consumers with the highest marginal utility and typically feature quantity premia rather than quantity discounts. These properties arise because the bias replaces consumer information rents with “curvature rents.” Whether or not a monopolist prefers consumers with average-price bias depends upon underlying preferences and costs. (JEL D11, D21, D42, L12)

Optimal Policies for Inventory Systems with Piecewise-Linear Concave Ordering Costs

We study infinite-horizon stochastic inventory problems with general demand distributions and piecewise linear concave ordering costs. Such costs arise in the important cases of quantity discounts or multiple suppliers. We consider the case of concave cost involving two linear segments. This corresponds to the case of one supplier with a fixed cost, a variable cost up to a given order quantity, and a quantity discount beyond that or, equivalently, the case of two suppliers, one with a low fixed cost along with a high variable cost and the other with a high fixed cost along with a low variable cost. We show that certain three and four parameter generalizations of the classical (s,S) policy are optimal. Our contributions consist of generalizing the demand, solving a functional Bellman equation for the value function that arises in the infinite-horizon framework, and providing an explicit solution in a special case of the exponential demand. We also give conditions under which our generalizations of the (s,S) policy reduce to the standard (s,S) policy. Finally and importantly, our method is also new in the sense that we construct explicitly the value function and we do not therefore need to utilize the notion of K-convexity used in the literature of inventory problems with fixed costs.

Integration of Multi-mode Resource-Constrained Project Scheduling under bonus-penalty policies with Material Ordering under Quantity Discount scheme for minimizing project cost

In this paper a mixed binary integer mathematical programming model is developed for integration of Multimode Resource-Constraint Project Scheduling Problem (MRCPSP) under bonus–penalty policies and Quantity Discount Problem in Material Ordering (QDPMO) with the objective of minimizing the total project cost. By proving a theorem, an important property of the optimum solution of the problem is found which reduces the search space significantly compared to previous studies. Since the RCPSP belongs to the class of problems that are NP-hard, four hybrid meta-heuristic algorithms called COA-GA, GWO-GA, PSO-GA and GA-GA is developed and tuned to solve the problem. Each of the proposed algorithms consists of outside and inside search components, which determine the best schedule, and materials procurement plan respectively. Finally a set of standard PROGEN test problems is solved by the proposed hybrid algorithms under fixed CPU time. The results show that the COA-GA algorithm outperforms others.

Coordinating biomass supply chains for remote communities: a comparative analysis of non-cooperative and cooperative scenarios

The absence of economies of scale is a major barrier in use of renewable energy sources in small and dispersed off-grid remote communities. For example, in northern Canada, diesel is currently the main source of electricity and heat generation. Coordination of biomass supply chains could play a key role in improving the cost efficiency and reliability of bioenergy generation through bundled ordering and creation of storage hubs. In this study, a supply chain management model with multiple suppliers and multiple end-user communities is formulated. The proposed model enables us to analyse and compare the outcomes of adopting a cooperative coordination strategy (with a joint pay-off for communities) versus a non-cooperative coordination strategy (with individual payoffs for communities). Other peculiar attributes of the proposed model rest in the addressing of restricted ordering schedules and quantities (due to unavailability of pathways) by advocating nonlinear ordering and distribution costs (to incorporate quantity discounts) achieved through coordinated and/or collective inventories. A real biomass supply chain case study of three northernmost Nunavik communities in Quebec is considered to show the applicability of the model and provide insights for uptake of bioenergy sources in remote off-grid communities.

An integrated methodology for the selection of sustainable suppliers and order allocation problem with quantity discounts, lost sales and varying supplier availabilities

In this study, selection of sustainable suppliers (SSS) and order allocation (OA) problem is generalized by considering multi-product, multi-supplier and multi-period scenarios with quantity discounts, lost sales and varying supplier availabilities. The study is designed in four phases. In the first phase, suppliers are ranked by using integrated the Fuzzy Analytic Hierarchy Process (F-AHP) and fuzzy Preference Ranking Organization Method for Enrichment Evaluation (F-PROMETHEE) considering social and environmental factors as well as economic factors. The output of the first phase is used in the second phase of the method. In the second phase, a fuzzy multi-objective optimization (FMOO) model is proposed to find quantities to be purchased from suppliers. In the third phase, both the Augmented ε-constraint (AUGMECON) method and LP-metrics are used to obtain the Pareto front of the problem. Finally, in the fourth phase, a solution is selected by the Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS) from the non-dominated solutions. The effectiveness of the proposed method is shown on real data from a firm selling medical devices.

Single Item Supplier Selection and Order Allocation Problem with a Quantity Discount and Transportation Costs

In this paper, we address a single item supplier selection, economic lot-sizing, and order assignment problem under quantity discount environment and transportation costs. A mixed-integer nonlinear program (MINP) model is developed with minimization of cost as its objective, while lead-time, the capacity of the supplier and demand of the product are incorporated as constraints. The total cost considered includes annual inventory holding cost, ordering cost, transportation cost and purchase cost. An efficient and effective genetic algorithm (GA) with problem-specific operators is developed and used to solve the proposed MINP model. The model is illustrated through a numerical example and the results show that the GA can solve the model in less than a minute. Moreover, the results of the numerical illustration show that the item cost and transportation cost are the deciding factors in selecting suppliers and allocating orders.
 Keywords: Supplier selection, Economic Order Quantity, Order allocation, Mixed-integer nonlinear programming.

Design of mathematical models for the integration of purchase and production lot-sizing and scheduling problems under demand uncertainty

This study addresses the multi-level lot-sizing and scheduling problem with complex setups and considers supplier selection with quantity discounts and multiple modes of transportation. The present research proposes a mixed-integer linear programming (MILP) model in which the purchase lot-sizing from multiple suppliers, production lot-sizing with multiple machines and scheduling of various products of different families are accomplished at the same time. However, these decisions are not integrated in traditional environments and are taken separately. In this study, two different types of lot-sizing models called aggregated and disaggregated are developed for the problem to evaluate and compare the computational efficiency of them under deterministic and stochastic demands and provide some managerial insights. To deal with the stochastic demands, Chance-Constrained Programming (CCP) approach is applied. Based on the results of this study, the average profit of the separated (purchase from production) lot-sizing model under demand choice flexibility and stochastic demand is 24% and 22% less than the integrated model, respectively. Moreover, the results also confirm the effect of discount structure on the amount of purchases, productions, revenues and costs.

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

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

Online ordering rules for the multi-period newsvendor problem with quantity discounts

In this paper, we study the multi-period newsvendor problem with quantity discounts and stationary demand, where order quantities need to be decided sequentially over a finite or infinite horizon without making statistical assumption on demands. The Weak Aggregating Algorithm (WAA), which is an online learning method of prediction with expert advice, is applied to the problem. We first consider the all-unit discount case, in which the reduced unit cost is applied to all units in an order. We present explicit online ordering rules by using the fixed-stock strategy as expert advice during the application of WAA. A modified gain function implying convoluted contracts between the newsvendor and his supplier is defined to obtain some theoretical guarantees, which ensure that the newsvendor’s average gains are almost as large as those from the best expert advice for a sufficiently large horizon. Further, we generalize the results to the multi-level incremental discount case, in which there are different unit costs for different quantity ranges. We also extend the results to cases where order quantities are integer-valued, and provide correspondingly online ordering rules and theoretical guarantees. Finally, numerical experiments are performed and show that the average gains obtained by the proposed online ordering rules are comparable to those offered by the best experts in hindsight. The results also indicate that the cumulative gains achieved by the ordering rules for the problem with all-unit discount are larger than those achieved by the ordering rules for the problem with incremental discount; and order quantities increase with the discount level for the all-unit discount while decrease for the incremental discount. The results obtained in this paper can provide competitive online ordering rules for industry managers who need to place long-term continuous orders for perishable products when the demand distribution is unknown.

Design of optimal quantity discounts for multi-period bilevel production planning under uncertain demands

The analysis of the quantity discount of the decentralized supply chain has been studied only for single-period planning models. This article presents the design of an optimal quantity discounts for multi-period bilevel production planning for two-echelon supply chains under demand uncertainty. In order to derive an optimal contract for multi-period production planning, the cumulative order quantity and production quantity are introduced. From our proposed model, a Stackelberg equilibrium is analytically derived for the supply chain when the supplier is the leader and the retailer is the follower. An optimal discount contract is analytically designed through the optimal solution of the centralized problem. Computational results show the effectiveness of the proposed discount contract under demand uncertainty.

Truthful auctions for e-market logistics services procurement with quantity discounts

Auctions are an important method for solving the logistics procurement problem in electronics markets. However, current auction methods rarely consider the existence of quantity discounts. To fill this research gap, we introduce quantity discounts into the procurement Vickrey–Clark–Groves (P-VCG) and truthful double-auction mechanisms and apply them to the logistics services procurement market. For a market with only one customer, we design a P-VCG auction with quantity discounts, and for a market with multiple customers, we construct a model for maximizing social welfare and propose a trade reduction with a quantity discount (TR-QD) double-auction mechanisms. We prove that both auction mechanisms ensure incentive compatibility, individual rationality, balanced budget, and asymptotical efficiency. Furthermore, compared with traditional truthful double-auctions, the TR-QD mechanism supports cooperative purchases—which allows more customers to enjoy discounts on large-scale logistics services—and bid time priority—which achieves the goal of meeting earlier requests earlier and improves auction efficiency. Numerical studies further show that the TR-QD auction mechanism can achieve an increase in customers’ total value, logistics companies’ total value, social welfare and total trading volume.

Single Machine Scheduling with Outsourcing Under Different Fill Rates or Quantity Discount Rates

In this paper, we consider two single machine scheduling problems with outsourcing under different fill rates or quantity discount rates. From the manufacturer point of view, to maintain a predefined high service level under limited production capacity, it is required that the number of outsourced jobs must belong to a given interval [Formula: see text]. We call this model “scheduling with outsourcing under different fill rates”. Meanwhile, from the outsourcers point of view, in order to encourage more outsourcing actions from the manufacturer, the outsourcers might provide an attractive discount scheme. Here, we assume that all discount rates depend only on the quantity (number) of the outsourced jobs. That is, the actual outsourcing cost equals to the original outsourcing cost multiplied by the corresponding discount rate. This model is called “scheduling with outsourcing under different quantity discount rates”. The objective is to minimize the sum of the makespan of the processed jobs and the (actual) outsourcing costs of the outsourced jobs. For the above two problems, some optimal algorithms, approximation algorithms and approximation schemes are proposed.

Effect of warranty and quantity discounts on a deteriorating production system with a Markovian production process and allowable shortages

This paper explores the retailer's optimal lot sizing and quantity backordering for a deteriorating production system with a two-state Markov production process in which quantity discounts are provided by the supplier. The products are sold with the policy of free reasonable repair warranty employing the fraction of nonconforming items in a lot size. Unlike the traditional economic production quantity (EPQ) model with warranty policy based on the elapsed time of the system in the control state follows an exponential distribution, this paper not only constructs an alternative mathematical model for EPQ model based on the fraction of nonconforming items in a lot size for an imperfect production system but also extends the topics of optimal quantity and shortage to a wider scope of academic research and further finds that some results are different from the traditional EPQ models. We seek to minimize the expected total relevant cost through optimal lot sizing and quantity backordering. We also demonstrate that the optimal lot size is bounded in a finite interval. An efficient algorithm is developed to determine the optimal solution. Moreover, a numerical example is given and sensitivity analysis is conducted to highlight management insights.

Integrated inventory system with freight costs and two types of quantity discounts

In this paper, we investigate an integrated inventory model for single supplier-buyer considering stochastic demand. We consider two quantity discounts with freight environment. The objective is to minimise the integrated total cost incurred by the supplier and buyer. Freight costs are the function of shipping weight and distance with two transportation modes: truckload (TL) and less-than-truckload (LTL) shipments. We develop two optimal models considering all-units quantity discount and incremental quantity discount. The study shows how freight costs and the two discount policies affect the total cost of the supplier and the buyer. Numerical examples are used to illustrate of two models.

Modeling and Analyzing Incremental Quantity Discounts in Transportation Costs for a Joint Economic Lot Sizing Problem

Joint economic lot sizing (JELS) addresses integrated inventory models in a supply chain. Most of the studies in this field either do not consider the role of the transportation cost in their analysis or consider transportation cost as a fixed part of the ordering costs. In this article, a model is developed to analyze an incremental quantity discount in transportation cost. Appropriate equations are derived to compute the costs related to the inventory systems in the buyer and vendor sites. Then, a procedure including five steps is proposed to optimize the model and determine the values of the decision variables. To analyze the performance of the incremental discount, the JELS problem is studied in two other states of transportation costs. These states include fixed transportation cost and all-unit quantity discount. Moreover, some numerical analyses are carried out to show the impact of transportation costs and inventory-related parameters on the system performance. According to the results of the sensitivity analyses, it is observed that all-unit quantity discount leads to a better performance of the system in comparison with the incremental quantity discount.

Nonlinear Pricing in Village Economies

This paper examines the prices of basic staples in rural Mexico. We document that nonlinear pricing in the form of quantity discounts is common, that quantity discounts are sizable for basic staples, and that the well‐known conditional cash transfer program Progresa has significantly increased quantity discounts, although the program, as documented in previous studies, has not affected unit prices on average. To account for these patterns, we propose a model of price discrimination that nests those of Maskin and Riley (1984) and Jullien (2000), in which consumers differ in their tastes and, because of subsistence constraints, in their ability to pay for a good. We show that under mild conditions, a model in which consumers face heterogeneous subsistence or budget constraints is equivalent to one in which consumers have access to heterogeneous outside options. We rely on known results to characterize the equilibrium price schedule, which is nonlinear in quantity. We analyze the effect of nonlinear pricing on market participation as well as the impact of a market‐wide transfer, analogous to the Progresa one, when consumers are differentially constrained. We show that the model is structurally identified from data on prices and quantities from a single market under common assumptions. We estimate the model using data on three commonly consumed commodities from municipalities and localities in Mexico. Interestingly, we find that relative to linear pricing, nonlinear pricing is beneficial to a large number of households, including those consuming small quantities, mostly because of the higher degree of market participation that nonlinear pricing induces. We also show that the Progresa transfer has affected the slopes of the price schedules of the three commodities we study, which have become steeper as consistent with our model, leading to an increase in the intensity of price discrimination. Finally, we find that a reduced form of our model, in which the size of quantity discounts depends on the hazard rate of the distribution of quantities purchased in a village, accounts for the shift in price schedules induced by the program.

Market diagnosis to learn about the commercial snack scene for pets

Dog snacks consist of their flour-based production, which is extracted from crickets, these snacks contain the same protein as producing a pound of beef which consumes two thousand times more water than producing a pound of crickets , plus more land and energy, and emits 100 times more greenhouse gases. On the other hand, insects have as much protein as beef or chicken, and even have more vitamins. PRODUCT Dog biscuits based on cricket flour. PRICE The price to the public is $100 MXN. 450 Gr. (12 pcs). PLAZA Supermarket, Convenience Stores, Pet Stores, Veterinary, Pet Accessories Stores and Website. Promotion - Online Coupons - Discounts on special dates - Quantity discounts - Free shipping from a certain amount of purchase on the website - Giveaways by Social Media General Objective. Get information to see the commercial viability of selling snacks for canines on the ZMG. Methodology. A quantitative study was conducted on pet owners, specifically dogs; having as an instrument of data collection a survey applied in the Metropolitan Zone of Guadalajara to a representative sample of 380 surveys of men and women over the age of 18 with previous filter question with a confidence level of 95% and a margin of 5% error. The survey was conducted by simple random subsampling by clusters and random home routes. Contribution. This study has three important purposes: 1. Incorporation and participation of students from the career of Engineering in Development and Business Innovation in project initiated pro students of TSU Environmental Technology to identify areas of commercial opportunity of the product. 2. Awareness and active participation of the university community, consumers and the general public in relation to the sustainability and care of the environment. 3. The results of the study will serve as the basis for the design and realization of a business plan

Supply Chain Contracts in the Presence of Gray Markets

ABSTRACTAbuse of channel incentives by a manufacturer's authorized retailers often encourages gray markets to emerge, which affects supply chain profit as well as the manufacturer's brand image. Therefore, myopically selecting a product distribution contract can be harmful. We analyze the performance of a number of contracts in the presence of a gray market—primarily wholesale price, revenue sharing, and quantity discounts—and analyze their impact on prices charged, quantity ordered, as well as profits. We also investigate their impact on consumer surplus and social welfare. Our results indicate that selection of an appropriate contract is quite crucial, as different contracts give different results across a variety of operating parameters. Their performance is governed by the relative trade‐offs involving diversion of excess quantity to the gray market at the end of the season, an extension of target market due to lower prices in the alternate channel, and the negative impact on the manufacturer's brand that also affects its revenue. We delineate these characteristics and find that, in general, the quantity discount contract performs the worst. Interestingly, if the blowback suffered by the manufacturer on account of product availability in the gray market is high, the wholesale price contract may outperform the other contracts, including the revenue‐sharing contract with a truthful retailer, which otherwise is a more attractive option. We discuss the implications of our analysis, and also provide strategies and pointers to manage the impact of gray markets.

Integrated inventory system with freight costs and two types of quantity discounts

In this paper, we investigate an integrated inventory model for single supplier-buyer considering stochastic demand. We consider two quantity discounts with freight environment. The objective is to minimise the integrated total cost incurred by the supplier and buyer. Freight costs are the function of shipping weight and distance with two transportation modes: truckload (TL) and less-than-truckload (LTL) shipments. We develop two optimal models considering all-units quantity discount and incremental quantity discount. The study shows how freight costs and the two discount policies affect the total cost of the supplier and the buyer. Numerical examples are used to illustrate of two models.