Bid Evaluation in Procurement Auctions with Piecewise Linear Supply Curves

Consider a marketplace operated by a buyer who wishes to procure large quantities of several heterogeneous products. Suppliers submit price curves for each of the commodities indicating the price charged as a function of the supplied quantity. The total amount paid to a supplier is the sum of the prices charged for the individual commodities. It is assumed that the submitted supply curves are piecewise linear as they often are in practice. The bid evaluation problem faced by the procurer is to determine how much of each commodity to buy from each of the suppliers so as to minimize the total purchase price. In addition to meeting the demand, the buyer may impose additional business requirements that restrict which contracts suppliers may be awarded. These requirements may result in interdependencies between the commodities which lead to suboptimal results if the commodities are traded in independent auctions rather than simultaneously. Even without the additional business constraints the bid evaluation problem is NP-hard. The main contribution of our study is a flexible column generation based heuristics that provides near-optimal solutions to the procurer’s bid evaluation problem. Our method scales very well due to the Branch-and-Price technology it is built on. We employ sophisticated rounding and local improvement heuristics to obtain quality solutions. We also developed a test data generator that produces realistic problems and allows control over the difficulty level of the problems using parameters.     

The traveling purchaser problem with stochastic prices: Exact and approximate algorithms

The paper formulates an extension of the traveling purchaser problem where multiple types of commodities are sold at spatially distributed locations with stochastic prices (each following a known probability distribution). A purchaser’s goal is to find the optimal routing and purchasing strategies that minimize the expected total travel and purchasing costs needed to purchase one unit of each commodity. The purchaser reveals the actual commodity price at a seller upon arrival, and then either purchases the commodity at the offered price, or rejects the price and visits a next seller. In this paper, we propose an exact solution algorithm based on dynamic programming, an iterative approximate algorithm that yields bounds for the minimum total expected cost, and a greedy heuristic for fast solutions to large-scale applications. We analyze the characteristics of the problem and test the computational performance of the proposed algorithms. The numerical results show that the approximate and heuristic algorithms yield near-optimum strategies and very good estimates of the minimum total cost.     

A multiple replenishment contract with ARIMA demand processes

This paper is concerned with a multiple replenishment contract with a purchase price discount in a supply chain. The chain is composed of one supplier, one buyer and consumers for a product. The replenishment contract is based upon the well-known (s, Q) policy, but allows us to contract replenishments at a future time with a price discount. Owing to the larger forecast error of future demand, the buyer should keep a higher level of safety stock to provide the same level of service as the usual (s, Q) policy. However, the buyer can reduce his purchase cost by ordering a larger quantity at a discounted price. Hence, there exists a trade-off between the price discount and the inventory holding cost. For the ARIMA demand processes, we present a model for the contract and an algorithm to find the number of the future replenishments. Computational experiments show that the algorithm finds the global optimum solution very quickly.     

Inventory Control with a Randomly Available Discount Purchase Price

A mathematical model is developed for a basic single-commodity storage system in which the stock controller is faced with a randomly fluctuating purchase price. High- and low-price periods are defined and a purchasing policy is specified which depends upon both the number of units in storage and the price period in which the system is operating. For the case of random demand the limiting stochastic behaviour of the system is obtained and the cost of operating the system is derived.     

A fuzzy mathematical model for the joint economic lot size problem with multiple price breaks

This paper applies fuzzy mathematical programming to solve the joint economic lot size problem with multiple price breaks. In order to entice the buyer to increase the order quantity, it is a common practice for the seller to offer quantity discounts to the buyer. From the system viewpoint, the joint cost for the seller and buyer can be minimized only when the buyer increases his economic order quantity. The problem is how to determine the number of price breaks, as well as the quantity discount and order quantity at each price break, to achieve the optimal joint cost. Fuzzy mathematical programming provides a very efficient algorithm to solve the above problem simultaneously from the perspectives of the seller and the buyer. Another common problem in joint economic lot size model is how to split the system profit between the seller and the buyer. Whereas the traditional approach to this problem is to divide the profit based on a certain ratio determined by the bargaining power of both parties, fuzzy mathematical programming can achieve the same satisfaction level to both parties based on their respective cost functions.     

Buyer behavior adaptation based on a fuzzy logic controller and prediction techniques

The current form of Web provides numerous product resources available to users. Users can rely on intelligent agents for purchase actions. These actions are taken in specific environments such as Electronic Markets (EMs). In this paper, we study the interaction process between buyers and sellers and focus on the buyer side. Each buyer has the opportunity to interact with a number of sellers trying to buy the most appropriate products. This interaction can be modeled as a finite horizon Bargaining Game (BG). In this game, players have opposite goals concerning the product price. We adopt a number of techniques in the buyer side trying to give the appropriate level of efficiency in the buyer decision process. The buyer uses a prediction mechanism in combination with the use of Fuzzy Logic (FL) theory in order to be able to predict the upcoming seller proposal and, thus, understand the seller pricing policy. Based on this, he/she can adapt his/her behavior when trying to purchase products. The buyer adaptation mechanism produces the belief that the buyer has about the seller pricing policy and a parameter that indicates his/her own pricing policy which yields the buyer offers in the upcoming rounds. Moreover, the buyer is based on FL system that derives the appropriate actions at every round of the BG. Our results show that the combination of Fuzzy Logic (FL) with the above-mentioned techniques provides an efficient decision mechanism in the buyer side that in specific scenarios outperforms an optimal stopping model.     

Dynamic Calibration of Price-Trend Parameters for Commodity Futures Trading

This paper addresses the problem of buying commodities through the futures markets and deals specifically with a heuristic rule developed for the scenario described as `purchasing under a deadline'. The rule is based on a short-term forecasts produced by Taylor's price-trend model. In a previous study applied to the Chicago Board of Trade (CBOT) corn futures market the price-trend parameters of the stochastic process generating the daily returns were shown to be nearly stable over time and hence could be estimated using a static procedure. However, the analysis presented in this paper concerning the CBOT soybean futures market strongly suggests that those parameters were unstable, impairing the successful application of the purchasing rule. The authors recommend the continuous CUSUM monitoring of the purchasing results and propose a procedure for dynamically calibrating the price-trend and buying parameters. Under this procedure the price-trend parameter estimates are derived from exponentially smoothed sample autocorrelation coefficients of the rescaled daily returns. The procedure was developed and tested using the 1972-87 series of CBOT daily soybean futures closing prices. The results suggest that it leads to an improvement on the purchasing results derived from the static parameter calibration procedure formerly adopted.     

Selection of contract suppliers under price and demand uncertainty in a dynamic market

In this paper, we consider a supply contracting problem in which the buyer firm faces non-stationary stochastic price and demand. First, we derive analytical results to compare two pure strategies: (i) periodically purchasing from the spot market; and (ii) signing a long-term contract with a single supplier. The results from the pure strategies show that the selection of suppliers can be complicated by many parameters, and is particularly affected by price uncertainty. We then develop a stochastic dynamic programming model to incorporate mixed strategies, purchasing commitments and contract cancellations. Computational results show that increases in price (demand) uncertainty favor long-term (short-term) suppliers. By examining the two-way interactions of contract factors (price, demand, purchasing bounds, learning and technology effect, salvage values and contract cancellation), both intuitive and non-intuitive managerial insights in outsourcing strategies are derived.     

Optimal purchasing policy in a two-component assembly system with different purchasing contracts for each component

This paper considers an assembly system where a firm produces a single product which is assembled using two types of components (component 1 and component 2). The components are provided by individual suppliers (supplier 1 and supplier 2). We assume that the firm makes different procurement contracts with supplier 1 and supplier 2. To supplier 1, the firm specifies the maximum inventory level of component 1 and makes a commitment to purchase the component as long as its inventory level is below this target level. To supplier 2, the firm has the option of purchasing or rejecting component 2 at each instant supplier 2 provides it. Formulating our model as a Markov decision problem, we identify a component 2 purchasing policy which maximizes the firm’s profits subject to the costs of rejecting component 1, holding component 2, and purchasing component 2. We also investigate how the changes in the sales price and cost parameters affect the optimal purchasing policy. Finally, we present numerical study for the optimal performance evaluation.This material is based upon work supported by the Korea Science and Engineering Foundation (KOSEF) through the Northeast Asia e-Logistics Research Center at University of Incheon.     

Optimal spot market inventory strategies in the presence of cost and price risk

We consider a firm facing random demand at the end of a single period of random length. At any time during the period, the firm can either increase or decrease inventory by buying or selling on a spot market where price fluctuates randomly over time. The firm’s goal is to maximize expected discounted profit over the period, where profit consists of the revenue from selling goods to meet demand, on the spot market, or in salvage, minus the cost of buying goods, and transaction, penalty, and holding costs. We first show that this optimization problem is equivalent to a two-dimensional singular control problem. We then use a recently developed control-theoretic approach to show that the optimal policy is completely characterized by a simple price-dependent two-threshold policy. In a series of computational experiments, we explore the value of actively managing inventory during the period rather than making a purchase decision at the start of the period, and then passively waiting for demand. In these experiments, we observe that as price volatility increases, the value of actively managing inventory increases until some limit is reached.     

Fighting strategies in a market with counterfeits

Counterfeiting is a widely spread phenomenon and has seen rapid growth in recent years. In this paper, we adopt the standard vertical differentiation model and allow consumers the choices of purchasing an authentic product, purchasing a counterfeit, or not buying. We focus on how non-deceptive counterfeits, which consumers know at time of purchase that the products are counterfeits with certainty, affect the price, market share and profitability of brand name products. We also consider the strategies for brand name companies to fight counterfeiting. We compare different fighting strategies in a market with one brand name product and its counterfeit, and derive equilibrium fighting strategies in a market with two competing brand name products and a counterfeit under general conditions.     

An analytical model for reverse automotive production planning and pricing

Automotive shredders need a reverse production planning strategy that includes determining at what price to purchase vehicle hulks from different sources. In this paper, we formulate the automotive reverse production planning and pricing problem in a nonlinear programming model, develop an approximate supply function for hulks when adjacent shredders price independently, and compare two hulk pricing strategies in three trends for ferrous metal and hulk prices: constant, increasing and decreasing. The case study results indicate that adjusting purchase price based on hulk composition in coordination with planning for purchasing, storing and processing can increase net revenue by 7–15%.     

Integrated inventory model with quantity discount and price-sensitive demand

Quantity discount has been a subject of study for a long time; however, little is known about its effect on integrated inventory models when price-sensitive demand is placed. The objective of this study is to find the optimal pricing and ordering strategies for an integrated inventory system when a quantity discount policy is applied. The pricing strategy discussed here is one in which the vendor offers a quantity discount to the buyer. Then, the buyer will adjust his retail price based on the purchasing cost, which will influence the customer demand as a result. Consequently, an integrated inventory model is established to find the optimal solutions for order quantity, retail price, and the number of shipments from vendor to buyer in one production run, so that the joint total profit incurred has the maximum value. Also, numerical examples and a sensitivity analysis are given to illustrate the results of the model.     

Optimal procurement strategies for online spot markets

Spot markets have emerged for a broad range of commodities, and companies have started to use them in addition to their traditional, long-term procurement contracts (forward contracts). In comparison to forward contracts, spot markets offer products at essentially negligible lead time, but typically command a higher expected price for this added flexibility while also exhibiting substantial price uncertainty. In our research, we analyze the resulting procurement challenge and quantify the benefits of using spot markets from a supply chain perspective. We develop and solve mathematical models that determine the optimal order quantity to purchase via forward contracts and the optimal quantity to purchase via spot markets. We analyze the most general situation where commodities can be both bought and sold via a spot market and derive closed-form results for this case. We compare the obtained results to the reference scenario of pure contract sourcing and we include results for situations where the use of spot markets is restricted to either buying or selling only. Our approaches can be used by decision makers to determine optimal procurement strategies based on key parameters such as, demand and spot price volatilities, correlation between demand and spot prices, and risk aversion. The results of our analysis demonstrate that significant profit improvements can be achieved if a moderate fraction of the commodity demand is procured via spot markets. The results also show that companies who use spot markets can offer a higher expected service level, but that they might experience a higher variability in profits than companies who do not use spot markets. We illustrate our analytical results with numerical examples throughout the paper.     

Sourcing decisions with capacity reservation contracts

By committing to long-term supply contracts, buyers seek to lower their purchasing costs, and have products delivered without interruption. When a long-term contract is available, suppliers are less pressured to find new customers, and can afford to charge a price lower than the prevailing spot market price. We examine sourcing decisions of a firm in the presence of a capacity reservation contract that this firm makes with its long-term supplier in addition to the spot market alternative. This contract entails delivery of any desired portion of a reserved fixed capacity in exchange for a guaranteed payment by the buyer. We investigate rational actions of the two parties under two different types of periodic review inventory control policies used by the buyer: the two-number policy, and the base stock policy. When typical demand probability distributions are considered, inclusion of the spot market source in the buyer’s procurement plan significantly reduces the capacity commitments from the long-term supplier.     

Collaborative pricing and replenishment policy for hi-tech industry

Owing to rapid technological innovation and severe competition, the upstream component price and the downstream product cost of hi-tech industries like computers and communication consumer's products usually decline significantly with time. From a practical viewpoint, there is a need to develop a collaborative pricing and replenishing model with finite horizon when the vendor's purchase cost and the end-consumer's market price are reduced simultaneously. To entice collaboration, the vendor may offer some price discount to the buyer using a negotiation factor to balance the net profit for each player. A numerical example and sensitivity analysis are carried out to illustrate the model. Our results indicate that higher decline-rate in the vendor's purchase cost leads to a smaller vendor lot size, and the higher decline-rate in the market price leads to a larger buyer lot size. The percentage increase in the net profit is approximately 6.57% when cost/price reduction is considered. Therefore, it is significant to consider the effect of the cost/price reduction, especially in hi-tech industries.     

2016年全国研究生数学建模竞赛E题赛题点评

首先阐明了2016年全国研究生数学建模竞赛E题"粮食最低收购价政策问题研究"的研究背景和问题研究的实际意义.接着,针对每一个问题,从研究思路、研究方法、研究结论等方面均作了详细的叙述.最后,对学生论文中出现的问题、难点以及创新性等方面做了点评.     

Impact of product pricing and timing of investment decisions on supply chain co-opetition

In supply chain co-opetition, firms simultaneously compete and co-operate in order to maximize their profits. We consider the nature of co-opetition between two firms: The product supplier invests in the technology to improve quality, and the purchasing firm (buyer) invests in selling effort to develop the market for the product before uncertainty in demand is resolved. We consider three different decision making structures and discuss the optimal configuration from each firm’s perspective. In case 1, the supplier invests in product quality and sets the wholesale price for the product. The buyer then exerts selling effort to develop the market and following demand potential realization, sets the resale price. In case 2, the supplier invests in product quality followed by the buyer’s investment in selling effort. Then, after demand potential is observed, the supplier sets the wholesale price and the buyer sets the resale price. Finally, in case 3, both firms simultaneously invest in product quality and selling effort, respectively. Subsequently, observing the demand potential, the supplier sets the wholesale price and the buyer sets the resale price. We compare all configuration options from both the perspective of the supplier and the buyer, and show that the level of investment by the firms depends on the nature of competition between them and the level of uncertainty in demand. Our analysis reveals that although configuration 1 results in the highest profits for the integrated channel, there is no clear dominating preference on system configuration from the perspective of both parties. The incentives of the co-opetition partners and the investment levels are mainly governed by the cost structure and the level of uncertainty in demand. We examine and discuss the relation between system parameters and the incentives in desiging the supply contract structure.     

A Day-to-Day Buying Policy for Commodities — A Study of Purchasing Maize

The majority of the imported raw materials used by European industry have to be purchased in commodity markets where prices fluctuate over time. The overall purchasing decision contains several component stages. The work described in this paper concentrates on the final stage of this process, the tactical buying policy. A major difficulty lies in the definition of a proper measure of performance, so as to assess the merits of any proposed buying policy. The measures previously suggested by Kingsman and Taylor are discussed, and a new measure, thought to be more appropriate, is put forward. The paper describes a new heuristic buying policy, which is applied to the purchasing of maize. The policy uses Taylor's price-trend forecasting model and leads to purchasing costs which are shown to be significantly lower than the average market prices and better than those obtained from Kingsman's pricebreak policy.     

A genetic algorithm for optimal operating parameters of VMI system in a two-echelon supply chain

This paper deals with the operational issues of a two-echelon single vendor–multiple buyers supply chain (TSVMBSC) model under vendor managed inventory (VMI) mode of operation. The operational parameters to the above model are: sales quantity and sales price that determine the channel profit of the supply chain, and contract price between the vendor and the buyer, which depends upon the understanding between the partners on their revenue sharing. In order to find out the optimal sales quantity for each buyer in TSVMBSC problem, a mathematical model is formulated. Optimal sales price and acceptable contract price at different revenue share are subsequently derived with the optimal sales quantity. A genetic algorithm (GA) based heuristic is proposed to solve this TSVMBSC problem, which belongs to nonlinear integer programming problem (NIP). The proposed methodology is evaluated for its solution quality. Furthermore, the robustness of the model with its parameters, which fluctuate frequently and are sensitive to operational features, is analysed.