Optimal Purchase Research Articles

A Micro-Founded Model for CLV

A consumer incurs a constant flow cost to keep track of information on a firm's new product, which updates her expected valuation according to a Brownian motion. The consumer's purchase need follows a Poisson arrival over time, and upon an arrival, she decides whether to make a purchase or not. Moreover, at any time, she decides whether to keep tracking information or to drop out so as to maximize expected utility. We characterize the consumer's optimal purchase and dropout decisions in closed form. We find that consumers who are about to drop out tend to purchase less frequently. Our model generates endogenous consumer loyalty due to survival bias--consumers who are alive are more likely to stay alive and continue to make purchases in the future. This is captured by a one-parameter formula for the individual-level retention rate that features an initial steep drop and an asymptotic slow decay at the rate of inverse square root of time. Moreover, we prove sub-exponential distribution of purchase instances and provide closed-form formula for the firm's expected revenue. We estimate the model numerically by two methods: random walk simulation and numerically solving a heat equation. A comprehensive study shows that after incorporating consumer heterogeneity in the need arrival rate, our model provides a similar level of fit and prediction accuracy compared with popular existing models such as Pareto/NBD and BG/NBD. For the study, consumers' information tracking cost is estimated to be about $4.5 per annum.

Evaluating optimal purchasing and selling decisions of beef cattle replacement females

PurposeThe objective of this research was to determine the optimal age and pregnancy status for buying and selling replacement of beef females for risk-neutral and risk-averse producers.Design/methodology/approachA hedonic pricing model was estimated to measure how age, pregnancy status, breed and cull cow prices impact the sale price of these cattle. Data came from an annual heifer and cow sale in Tennessee between 2009 and 2018. A financial simulation model was developed to generate distributions of net present value (NPV) for buying replacement females at various ages and pregnancy status and then selling that female at various ages and pregnancy status.FindingsThe hedonic pricing model indicates sale prices were highest for five-year-old cows that were between four to five months pregnant. NPV was higher for buying heifers versus buying cows and for buying an open female versus a pregnant female. Regardless of age and pregnancy status when purchased, NPV was higher when the female was sold as pregnant prior to the end of her productive life. The risk analysis showed that risk aversion, buying older open cows and selling them as pregnant earlier in their productive life was preferredOriginality/valueThis research offers unique insight into how pregnancy status and age at sale impacts the animal's NPV while considering risk. These results have implications for educating producers on purchasing and selling decisions of heifers and cows as well as for lenders who finance these purchases.

Determination of minimum stock on system retail using forecast, economic order quantity and reorder point methods

In a globalization era, where retail business competition is getting tougher, a retail business has to have more advantages such as competitive selling prices, stock availability and others. In order to have competitive selling prices, a retail business should be able to arrange planning regarding goods availability to maintain balance between demand and existing stock (supply). The need for information on the availability of stock of goods in accordance with the sales that occur becomes very important. It is needed to avoid the goods accumulated excessively in the warehouse or even shortage of goods. If this kind of information about stocks both in a warehouse or the one that has been sold does not properly provided, it can cause reduction on the company’s profit because it can lead to more expenses on buying other goods as guessing that the stock of certain goods are running low or even more miscalculating to buy more goods that is actually still on the warehouse with sufficient quantities. These kind of situations were often occurred when a retail business do not have a tool to ensure the estimated purchase of stock needed for a certain period of time during selling. Therefore, it is required a system to help facilitate companies in carrying out retail business activities by using the Forecasting Method to help estimate quantitatively what will happen in the future with the stocks, based on relevant data in the past. In accordance with the results of the identification of demand patterns, the Forecasting Method used is Moving Average (MA), Weighted Moving Average (WMA), Single Exponential Smoothing (SES) and Double Exponential Smoothing (DES). After Forecasting, the best Forecast Method which has the lowest Mean Absolute Deviation (MAD) selection is made. This Economic Order Quantity (EOQ) method helps to determine the optimal purchase frequency. Through determining the optimal number and frequency of purchases, then optimal inventory control is obtained. The Reorder Point method can be used to find out what the minimum point is to be able to order a stock back, so that it is expected that the amount of stock that is not excessive and can meet sales needs optimally.

On multi-resource procurement in internet access markets: Optimal strategies and market equilibrium

With the increasing popularity and significance of content delivery services, especially video streaming, stringent Quality of Service (QoS) requirements have been placed upon Internet content providers (CPs). As a result, CPs have strong incentives to pay for resources such as premium peering bandwidth and cache capacity that ameliorate service quality. In this paper, we study an Internet access market with multiple access resources that CPs can purchase to enhance service quality. We build a detailed content delivery model, through which we characterize the traffic throughput and the resulting utilities of CPs and social welfare. We show that a market equilibrium exists for a multi-resource market, at which the optimization problems for individual utilities and social welfare coincide. Furthermore, we characterize the optimal purchasing strategies of CPs as well as how varying parameters are going to change the market equilibrium via sensitivity analysis.

Data-Driven Optimization for Commodity Procurement Under Price Uncertainty

Problem definition: We study a practice-motivated multiperiod stochastic commodity procurement problem under price uncertainty with forward and spot purchase options. Existing approaches are based on parametric price models, which inevitably involve price model misspecification and generalization error. Academic/practical relevance: We propose a nonparametric, data-driven approach (DDA) that is consistent with the optimal procurement policy structure but without requiring the a priori specification and estimation of stochastic price processes. In addition to historical prices, DDA is able to leverage real-time feature data, such as economic indicators, in solving the problem. Methodology: This paper provides a framework for prescriptive analytics in dynamic commodity procurement, with optimal purchase policies learned directly from data as functions of features, via mixed integer linear programming (MILP) under cost minimization objectives. Hence, DDA focuses on optimal decisions rather than optimal predictions. Furthermore, we combine optimization with regularization from machine learning (ML) to extract decision-relevant data from noise. Results: Based on numerical experiments and empirical data, we show that there is a significant value of feature data for commodity procurement when procurement policy parameters are learned as functions of features. However, overfitting deteriorates the performance of data-driven solutions, which asks for ML extensions to improve out-of-sample generalization. Compared with an internal best-practice benchmark, DDA generates savings of on average 9.1 million euros per annum (4.33%) for 10 years of backtesting. Managerial implications: A practical benefit of DDA is that it yields simple but optimally structured decision rules that are easy to interpret and easy to operationalize. Furthermore, DDA is generalizable and applicable to many other procurement settings.

Estimation of endogenously sampled time series: The case of commodity price speculation in the steel market

We consider the problem of estimating a Markov process that is endogenously sampled. We observe a discrete-time Markov process {pt} at a set of random times {t1,…,tn} that depend on the outcome of a probabilistic sampling rule that depends on the state of the process and other observed covariates xt. We focus on a particular example where pt is the daily wholesale price of a standardized steel product. The endogenous sampling problem arises from the fact that we only observe pt on the days the firm purchases steel. We show how to solve this problem under two different assumptions about firm behavior: (1) optimality: the timing of steel purchases is governed by an optimal purchasing strategy that maximizes expected discounted profits, and (2) potential suboptimality: we allow the firm to use any randomized, Markovian purchasing strategy. In the latter case, the estimation problem becomes semi-parametric and we use the method of sieves to estimate a flexible parametric approximation to the firm’s purchasing behavior that best fits the data without imposing optimality. We show how estimation of this model becomes tractable under either of these assumptions using the method of simulated moments (MSM). We simulate realizations of wholesale steel prices and sample them in the same way as they are sampled in the actual data, i.e. only on days where purchases occur. We use the MSM estimator to estimate a truncated lognormal AR(1) model of the wholesale price processes for particular types of steel plate and test and reject the assumption that the firm is behaving optimally.

Optimal consumption, investment, and life insurance purchase: a state-dependent utilities approach

We consider the problem of an individual who has to make decisions (under uncertainty) about optimal consumption, investment, and life insurance purchase in a financial market with a finite number of securities; the role of the life insurance is to protect the individual's family of an eventually early death. We propose facing the problem of optimal election under the alternative approach of state-dependent utilities; so we assume that preferences measure the agent's satisfaction for future cash flows valued by the market when the individual is making his/her decisions.

Analysis of two subsidies for EVs: Based on an expanded theoretical discrete-choice model

Electric vehicles (EVs) are one of the main tools to decrease greenhouse gas emissions. This study expands a welfare model by considering two goals for improving EV markets in China: subsidizing consumers and incentivizing innovation in EVs by conventional gasoline vehicle (GV) enterprises. By optimizing the welfare model, we analyze the optimal purchase and electricity subsidies. The effects of gasoline and electricity taxes are also analyzed. The results are as follows. First, optimal subsidies include two parts: the environmental cost of GHG emissions, and the part of the enterprise’s profits excluding the innovation risk. Second, the scale of the EV market, the level of technology, and the elasticity coefficient of capital-output can influence optimal subsidies. Third, the strength of both tax effects has an inverted-U shaped relationship with the EV market ratio. Finally, we offer some suggestions for Chinese subsidy regulation based on our study.

Optimalisasi Pembelian Perangkat Jaringan Telekomunikasi

Buana Selaras Globalindo company is a company which focuses on providing telecommunication equipment network. The main problem in this research is to find out how the optimal purchase of telecommunication network equipment at Buana Selaras Globalindo Jakarta company. The purpose of this research is to know the number of optimal purchases, the amount of safety provided, the time when repurchase is carried out, the maximum procurement (maximum inventory) and the total cost telecommunication equipment. The data was taken from field and library. The data was analysed with Economic Order Quantity (EOQ). The result of the analysis and discussion shows that the optimal purchase of OTB equipment is 1.429 units, ODP is 1.676 units, Closure is 1.728 units with four times frequency purchase. The safety stock for OTB equipment is 564 units, ODP is 406 units, Closure is 485 units. The ROP for OTB equipment is 1.402 units, ODP is 1.576 units, Closure is 1.729 units. The maximum inventory for OTB equipment is 1.983 units, ODP is 2,082 units, Closure is 2.213 units. The total inventory cost according to the EOQ method for OTB equipment is USD 1.121.144, ODP is USD 1.901.009, Closure is USD 1.976.334

Stackelberg Game Model of Railway Freight Pricing Based on Option Theory

In recent years, although rail transport has contributed significantly to the productivity of the Chinese economy, it has also been faced with the fierce competition and challenge from other modes of transportation, and therefore, freight-pricing issue has received more attention by researchers. In this paper, the rail freight option (RFO) based on option theory is proposed to study the optimal pricing decision of the railway transportation enterprise and contract customers’ optimal purchase decisions. To obtain an effective RFO contract, the railway freight contract transaction process is first analyzed. Then, the theoretical framework for the RFO contract trading is put forward in the railway freight market. Next, a two-stage Stackelberg game theoretic approach is presented based on the principle of utility maximization to achieve the optimal decision of RFO contract. Subsequently, the reverse reasoning method in dynamic programming is used to solve the optimal combination decision of the contract customer. Finally, the optimal pricing decision of RFO is discussed using Kuhn–Tucker conditions and Lagrangian function. The result shows that the railway transportation enterprise should pay more attention to the option strike price w1 in terms of maximizing system utility and achieving Pareto optimal.

Food Transparency as a Useful Guide to Optimal Food Purchases

The present interview study, with consumers living in Washington state, USA, set out to explore consumers’ perceptions of quality, safety and transparency and see how these influence shopping preferences. The results indicate that consumers are guided by subjective perceptions of food quality, as well as concerns driven by personal values and ethical and environmental considerations. Food safety was found to be confusing for almost all of the consumers in this study, with many expecting stores to provide safe foods. The study also utilized a concept testing method, to evaluate the concept of food transparency and examine how it compares against the established food certifications (organic and free range). Consumers exhibited trust in organic labels, expecting organic farming to ensure good farming practices and quality of life for animals reared for consumption, however they were also aware that this trust is based on assumptions. As a result, they were receptive to more accurate and informative solutions, such as transparency, that could guide their decisions and give them more certainty. Transparency was seen as a useful tool in identifying quality products, which align with personal values and as such, it was received well with consumers in the present study.

Coordination of Purchasing and Bidding Activities Across Markets

In both consumer purchasing and industrial procurement, combinatorial interdependencies among the items to be purchased are commonplace. E-commerce compounds the problem by providing more opportunities for switching suppliers at low costs, but also potentially eases the problem by enabling automated market decision-making systems, commonly referred to as trading agents, to make purchasing decisions in an integrated manner across markets. Most of the existing research related to trading agents assumes that there exists a combinatorial market mechanism in which buyers (or sellers) can bid (or sell) service or merchant bundles. Today's prevailing e-commerce practice, however, does not support this assumption in general and thus limits the practical applicability of these approaches. We are investigating a new approach to deal with the combinatorial interdependency challenges for online markets. This approach relies on existing commercial online market institutions such as posted-price markets and various online auctions that sell single items. It uses trading agents to coordinate a buyer's purchasing and bidding activities across multiple online markets simultaneously to achieve the best overall procurement effectiveness. This paper presents two sets of models related to this approach. The first set of models formalizes optimal purchasing decisions across posted-price markets with fixed transaction costs. Flat shipping costs, a common e-tailing practice, are captured in these models. We observe that making optimal purchasing decisions in this context is NP-hard in the strong sense and suggest several efficient computational methods based on discrete location theory. The second set of models is concerned with the coordination of bidding activities across multiple online auctions. We study the underlying coordination problem for a collection of first or second-price sealed-bid auctions and derive the optimal coordination and bidding policies.

A fuzzy multi-objective decision system for recoverable remanufacturing planning

This study develops a novel fuzzy multi-objective decision system (FMODS) that uses the Simplex method, Access database technology and the JAVA programming language, for recoverable product of remanufacturing planning. The system can be used to determine optimal purchase quantities and lot release sizes to make decision system for remanufacturing planning more effective, more convenient and smarter. The system has both single-objective linear programming (SOLP) and fuzzy multi-objective linear programming (FMOLP) functions to help managers in practical situations. The results in this investigation indicate that the proposed FMODS has a very favorable solution time in cases of large demand, and can significantly shorten the production planning time.

Peer-to-Peer Energy Trading Between Wind Power Producer and Demand Response Aggregators for Scheduling Joint Energy and Reserve

In this article, a stochastic decision-making framework is presented in which a wind power producer (WPP) provides some required reserve capacity from demand response aggregators (DRAs) in a peer-to-peer (P2P) structure. In this structure, each DRA is able to choose the most competitive WPP, and purchase energy and sell reserve capacity to that WPP under a bilateral contract-based P2P electricity trading mechanism. Based on this structure, the WPP can determine the optimal buying reserve from DRAs to offset part of wind power deviation. The proposed framework is formulated as a bilevel stochastic model in which the upper level maximizes the WPP's profit based on the optimal bidding in the day-ahead and balancing markets, whereas the lower level minimizes DRAs' costs. In order to incorporate the risk associated with the WPP's decisions and to assess the effect of scheduling reserves on the profit variability, conditional value at risk is employed.

Optimal purchase subsidy design for human-driven electric vehicles and autonomous electric vehicles

This paper studies the purchase subsidy design problem for human-driven electric vehicles (HDEVs) and autonomous electric vehicles (AEVs). The proposed range- and mode-specific purchase subsidy aims to maximize the social benefits from vehicle electrification and automation. In this study, we first classify electric vehicles (EVs) into several classes based on electric driving ranges. Each EV class contains two driving modes, i.e., human driving and automated driving. We provide a simplified model to estimate the greenhouse gas (GHG) emission and the inconvenience costs of vehicle charging. The nested logit model is used to characterize users’ vehicle choice behaviors. A mixed integer nonlinear programming (MINLP) model is formulated for the purchase subsidy design problem. A customized branch-and-bound (B&B) method is developed to seek a globally optimal solution to the formulated MINLP model. The numerical examples show that the developed solution method can effectively solve the proposed problem in a reasonable time. The local search strategy embedded in the customized B&B method helps reduce 7% computation time on average. Some managerial insights obtained from the numerical experiments are discussed, which can help the government agency to achieve a reasonable budget allocation between HDEVs and AEVs with different electric driving ranges.

Service quality guarantee design: obedience behavior, demand updating and information asymmetry

With the increasingly fierce market competition and the rapid development of advanced logistics technology, service quality guarantee and demand updating become effective ways to promote procurement decisions in logistics supply chain. However, information asymmetry and obedience behavior have made it more complicated. In this paper, we considered the above factors, and studied the capacity procurement issue in a logistics service supply chain consisting of a logistics service integrator (LSI) and a functional logistics service provider (FLSP) in two periods. First, we find the optimal purchase quantities increase with the FLSP’s obedience factor, in specific conditions, the LSI’s guaranteed service quality and FLSP’s obedience behavior can reach the upper limit (or lower limit). Second, the information symmetry creates a win–win situation iff the penalty cost to the FLSP is moderate and the demand is incompletely revealed. Third, demand updating relaxes the condition for the LSI’s service quality guarantee reaching to the upper limit. For FLSP, when the penalty cost is moderate, the demand updating makes FLSP less obedient in case that the demand is completely revealed and more obedient when the demand is incompletely revealed.

Optimal Purchasing Policy for Fresh Products from Multiple Supply Sources with Considerations of Random Delivery Times, Risk, and Information

ABSTRACTWe consider a problem in which a distributor purchases fresh products from multiple supply sources for subsequent sale at a wholesale market. Due to uncontrollable factors such as traffic congestion or bad weather conditions, the time taken for the product to be delivered from each production origin is uncertain. As the wholesale market is open for trading only in a fixed‐time window, any fresh products arriving earlier face the risk of decay, and any arriving later cannot be sold. The market demand for the product is random and follows a general distribution. We formulate the basic problem as a multi‐source selection model with random yield, taking into account the trade‐off between purchasing cost and other costs such as deterioration loss arising from delivery uncertainty. We derive the optimal order quantities from different origins and propose algorithms to search for them. We also investigate the effects of delivery uncertainty on service level and transport mode selection. Finally, we examine two extensions. One considers a capacity limit in each production origin, and the other incorporates information updating. For the first extension, we propose algorithms to compute the optimal solution based on its structural properties. For the second problem, we derive the optimal purchasing policy according to updated information such as details of the arrivals of previous orders.

The three-dimensional bone mass distribution of the posterior pelvic ring and its key role in transsacral screw placement

To optimize the placement of iliosacral screws in osteoporotic bone it is essential to know where to find the best purchase. The aim of this study was to determine and visualize the distribution of bone mass in the posterior pelvic ring by using a color-coded thermal map, to differentiate the bone distribution patterns in normal pelvises and in pelvises with impaired bone density and to identify zones in S1 and S2 with particularly good bone quality, in both healthy and osteoporotic pelvises. A total of 324 pelvises were included. The bone density of the posterior pelvic ring, the fifth lumbar vertebral body (L5) and screw corridors S1 and S2 were visualized. Each individual pelvis was measured with a 3D automated program. Two groups were selected - patients with mean bone density in L5 of ≤100 HU (group 1, n = 52) and those with mean bone density >100 HU (group 2, n = 272). Color-coded thermal maps are presented of the bone density distribution in the pelvises. Bone density in L5 correlated significantly with S1 and S2; bone density was significantly higher in the S1 than in the S2 corridor (p < 0.001). Bone was denser in the posterior and upper parts of the S1 body. Bone density was significantly lower in group 2 than in group 1 (p < 0.001). The color-coded “thermal” maps of bone mass distribution can help surgeons to decide where sacroiliac screws are likely to find optimal purchase.

Product assortment and space allocation strategies to attract loyal and non-loyal customers

Assortment planning deserves much attention from practitioners and academics due to its direct impact on retailers’ commercial success. In this paper we focus on the increasingly popular retail practice to use combined product assortments with both “standard” and more fashionable and short-lived “variable” products for building up store traffic of “loyal” and “non-loyal” heterogeneous customers and enlarging the sales due to the potential cross-selling effect.Addressing the assortment planning as a bilevel optimization problem, we focus on decision-dependent uncertainties: the retailer’s binary decision about product inclusion influences the distribution of the product’s demand. Furthermore, our model accounts for customers’ optimal purchase quantities, which depend on budget constraints limiting the basket that a customer is able to purchase.We propose iterative heuristics using optimal quantization of demand and customers budget distributions to define the total assortment and the inventory level per product. These heuristics provide lower bounds on the optimal value. We conduct a comparison to other existing lower bounds and we formulate upper bounds via linear (LP) and semidefinite (SDP) relaxations for the performance evaluation of the heuristics and for an efficient numerical solution in high-dimensional cases.For managerial insights, we compare the proposed approach with three assortment planning strategies: (1) the retailer does not carry variable products; (2) the retailer ignores the cross-selling effect; and (3) the maximum space allocated to each product is fixed. Our results suggest that variable assortment boosts the retailers profits if the cross-selling effect is not neglected in the decision about products quantities.

Analysis and Design of Interruptible Gas Contract in China under Energy Market Reform

Under the background of economic development, energy security and environmental demands, the development of clean and low-carbon energy has promoted natural gas and non-fossil energy to become the main direction of world energy development. China’s natural gas consumer market has wide seasonal peaks and valleys. Because China’s natural gas peak shaving practices have some problems, we concluded that interruptible gas management has become a viable short-term emergency peak shaving method for natural gas systems in the transition period. In this paper, we take Shaanxi Province as an example. From the perspective of option pricing, this paper explains the method of using interruptible gas management to deal with the short-term supply and demand imbalance of natural gas. Therefore, we propose an interruptible gas contract trading mode, discuss the content of the interruptible gas contract and the relevant market organization form, and try to use the Black–Scholes model to calculate the option price of the interruptible gas contract. Finally, based on the price of interruptible gas and the option price of the interruptible gas contract to meet the maximum capacity shortage constraint, a provincial natural gas pipeline network company’s optimal purchase model for the interruptible gas was established, and the model was solved using the dynamic queuing method. The results show that the interruptible gas contract can not only reduce the market risk of the provincial natural gas pipeline network company and maintain the stable operation of the gas pipeline, but also reduce the cost of the interruptible users and make up for gas shortage losses.