Coordinating a two-supplier and one-retailer supply chain with forecast updating

We consider the component-purchasing problem for a supply chain consisting of one retailer and two complementary suppliers with different lead-times. The retailer purchases a specific component from each supplier for assembling into a fashionable product. After ordering from the long-lead-time supplier (Supplier 1) and before ordering from the short-lead-time supplier (Supplier 2), the retailer can update its demand forecast for the product. The retailer can partially cancel its order from Supplier 1 after forecast updating. By formulating the problem as a dynamic optimization problem, we explore the measures that can be deployed to coordinate the retailer’s ordering decisions with forecast updating. We analytically show that the supply chain can be coordinated if both suppliers offer a returns policy and Supplier 1 charges an order-cancelation penalty to the retailer. We find that the coordination mechanism is independent of demand distribution and the forecast updating process. We further show that it is easier for the suppliers to coordinate the supply chain if market observation indicates the future market demand is sufficiently large. We also study the case where demand is price-dependent and propose a generalized revenue-sharing contract to coordinate the supply chain. We discuss the academic and managerial implications of the theoretical findings.     

Optimal decision making in multi-product dual sourcing procurement with demand forecast updating

In this paper, we will investigate a buyer's decision making problem in procuring multiple products, each treated as a newsvendor, from two markets. The contract market has a long lead time, a fixed wholesale price and resource constraints. While the spot market has an instant lead time and a highly volatile price. The purchasing decision at the spot market can be made near the beginning of the selling season to take the advantage of the most recent demand forecast. The buyer needs to determine the purchasing quantity for each product at the two markets to maximize the expected profit by trading off between the resource availability, demand uncertainty and price variability. The procurement decision making is modeled as a bi-level programming problem under both a single resource constraint and under multiple resource constraints. We show that this bi-level programming problem can be formulated as a single-level concave programming problem. We then develop a sequential algorithm which solves for a linear approximation of the concave programming problem in each iteration. This algorithm can be used to solve a real world problem with up to thousands of kinds of products, and is found to be highly efficient and effective.     

Supply chain structure and demand risk

V. Agrawal and S. Seshadri (2000) [Risk intermediation in supply chains. IIE Transactions, 32, 819-831] considered a problem in which a single risk neutral distributor supplies a short-lifecycle, long-leadtime product to several retailers that are identical except in their attitudes towards risk. They proved that the distributor should not offer the same terms to every retailer but instead offer less risky (from the demand risk perspective) contracts to more risk averse retailers. They did not prove the optimality of their menu.In this paper we reconstruct their results when the number of retailers is infinite and their coefficient of risk aversion is drawn from a continuous distribution. We use optimal control theory to solve this problem. We show that this distribution uniquely determines the channel structure. Moreover, the optimal contract menu not only has the same structure as in Agrawal and Seshadri but is also optimal among nearly all contracts. The implications of these findings for channel design are discussed.     

Optimal decisions for a two-echelon supply chain with capacity and demand information

Due to the applications of Internet of Things and big data in the Industry 4.0 context, more information in and out of a smart factory can be collected and shared between manufacturers and retailers. In this study, we consider two types of information that can be available in a supply chain consisting of a manufacturer and a retailer in Industry 4.0: the capacity information for the later rush production and the demand information shared between the retailer and manufacturer. In the supply chain, the manufacturer provides two orders with maximum limits by using a capacitated normal production and two capacitated rush production modes. To study the effects of the information, we investigate the optimal decisions and profits for the supply chain with and without the capacity information and demand information sharing. In addition, we propose a coordination mechanism for the supply chain with both the capacity information and demand information sharing. The coordination mechanism does not only rely on cost parameters, but also on the capacity and demand information. The numerical examples show that the supply chain profit can be improved by as large as 16.76% in the coordinated system, compared with the original system without the capacity information and demand information sharing.     

Ordering,wholesale pricing and lead-time decisions in a three-stage supply chain under demand uncertainty

This paper develops a game theoretic model of a three-stage supply chain consisting of one retailer, one manufacturer and one subcontractor to study ordering, wholesale pricing and lead-time decisions, where the manufacturer produces a seasonal/perishable product. We explicitly model the effects of the lead-time and the length of selling season on both demand uncertainty and inventory-holding costs. We present the equilibrium outcome of the decentralized supply chain. When the lead-time increases, we find that the retailer increases the order quantity, the manufacturer offers a lower unit-wholesale price and the subcontractor decreases its unit-wholesale price if the manufacturer subcontracts part of the retailer’s order. In the endogenous lead-time setting, we illustrate the effects of some factors such as unit holding cost and capacity on the equilibrium outcome. We find that a higher unit holding cost implies a lower optimal lead-time and order quantity while higher unit-wholesale prices; the basic demand uncertainty increases the optimal lead-time and order quantity while decreases the unit-wholesale prices. The effects of distribution form on equilibrium outcome/profits are investigated by employing a numerical example. The profit loss of decentralization decreases (increases) with the basic demand uncertainty and manufacturer’s capacity (mean demand).     

Sourcing with random yields and stochastic demand: A newsvendor approach

We studied a supplier selection problem, where a buyer, while facing random demand, is to decide ordering quantities from a set of suppliers with different yields and prices. We provided the mathematical formulation for the buyer's profit maximization problem and proposed a solution method based on a combination of the active set method and the Newton search procedure. Our computational study shows that the proposed method can solve the problem efficiently, and is able to generate interesting and insightful results that lead us to various managerial implications.

Scope and purpose

In today's globally competitive environment, decision makers in supply chains face numerous challenges particularly regarding the selection of suppliers or outsourcing partners. To assist in this endeavor, we examined a double-layered supply chain where a buyer facing the end users has the option of selecting among a cohort of suppliers. The available suppliers may have different yield rates and unit costs. The buyer has to decide, given the stochastic nature of the problem's governing parameters, whether or not to order from each supplier, and if so how much. We developed a ‘newsvendor-style’ model for the problem, and proposed a solution algorithm for it. Numerical studies were performed to provide some insights for supplier selection and order quantity decisions.     

基于需求偏差的供应链协调问题

分析了单供应商和单零售商组成的供应链在需求预测偏差下的协调问题.当市场规模和价格敏感系数同时发生变化时,为使供应链收益最大,提出了调整生产计划和零售价格的协调机制.进一步证明了利用数量折扣机制可协调需求偏差下的分权供应链,而且该机制还实现了供应链收益在供应商和零售商间的任意分配.最后进行了实例分析.     

Economic value added of supply chain demand planning: A system dynamics simulation

The development of a successful demand plan is typically a joint effort between different functional units such as Logistics, Marketing, Sales and executive management at one hand and between different business units on the other. Starting a project to structurally improve the demand planning often requires convincing all parties involved in such an effort. The key is to quantify the bottom-line impact of an increased demand planning reliability in the supply chain. This paper proposes a system dynamics simulation modeling framework that allows different managers to examine how improvements in their demand reliability will impact the overall corporate bottom-line. For example, supply chain managers can investigate how proposed changes in the supply chain demand forecasting structure, different suppliers, different logistics routes, or alternative inventory methods, may increase the overall profitability. The simulation model has been tested, validated with a real-life case of LG. Philips Displays Europe.     

Pricing and production decisions in dual-channel supply chains with demand disruptions

This paper develops a two-period pricing and production decision model in a one- manufacturer-one-retailer dual-channel supply chain that experiences a disruption in demand during the planning horizon. While disruption management has long been a key research issue in supply chain management, little attention has been given to disruption management in a dual-channel supply chain once the original production plan has been made. Generally, changes to the original production plan induced by a disruption may impose considerable deviation costs throughout the supply chain system. In this paper, we examine how to adjust the prices and the production plan so that the potential maximal profit is obtained under a disruption scenario. We first study the scenario where the manufacturer and the retailer are vertically integrated with demand disruptions. Then we further assume that the manufacturer bears the deviation costs and obtain the manufacturer’s and the retailer’s individual optimal pricing decision, as well as the manufacturer’s optimal production quantity in a decentralized decision-making setting. We derive conditions under which the maximum profit can be achieved. The results indicate that the optimal production quantity has some robustness under a demand disruption, in both centralized and decentralized dual-channel supply chains. We also find that the optimal pricing decisions are affected by customers’ preference for the direct channel and the market scale change, in both centralized and decentralized dual-channel supply chains.     

Price competition in duopoly supply chains with stochastic demand

In the literature, substantial researches have been carried out on supply chain coordination. The majority of these studies suggest a mechanism that enforces the supply chain members to follow the strategies that produce the equilibrium of an integrated supply chain. Moreover, most of researches do not consider the competition among supply chains.In this study, we consider an industry consisting of two distinct supply chains which compete with each other over price. Three algorithms are presented to calculate the equilibrium of three possible industry structures. It is assumed that demand is stochastic with additive form whose random component has a uniform distribution. Furthermore, the effect of competition and demand uncertainty intensity on the Nash equilibrium of the structures and supply chains’ profits are discussed in a numerical example.     

Commitment decisions with demand information updating and a capital‐constrained supplier

In this paper, we study a single two‐echelon supply chain with a capital‐constrained supplier (manufacturer) and a retailer. The supply chain faces a stochastic demand. As the production lead time is long, the market demand is updated during the supplier's production lead time. The supplier needs to determine the production quantity based on the original demand forecast, and the retailer needs to determine the time and quantity to order. The retailer can place an order before the supplier's production (preorder) or after the supplier's production (regular order). We prove the existence of optimal equilibrium solutions under both preorder and regular order strategies. We analytically investigate the order strategies for the supply chain agents under perfect and worthless market information updating. Moreover, we numerically analyze the impact of the information updating quality on the order strategy selection, and the effect of exogenous shocks on the supply chain agents.     

On ordering adjustment policy under rolling forecast in supply chain planning

Rolling forecast is a useful tool for lowering total cost with regard to practical inventory management. The details regarding a rolling forecast are obtained from a customer’s projected ordering data. The customer estimation of a rolling forecast may deviate from actual orders because of unstable conditions or customer’s deliberation. This study investigates what measures a customer might apply in responding to a situation where the rolling forecast deviates from the actual order. In addition, an appropriate ordering adjustment policy is proposed for better monitoring the supply chain performance with regard to a variant level of error concerning rolling forecast data. This study also considers the influence of lead time and inventory cost structure. We adopted a simulation approach, employing a model developed and examined in several different settings. The proposed ordering adjustment policies are determined by AVG, SD, and RMSE calculated from differences existing between historical forecasts and realized data. Levels of estimate error and estimate bias in a rolling forecast are included in the experimental procedure. Results reveal that the RMSE ordering adjustment policy is the most effective in situations of normal and downside estimation bias, whereas the AVG policy is more appropriate in the case of upside estimation bias. The level of estimation error is irrelevant to the selection of ordering adjustment policies, but it is positively associated with inventory costs. Stock-out costs and lead time are positively associated with inventory costs. Accuracy of the rolling forecast is therefore deemed to be essential in a situation involving a long lead time with high stock-out costs.     

The optimal integrated inventory policy with price-and-credit-linked demand under two-level trade credit

In this paper, we proposed a generalized, integrated, supplier–retailer inventory model using a trade credit policy. The trade credit policy adopted here is a two-level trade credit policy in which the supplier offers the retailer a permissible delay period M, and the retailer in turn provides customers a permissible delay period N. Cases where M > N and M ? N are explored thoroughly. In addition, the demand rate is assumed to be a function of both retail price and the customers’ credit period. Consequently, this paper deals with the problem of determining the optimal retail price, economic order quantity, and the number of shipments from the supplier to the retailer in one production run for an integrated inventory system under both two-level trade credit and price-and-credit-linked demand rate. Algorithms are developed in order to determine the joint optimal policies. Numerical examples are presented to illustrate the proposed models, as well as sensitivity analysis of key parameters.     

Formulating and solving parametric design problems involving non-interference constraints

Improvements in computer-aided design (CAD) tools can significantly increase designer productivity, since the ability to explore a variety of possible designs quickly and effectively is essential for a designer. Using an optimization tool, systematic exploration of design spaces can be achieved readily. The general goal of the work presented here is to aid design by combining the strengths of optimization techniques with those of CAD systems. The specific objective of this paper is to introduce goal directed geometry (GDG) as a computational framework for parametric design, aiding the formulation of engineering problems with geometric considerations and their solution with a multi-objective optimization package. Using GDG, What if questions can be posed and answered in a systematic fashion. Specific issues to be addressed include the development of a general parametric design problem formulation, development of static and dynamic geometric non-interference constraints for use in this formulation, and investigation of the efficacy of the adaptive linear programming (ALP) multiobjective optimization algorithm in solving such problems. Two examples are presented, one each to illustrate the use of the static and dynamic non-interference constraints. Results demonstrate that the GDG formulation can be applied readily to a wide variety of parametric design problems. Additionally, the ALP algorithm successfully navigates around geometric constraints, although care must be taken when linearizing highly non-linear design spaces.     

Solving quality control problems with an algorithm for minimax programs with coupled constraints

We propose a systematic algorithm to tackle a set of acceptance sampling problems introduced by Seidel [1] and their generalization when no prior knowledge is assumed. The problems are modeled as minimax problems with coupled or decoupled constraints. We use ideas from recent work on bi-level programming, reformulating the problem as a semi-infinite program with disjunctive constraints and employing a two phase discretization method to solve it. We use the KKT conditions of the inner problem of minimax to tighten the relaxation of the semi-infinite problem obtained by discretization. In addition, to avoid convergence trouble, a strategy based on a feasibility test relative to the objective value of the outer program is used.     

Impact of demand correlation and information sharing in a capacity constrained supply chain with multiple-retailers

This paper considers a single product, two-echelon capacity constrained supply chain consisting of a supplier and two retailers facing correlated end-item demand. We use a decentralized Markov decision process with restricted observations to represent this system and conduct a numerical study to quantify the benefits of information sharing to the retailers under varying levels of supplier capacity and supply allocation mechanisms. Our results show an inverse relationship between capacity and information and indicate the retailers can achieve significant benefits as a result of the information sharing partnership.     

需求不确定下考虑网络营销的供应链决策模型

利用报童理论和退货政策模型,研究了传统市场与电子商务市场的内在关系,建立了供应商参与两种市场联合营销情况下的供应链管理模型.重点分析了供应商如何在电子商务环境下组织生产,如何通过实施协作提高供应链总利润,如何评估两种市场上的销售策略.最后采用算例分析的方法,证明了模型和算法的有效性和可行性.     

Quantitative analysis of semiconductor supply chain contracts with order flexibility under demand uncertainty: A case study

The evidence base for the configuration of rolling horizon flexibility (RHF) contracts (a type of quantity flexibility contract) used in the semiconductor industry to coordinate production and demand remains meagre, more art than science. Informed by the characteristics of actual clauses and demand behaviors drawn from a company’s experience, a discrete-event simulation model is developed to represent the company’s supply chain. It comprises of three parties: a customer, a supplier (semiconductor manufacturer), and a capacity provider. Through analysis of customer forecasted demand the paper characterizes forecast demand as being under, over or unbiased. Models of these forecasted demands drives both long and short term planning. In long term planning, which is given twelve months before an order is delivered, capacity at the capacity provider is booked. Short term planning is also driven by this forecast which, within a binding period, is governed by an RHF contract. Results from the model report inventory levels, and delivery compliance, namely Delivery Performance (DP) and Delivery Reliability (DR), measures widely used in this sector. It is concluded from this work that on the balance of performance measures RHF contracts with asymmetrical flexibility bounds are substantially better than those with symmetrical boundaries, and that this conclusion is robust with regard to both over-planning and under-planning behaviors. This robustness is a critical attribute with respect to the endemic medium-term vacillation between both states experienced in practice in this sector.     

Exact solutions to some minimum time problems with inequality state constraints

A heuristic method is developed for generating exact solutions to certain minimum time problems, with inequality state and control constraints. The control equation is linear and autonomous, with scalar-valued control. The state constraints are also linear inequalities. Assuming knowledge of a finite sequence, in which state and/or control constraints become active along an optimal path, the maximum principle is reduced to a set of equations and inequalities in a finite number of unknowns. A solution to the equations and inequalities determines both the solution path and a proof of its optimality. Certain types of constraint sequences lead to overdetermined equation systems, and this fact is interpreted in terms of the qualitative behavior of solutions to these problems. Two path-planning problems are solved, as illustrations of the solution technique.     

带运输时间的无等待供应链在线调度问题研究

研究了供应链在线调度问题.该问题具有工件无等待、工序之间存在运输时间、加工时间介于一个区间等特点,制造商随时可能接到顾客订单,订单到达前,所有信息如订单数量、到达时间及加工时间等均未知.研究了在不改变已有工件调度的情况下,使用资源的可用时间区间最早完成临时订单的算法.计算机仿真表明,使用该算法求解大规模临时订单问题是十分有效的.