A dynamic inventory model with supplier selection in a serial supply chain structure

Considering the inherent connection between supplier selection and inventory management in supply chain networks, this article presents a multi-period inventory lot-sizing model for a single product in a serial supply chain, where raw materials are purchased from multiple suppliers at the first stage and external demand occurs at the last stage. The demand is known and may change from period to period. The stages of this production–distribution serial structure correspond to inventory locations. The first two stages stand for storage areas for raw materials and finished products in a manufacturing facility, and the remaining stages symbolize distribution centers or warehouses that take the product closer to customers. The problem is modeled as a time-expanded transshipment network, which is defined by the nodes and arcs that can be reached by feasible material flows. A mixed integer nonlinear programming model is developed to determine an optimal inventory policy that coordinates the transfer of materials between consecutive stages of the supply chain from period to period while properly placing purchasing orders to selected suppliers and satisfying customer demand on time. The proposed model minimizes the total variable cost, including purchasing, production, inventory, and transportation costs. The model can be linearized for certain types of cost structures. In addition, two continuous and concave approximations of the transportation cost function are provided to simplify the model and reduce its computational time.     

Coordination of dynamic lot-sizing in supply chains

This paper presents a new scheme for the coordination of dynamic, uncapacitated lot-sizing problems in two-party supply chains where parties’ local data are private information and no external or central entity is involved. This coordination scheme includes the following actions: At first, the buyer generates a series of different supply proposals using an extension of her local lot-sizing problem. Then the supplier calculates his cost changes that would result from the implementation of the buyer’s proposals. Based on these information, parties can identify the best proposal generated. The scheme identifies the system-wide optimum in different settings—for instance in a two-stage supply chain where the supplier’s costs for holding a period’s demand in inventory exceed his setup costs.     

Inventory control with an order-time constraint: optimality,uniqueness and significance

This paper analyzes a stochastic inventory problem with an order-time constraint that restricts the times at which a manufacturer places new orders to a supplier. This constraint stems from the limited upstream capacity in a supply chain, such as production capacity at a supplier or transportation capacity between a supplier and a manufacturer. Consideration of limited upstream capacity extends the classical inventory literature that unrealistically assumes infinite supplier/transporter capacity. But this consideration increases the complexity of the problem. We study the constraint under a Poisson demand process and allow for a fixed ordering cost. In presence of the constraint, we establish the optimality of an (s,S) policy under both the discounted and average cost objectives. Under the average cost objective, we show the uniqueness of the order-up-to level S. We numerically compare our model with the classical unconstrained model. We report significant savings in costs that can be achieved by using our model when the order time is constrained.     

A practical solution approach for the cyclic inventory routing problem

Vendor managed inventory (VMI) is an example of effective cooperation and partnering practices between up- and downstream stages in a supply chain. In VMI, the supplier takes the responsibility for replenishing his customers’ inventories based on their consumption data, with the aim of optimizing the over all distribution and inventory costs throughout the supply chain. This paper discusses the challenging optimization problem that arises in this context, known as the inventory routing problem (IRP). The objective of this IRP problem is to determine a distribution plan that minimizes average distribution and inventory costs without causing any stock-out at the customers. Deterministic constant customer demand rates are assumed and therefore, a long-term cyclical approach is adopted, integrating fleet sizing, vehicle routing, and inventory management. Further, realistic side-constraints such as limited storage capacities, driving time restrictions and constant replenishment intervals are taken into account. A heuristic solution approach is proposed, analyzed and evaluated against a comparable state-of-the-art heuristic.     

Integrated location and two-echelon inventory network design under uncertainty

In this paper, we propose a two-stage stochastic model to address the design of an integrated location and two-echelon inventory network under uncertainty. The central issue in this problem is to design and operate an effective and efficient multi-echelon supply chain distribution network and to minimize the expected system-wide cost of warehouse location, the allocation of warehouses to retailers, transportation, and two-echelon inventory over an infinite planning horizon. We structure this problem as a two-stage nonlinear discrete optimization problem. The first stage decides the warehouses to open and the second decides the warehouse-retailer assignments and two-echelon inventory replenishment strategies. Our modeling strategy incorporates various probable scenarios in the integrated multi-echelon supply chain distribution network design to identify solutions that minimize the first stage costs plus the expected second stage costs. The two-echelon inventory cost considerations result in a nonlinear objective which we linearize with an exponential number of variables. We solve the problem using column generation. Our computational study indicates that our approach can solve practical problems of moderate-size with up to twenty warehouse candidate locations, eighty retailers, and ten scenarios efficiently.     

The impact of forecasting model selection on the value of information sharing in a supply chain

This paper presents a study on the impact of forecasting model selection on the value of information sharing in a supply chain with one capacitated supplier and multiple retailers. Using a computer simulation model, this study examines demand forecasting and inventory replenishment decisions by the retailers, and production decisions by the supplier under different demand patterns and capacity tightness. Analyses of the simulation output indicate that the selection of the forecasting model significantly influences the performance of the supply chain and the value of information sharing. Furthermore, demand patterns faced by retailers and capacity tightness faced by the supplier also significantly influence the value of information sharing. The result also shows that substantial cost savings can be realized through information sharing and thus help to motivate trading partners to share information in the supply chain. The findings can also help supply chain managers select suitable forecasting models to improve supply chain performance.     

An integrated model for lot sizing with supplier selection and quantity discounts

Good inventory management is essential for a firm to be cost competitive and to acquire decent profit in the market, and how to achieve an outstanding inventory management has been a popular topic in both the academic field and in real practice for decades. As the production environment getting increasingly complex, various kinds of mathematical models have been developed, such as linear programming, nonlinear programming, mixed integer programming, geometric programming, gradient-based nonlinear programming and dynamic programming, to name a few. However, when the problem becomes NP-hard, heuristics tools may be necessary to solve the problem. In this paper, a mixed integer programming (MIP) model is constructed first to solve the lot-sizing problem with multiple suppliers, multiple periods and quantity discounts. An efficient Genetic Algorithm (GA) is proposed next to tackle the problem when it becomes too complicated. The objectives are to minimize total costs, where the costs include ordering cost, holding cost, purchase cost and transportation cost, under the requirement that no inventory shortage is allowed in the system, and to determine an appropriate inventory level for each planning period. The results demonstrate that the proposed GA model is an effective and accurate tool for determining the replenishment for a manufacturer for multi-periods.     

Approximate analysis and optimization of batch ordering policies in capacitated supply chains

Devising manufacturing/distribution strategies for supply chains and determining their parameter values have been challenging problems. Linking production management to stock keeping processes improves the planning of the supply chain activities, including material management, culminating in improved customer service levels. In this study, we investigate a multi-echelon supply chain consisting of a supplier, a plant, a distribution center and a retailer. Material flow between stages is driven by reorder point/order quantity inventory control policies. We develop a model to analyze supply chain behavior using some key performance metrics such as the time averages of inventory and backorder levels, as well as customer service levels at each echelon. The model is validated against simulation, yielding good agreement of robust performance metrics. The metrics are then used within an optimization framework to design the supply chain so as to minimize expected total system costs. The outcome of the optimization framework specifies how to move inventory throughout the supply chain and how to set inventory control parameters, i.e., reorder levels and replenishment batch sizes.     

Profit maximization in an inventory system with time-varying demand,partial backordering and discrete inventory cycle

In this paper, an inventory problem where the inventory cycle must be an integer multiple of a known basic period is considered. Furthermore, the demand rate in each basic period is a power time-dependent function. Shortages are allowed but, taking necessities or interests of the customers into account, only a fixed proportion of the demand during the stock-out period is satisfied with the arrival of the next replenishment. The costs related to the management of the inventory system are the ordering cost, the purchasing cost, the holding cost, the backordering cost and the lost sale cost. The problem is to determine the best inventory policy that maximizes the profit per unit time, which is the difference between the income obtained from the sales of the product and the sum of the previous costs. The modeling of the inventory problem leads to an integer nonlinear mathematical programming problem. To solve this problem, a new and efficient algorithm to calculate the optimal inventory cycle and the economic order quantity is proposed. Numerical examples are presented to illustrate how the algorithm works to determine the best inventory policies. A sensitivity analysis of the optimal policy with respect to some parameters of the inventory system is developed. Finally, conclusions and suggestions for future research lines are given.

     

Evaluating and selecting the supplier in detergent production industry using hierarchical fuzzy TOPSIS

Supply chain management has increasingly attracted attention as a systematic approach to integrate the supply chain in order to planning and controlling the materials and information from suppliers to customers. One of the most important issues in supply chain management is selection of the appropriate supplier which has significant effect on purchasing cost decrease and increase in the organization’s competition ability. Selection of the best supplier is naturally complex with no definite structure, and dependent on the type of suppliers’ activity. In the process of decision making about suppliers and many qualitative and quantitative performance indicators such as quality, price, flexibility, and due date should be considered. Then, the supplier selection problem is a multi-criteria decision making problem where numerous methods have been proposed to solve this problem so far. In the current paper, four suppliers of imported raw material “Tripolyphosphate (TPP)” (primary material to produce the detergent powder with a case study in Iran) are evaluated based on 25 effective criteria using the hierarchical fuzzy TOPSIS (HFTOPSIS) approach.     

Integrated inventory management and supplier base reduction in a supply chain with multiple uncertainties

This paper considers a manufacturing supply chain with multiple suppliers in the presence of multiple uncertainties such as uncertain material supplies, stochastic production times, and random customer demands. The system is subject to supply and production capacity constraints. We formulate the integrated inventory management policy for raw material procurement and production control using the stochastic dynamic programming approach. We then investigate the supplier base reduction strategies and the supplier differentiation issue under the integrated inventory management policy. The qualitative relationships between the supplier base size, the supplier capabilities and the total expected cost are established. Insights into differentiating the procurement decisions to different suppliers are provided. The model further enables us to quantitatively achieve the trade-off between the supplier base reduction and the supplier capability improvement, and quantify the supplier differentiation in terms of procurement decisions. Numerical examples are given to illustrate the results.     

Profit oriented supply chain network optimization

This paper proposes a novel mixed integer linear programming model to solve a supply chain network design problem. The proposed model deals with major issues for supply chains; product quality and cost. These issues are usually solved separately, but in this paper, we investigate effects of product quality on supply chain design and transportation flow. A trade-off between raw material quality, its purchasing and reprocessing costs was considered. Assuming decision maker (DM) wishes to work with a supplier which serves a low quality raw material; this raw material should be in need of reprocessing. To avoid the reprocessing costs, a supplier which serves a high quality raw material should be chosen but at this time the DM has to face a high purchasing cost. A supply chain network which consists of multiple suppliers, manufacturers, distribution centers and retailers is tried to be designed to accomplish aforementioned above trade-offs. The paper examines and discusses the relationship between product quality and supply chain design and offers several managerial insights.     

JIT环境下三级供应链供需协调模型研究

模型以整个供应链成本最低为目标,在JIT环境下通过对原材料供应商、制造商和零售商等各阶段库存模型以及其他相关成本的研究,得到供应链的最优物料补充策略,制造商的最优生产策略以及产成品运输策略。供应链结构包括一个制造商,多个原材料供应商和零售商。研究表明,通过有效的加强整条供应链的协作,能够有效降低供应链的总成本。     

Production control and replenishment strategy with multiple suppliers

This paper considers the joint supplier selection, replenishment and manufacturing control problem in a dynamic stochastic context. This problem is characterized by conflicting interests between suppliers, the manufacturer, and clients, which raise the need for coordination and information sharing. This paper contributes to the discourse mainly by developing and resolving an integrated mathematical model leading to information sharing strategies for supplier selection, replenishments and production activities. This is an optimal control problem with state constraints and hybrid dynamics. A dynamic stochastic model is thus proposed, and the optimality conditions obtained are then solved numerically. It is shown that the problem considered leads to a modified state-dependent multi-level (s, S) policy for the supplier selection and replenishment strategy and a base-stock policy for the production activities. The fact that these control policies are coupled confirms the necessity of considering the interactions present in the system in an integrated model. The obtained results show clearly that it is always profitable to consider multiple suppliers to make replenishment and production decisions. Moreover, it is shown that the availability rates of the supply chain actors and the replenishment lead time are important parameters to consider when choosing the best supplier.     

考虑供应链风险和绩效的供应商选择的模糊动态非线性多目标规划模型

基于供应链风险和供应链绩效的模糊性和供应商选择问题的动态性,本文考虑供应链风险和供应链绩效作为模糊变量,讨论如何给生产商一个满意的动态多目标供应商选择方案,确定供应链风险和总成本最小,以及供应链绩效最大。然后对该问题提出了一个动态多目标多产品供应商选择模型,该模型是首次同时考虑供应商选择,订单分配,供应链风险和供应链绩效的一个模糊动态非线性多目标规划模型。为了去模糊化和求解该模型,给出了一个风险和绩效的模糊评估法。最后给出一个数值算例验证了该模型的可行性,为决策者选择供应商提供了理论依据。     

Inventory decisions for a finite horizon problem with product substitution options and time varying demand

The inventory control of substitutable products has been recognized as a problem worthy of study in the operations management literature. Product substitution provides flexibility in supply chain management and enhances response time in production control. This paper proposes a finite horizon inventory control problem for two substitutable products, which are ordered jointly in each replenishment epoch. Demand for the products are assumed to be time–varying. In case of a stock–out for one of the products, its demand is satisfied by using the stock of the other product. The optimal ordering schedule, for both products, that minimizes the total cost over a finite planning horizon is derived. Numerical examples along with sensitivity analyses are also presented.     

Effect of coordinated replenishment policies on quality

Coordinated replenishment is a supply chain policy that affects many operational performance measures, including cost, lead time, and quality. In this paper, we develop a mathematical model of a simplified supply chain in which conformance quality is one of the supplier's decision variables and both the supplier and its customer are trying to minimize expected annual cost. Our expected cost model includes the important quality costs (appraisal, prevention, internal failure, and external failure) as well as holding, set-up, and ordering costs. Our results indicate that coordination leads to a decline in total cost but that coordination does not necessarily lead to an improvement in quality. In other words, buyers who are using coordinated replenishment may be trading higher quality for lower cost.     

Coordination mechanism for capacity reservation by considering production time,production rate and order quantity

In this paper we study the coordination of a dyadic supply chain producing a high-tech product by contracts. The product has a short life cycle and the buyer faces stochastic demands during the selling period. We consider the production time, which causes the inventory costs on supplier’s side. As the supplier builds production capacity in advance, the production rate is limited to the capacity created during the production time. In addition, we take into account the inventory cost and operational cost for the buyer. We examine the model under both full information and partial information updating situations, and propose a coordinating contract for each case. Our analysis includes the study of members’ decisions under both forced and voluntary compliance regimes. Numerical results are presented to provide more insights into the models developed and the mechanisms proposed.