Operations planning for a multi-stage kanban system

A multi-stage production line which operates under a just-in-time production philosophy with linear demand is considered here. The first workstation processes the raw materials after receiving them from suppliers, a kanban mechanism between the workstations transports the work-in-process to the succeeding workstation, and after processing them, delivers the finished products to a buyer or a warehouse. The problem is to find optimally the number of raw material orders, kanbans circulated between workstations, finished goods shipments to the buyers, and the batch size for each shipment (lot). A cost function is developed based on the costs incurred due to the raw materials, the work-in-process between workstations, and the finished goods. Optimal number of raw material orders that minimizes the total cost is obtained, which is then used to find the optimal number of kanbans, finished goods shipments, and the batch sizes for shipments. Numerical examples are used to demonstrate the computations of optimal parameters, and to configure the kanban mechanism on a timescale. Several avenues for future research are also indicated.     

An Optimal Batch Size for a Production System Operating Under a Fixed-Quantity,Periodic Delivery Policy

A manufacturing system which procures raw materials from suppliers and processes them to convert to finished products is considered here. This paper develops an ordering policy for raw materials to meet the requirements of a production facility which, in turn, must deliver finished products demanded by outside buyers at fixed interval points in time. First, a general cost model is developed considering both supplier (of raw material) and buyer (of finished products) sides. This model is used to determine an optimal ordering policy for procurement of raw materials, and the manufacturing batch size to minimize the total cost for meeting equal shipments of the finished products, at fixed intervals, to the buyers. The total cost is found to be a piece-wise convex cost function. An interval that contains the optimal solution is first determined followed by an optimization technique to identify the exact solution from this interval.     

时变需求等量进货情形下集成供应链生产订货策略研究

构建了一个包含原料采购、生产和销售过程的集成供应链模型,研究了由原料、生产商和销售商产品构成的三层库存系统的生产订货问题。在有限的规划期内,销售商每次进货量相同,生产商按照EOQ模型采购原材料。以最小化供应链系统的总运营成本为目标,构建一个混合整数非线性规划模型,寻找销售商最优订货方案和生产商最佳生产策略。首先利用网络优化方法求解生产商的最优生产计划,其次利用定界穷举法寻求销售商最优的订货周期,给出了具体的计算方法和Matlab程序。通过算例分析验证了算法的有效性,并研究了各参数对最小费用及最优解的影响。     

A deterministic,multi-item inventory model with supplier selection and imperfect quality

This paper considers the scenario of supply chain with multiple products and multiple suppliers, all of which have limited capacity. We assume that received items from suppliers are not of perfect quality. Items of imperfect quality, not necessarily defective, could be used in another inventory situation. Imperfect items are sold as a single batch, prior to receiving the next shipment, at a discounted price. The demand over a finite planning horizon is known, and an optimal procurement strategy for this multi-period horizon is to be determined. Each of products can be sourced from a set of approved suppliers, a supplier-dependent transaction cost applies for each period in which an order is placed on a supplier. A product-dependent holding cost per period applies for each product in the inventory that is carried across a period in the planning horizon. Also a maximum storage space for the buyer in each period is considered. The decision maker, the buyer, needs to decide what products to order, in what quantities, with which suppliers, and in which periods. Finally, a genetic algorithm (GA) is used to solve the model.     

Operations policy for a supply chain system with fixed-interval delivery and linear demand

This research addresses a production-supply problem for a supply-chain system with fixed-interval delivery. A strategy that determines the optimal batch sizes, cycle times, numbers of orders of raw materials, and production start times is prescribed to minimize the total costs for a given finite planning horizon. The external demands are time-dependent following a life-cycle pattern and the shipment quantities follow the demand pattern. The shipment quantities to buyers follow various phases of the demand pattern in the planning horizon where demand is represented by piecewise linear model. The problem is formulated as an integer, non-linear programming problem. The model also incorporates the constraint of inventory capacity. The problem is represented using the network model where an optimal characteristic has been analysed. To obtain an optimal solution with N shipments in a planning horizon, an algorithm is proposed that runs with the complexity of Θ(N²) for problems with a single-phase demand and O(N³) for problems with multi-phase demand.     

A just-in-time three-level integrated manufacturing system for linearly time-varying demand process

This paper considers a just-in-time (JIT) manufacturing system in which a single manufacturer procures raw materials from a single supplier, process them to produce finished products, and then deliver the products to a single-buyer. The customer demand rate is assumed to be linearly decreasing time-varying. In the JIT system, in order to minimize the suppliers as well as the buyers holding costs, the supply of raw materials and the delivery of finished products are made in small quantities. In this case, both the supply and the delivery may require multiple installments for a single production lot. We develop a mathematical model for this problem, propose a simple methodology for solving the model, and illustrate the effectiveness of the method with numerical examples.     

An integrated inventory model with controllable lead time and distribution‐free demand

The impact of lead time reduction on an integrated periodic review inventory system comprising a single vendor and multiple buyers with a step crashing cost function and service‐level constraints is studied. The probability distribution of demand during the protection period for each buyer is unknown, but the mean and the variance are given. Each production lot of the vendor can be delivered in a number of shipments to all buyers. A minimax distribution‐free procedure with Lagrange multipliers is applied to determining the lead time, the common shipment cycle time, the target levels of replenishments and the number of shipments per production cycle so that the expected total system cost is minimized. Numerical experiments along with sensitivity analysis were performed to illustrate the effects of parameters on the decision and the total system cost. Copyright © 2009 John Wiley & Sons, Ltd.     

基于时变需求的集成多级供应链生产订货策略研究

考虑一个时变需求环境下集成多级供应链问题,在有限的规划时间内销售商以固定周期订货,而生产商以不同的周期生产,目的是寻找销售商最优的订货周期和生产商最佳的生产策略,从而使供应链系统的总运营成本最少.建立了该问题的混合整数非线性规划模型,求解该模型分为两步：先求对应一个订货周期的最佳生产策略,再求最优的订货周期,第一步用到了图论里求最短路方法.给出了两个步骤的算法和程序,实验证明它们是有效的.通过算例对模型进行了分析,研究了各参数对最优解及最小费用的影响.     

Single-vendor multi-buyer integrated production-inventory model with controllable lead time and service level constraints

This paper presents an integrated production-inventory model where a vendor produces an item in a batch production environment and supplies it to a set of buyers. The buyer level demand is assumed to be independent normally distributed and lead time of every buyer can be reduced at an added crash cost. The buyers review their inventory using continuous review policy, and the unsatisfied demand at the buyers is completely backordered. A model is formulated to minimize the joint total expected cost of the vendor–buyers system to determine the optimal production-inventory policy. Since it is often difficult to estimate the stock-out cost in inventory systems, and so instead of having stock-out cost component in the objective function, a service level constraint (SLC) corresponding to each buyer is included in the model. A Lagrangian multiplier technique based algorithmic approach is proposed, which evaluates a very limited number of combinations of lead time of the buyers to find simultaneously the optimal lead time, order quantity and safety factor of the buyers and the number of shipments between the vendor and the buyers in a production cycle. Finally, a numerical example and effects of the key parameters are included to illustrate the results of the proposed model.     

A coordination system for seasonal demand problems in the supply chain

This article considers a single product coordination system using a periodic review policy, participants of the system including a supplier and one or more heterogeneous buyers over a discrete time planning horizon in a manufacturing supply chain. In the coordination system, the demand of buyer in each period is deterministic, the supplier replenishes all the buyers, and all participants agree to plan replenishment to minimize total system costs. To achieve the objective of the coordination system, we make use of small lot sizing and frequent delivery policies (JIT philosophy) to transport inventory between supplier and buyers. Moreover, demand variations of buyers are allowed in the coordination system to suit real-world situations, especially for hi-tech industries. Furthermore, according to the mechanisms of minimizing the total relevant costs, the proposed method can obtain the optimal number of deliveries, shipping points and shipping quantities in each order for all participants in the coordination system.     

Newsvendor with multiple options of expediting

We consider a manufacturer facing single period inventory planning problem with uncertain demand and multiple options of expediting. The demand comes at a certain time in the future. The manufacturer may order the product in advance with a relatively low cost. She can order additional amount by expediting after the demand is realized. There are a number of expediting options, each of which corresponds to a certain delivery lead time and a unit procurement price. The unit procurement price is decreasing over delivery lead time. The selling price is also decreasing over time. In this paper, we assume that the manufacturer must deliver all products to the customer in a single shipment. The problem can be formulated as a profit maximization problem. We develop structural properties and show how the optimal solution can be identified efficiently. In addition, we compare our model with the classical newsvendor model and obtain a number of managerial insights.     

上升线性需求条件下考虑资金时间价值的变质性物品生产库存模型

变质性物品生产库存系统的研究具有重要实际意义.本文研究了变质性物品生产库存系统在上升趋势线性需求条件下,考虑资金的时间价值,在有限计划时间水平内,如何确定最优生产周期,各周期最优生产率,以及最优库存安排策略.通过本文的研究,得到了一些有用的结论.     

Competitive strategies and market segmentation for suppliers with substitutable products

This research studies the competition between two coexisting suppliers in a two-echelon supply chain. The suppliers have different inventory cost structures (holding cost and setup cost). Each supplier offers one type of the two substitutable products to multiple buyers. Buyers’ preferences between the substitutable products differ. Each buyer has a particular order profile (order frequency and quantity). A buyer chooses between the suppliers based on the prices offered by both suppliers and his/her own preference. A Hotelling-type model is used to describe buyers’ preferences for the products. We are able to describe the conditions for buyers to switch between the suppliers, and therefore spot the buyer groups that may or may not switch when the suppliers compete. Pricing strategies for different buyer groups are suggested to the competitive suppliers accordingly. Furthermore, equilibrium prices, market segments, and overall profits for the suppliers are revealed based on Game Theory. An algorithm is also proposed to forecast buyers’ reactions to suppliers’ pricing strategies given the buyers’ order profiles and preferences between the substitutable products.     

线性需求合并短缺的变质性物品的生产——库存模型

本文发展了线性需求合并短缺的变质性物品的生产——库存模型，以系统平均总费用最小为目标，提供了有限计划期内的生产调整策略以便适应市场需求的变化．同时还提供了无短缺情形的相应模型，最后出示了一些数字例子     

Dynamic dairy facility location and supply chain planning under traffic congestion and demand uncertainty: A case study of Tehran

In this paper, dynamic dairy facility location and supply chain planning are studied through minimizing the costs of facility location, traffic congestion and transportation of raw/processed milk and dairy products under demand uncertainty. The proposed model dynamically incorporates possible changes in transportation network, facility investment costs, monetary value of time and changes in production process. In addition, the time variation and the demand uncertainty for dairy products in each period of the planning horizon is taken into account to determine the optimal facility location and the optimal production volumes. Computational results are presented for the model on a number of test problems. Also, an empirical case study is conducted in order to investigate the dynamic effects of traffic congestion and demand uncertainty on facility location design and total system costs.     

Modeling a stochastic multi-objective supplier quota allocation problem with price-dependent ordering

One of the interesting subjects in supply chain management is supply management, which generally relates to the activities regarding suppliers such as empowerment, evaluation, partnerships and so on. A major objective of supplier evaluation involves buyers determining the optimal quota allocated to each supplier when placing an order. In this paper, we propose a multi-objective model in which purchasing cost, rejected units, and late delivered units are minimized, while the obtained total score from the supplier evaluation process is maximized. We assume that the buyer obtains multiple products from a number of predetermined suppliers. The buyer faces a stochastic demand with a probability distribution of Poisson regarding each product type. A major assumption is that the supplier prices are linearly dependent on the order size of each product. Since demand is stochastic, the buyer may incur holding and stockout costs in addition to the regular purchasing cost. We use the well-known L-1 metric method to solve the supplier evaluation problem by utilizing two meta-heuristic algorithms to solve the corresponding mathematical problems.     

Supply planning models for a remanufacturer under just-in-time manufacturing environment with reverse logistics

We study a supply planning problem in a manufacturing system with two stages. The first stage is a remanufacturer that supplies two closely-related components to the second (manufacturing) stage, which uses each component as the basis for its respective product. The used products are recovered from the market by a third-party logistic provider through an established reverse logistics network. The remanufacturer may satisfy the manufacturer’s demand either by purchasing new components or by remanufacturing components recovered from the returned used products. The remanufacturer’s costs arise from product recovery, remanufacturing components, purchasing original components, holding inventories of recovered products and remanufactured components, production setups (at the first stage and at each component changeover), disposal of recovered products that are not remanufactured, and coordinating the supply modes. The objective is to develop optimal production plans for different production strategies. These strategies are differentiated by whether inventories of recovered products or remanufactured components are carried, and by whether the order in which retailers are served during the planning horizon may be resequenced. We devise production policies that minimize the total cost at the remanufacturer by specifying the quantity of components to be remanufactured, the quantity of new components to be purchased from suppliers, and the quantity of recovered used products that must be disposed. The effects of production capacity are also explored. A comprehensive computational study provides insights into this closed-loop supply chain for those strategies that are shown to be NP-hard.     

Impact of supply base heterogeneity in electronic markets

Internet based marketplaces have enabled industrial buyers to locate suppliers from geographically diverse locations. This has resulted in increased variations in certain supplier parameters such as capacity and cost among the participating suppliers. However, the impact of this increased heterogeneity on the procurement practices are not well understood. In this paper we consider three supplier parameters that can affect the price the buyer pays and the number of suppliers that the buyer will select for award of contract. These attributes are capacity, production cost and demand for supplier’s capacity. We show how these parameters impact the price that a supplier quotes. We also show how the buyer will determine the optimum number of suppliers using a reverse auction mechanism when he does not have perfect knowledge of the suppliers’ parameters. Our model suggests that buyers need to adjust some of the input parameters while procuring capacity from a heterogeneous supply base. For instance, buyers need to pre-qualify more suppliers if the supply base has greater heterogeneity.     

Multiple-buyer multiple-vendor multi-product multi-constraint supply chain problem with stochastic demand and variable lead-time: A harmony search algorithm

In this paper, a multi-buyer multi-vendor supply chain problem is considered in which there are several products, each buyer has limited capacity to purchase products, and each vendor has warehouse limitation to store products. In this chain, the demand of each product is stochastic and follows a uniform distribution. The lead-time of receiving products from a vendor to a buyer is assumed to vary linearly with respect to the order quantity of the buyer and the production rate of the vendor. For each product, a fraction of the shortage is backordered and the rest are lost. The ordered product quantities are placed in multiple of pre-defined packets and there are service rate constraints for the buyers. The goal is to determine the reorder points, the safety stocks, and the numbers of shipments and packets in each shipment of the products such that the total cost of the supply chain is minimized. We show that the model of this problem is of an integer nonlinear programming type and in order to solve it a harmony search algorithm is employed. To validate the solution and to compare the performance of the proposed algorithm, a genetic algorithm is utilized as well. A numerical illustration and sensitivity analysis are given at the end to show the applicability of the proposed methodology in real-world supply chain problems.     

The scheduling of deliveries in a production-distribution system with multiple buyers

In a real production and distribution business environment with one supplier and multiple heterogeneous buyers, the differences in buyers’ ordering cycles have influence on production arrangements. Consequently, the average inventory level (AIL) at the supplier’s end is affected by both the production policy and the ordering policy, typically by the scheduling of deliveries. Consequently, the average inventory holding cost is most deeply affected. In this paper, it is proposed that the scheduling of deliveries be formulated as a decision problem to determine the time point at which deliveries are made to buyers in order to minimize the supplier’s average inventory. A formulation of the average inventory level (AIL) in a production cycle at the supplier’s end using a lot-for-lot policy is developed. Under the lot-for-lot policy, the scheduling of deliveries (SP) is formulated as a nonlinear programming model used to determine the first delivery point for each buyer with an objective to minimize the sum of the product of the individual demand quantity and the first delivery time for each buyer. Thus, the SP model determines not only the sequence of the first deliveries to individual buyers, but also the time when the deliveries are made. An iterative heuristic procedure (IHP) is developed to solve the SP model assuming a given sequence of buyers. Six sequence rules are considered and evaluated via simulation.