A Simulation Study of Dynamic Order-up-to Policies in a Supply Chain with Non-Stationary Customer Demand and Information Sharing

This study deals with the development of heuristic settings for dynamic order-up-to levels at different installations in a supply chain with non-stationary customer demand, in order to minimize the sum of inventory, shortage and transport costs. Balance equations are developed to capture the dynamics of supply chain. Mathematical expressions are derived to determine the dynamic order-up-to levels as a function of forecasted demand, forecasted replenishment leadtime and safety factor. Towards this attempt, different heuristic settings with respect to the safety factor are first proposed. Next, three levels of information sharing among the members of the supply chain are considered to study the impact of information sharing on the total cost. Finally, the use of a forecasting technique for predicting the replenishment leadtime is considered. A supply chain is simulated to evaluate the proposed dynamic order-up-to policies based on various heuristic settings. It is found that the use of forecast of replenishment leadtime and customer demand information sharing, and the proposed safety-stock heuristic settings in the determination of dynamic order-up-to levels, significantly reduce the sum of discounted inventory, shortage and transport costs of the supply chain.     

Optimal pricing and replenishment policies of an EOQ model for non-instantaneous deteriorating items with shortages

This paper discusses the optimal pricing and replenishment policies of an economic order quantity model for non-instantaneous deteriorating items with partial backlogging over an infinite time horizon. The model is studied under the replenishment policy starting with no shortages. The backlogging rate is any non-increasing function of the waiting time up to the next replenishment. The objective of this model is to maximize the total profit which includes the sales revenue, purchasing cost, set up cost, holding cost, shortage cost, and opportunity cost due to lost sales. Here, the selling price, replenishment quantity, replenishment cycle length, and the time duration of the positive inventory level are taken as decision variables to maximize the profit of the inventory system. The existence and the uniqueness of the solution of the proposed inventory system are examined. We suggest a solution procedure to find the optimal solution of the described model. Numerical examples are presented to determine the developed model and the solution procedure. Sensitivity analysis of the optimal solution with respect to major parameters is carried out and some useful managerial results are obtained.     

A replenishment policy based on joint optimization in a downstream pharmaceutical supply chain: centralized vs. decentralized replenishment

This paper considers a number of problems in a pharmaceutical downstream supply chain under specific constraints related to pharmaceutical products (e.g., their expiry date and regulations) and to inventory control (e.g., low prices of products, gift products or prices near zero, shortages prohibited but excess inventory allowed). As traditional models of inventory control and replenishment cannot optimize the total cost of the system, it is very important to consider the transportation cost as well. In this paper, we take into account some of these constraints and propose two models for multi-product replenishment policies, namely centralized and decentralized models. We seek to identify the best quantity and period of replenishment of products for a joint optimization of inventory and transportation costs. The proposed models can be applied to a specific family of products with a stable demand and high turnover rate, low prices (or gift products for some of them), and without any shortage. These two models are compared and the global approach is illustrated by a numerical example taken from a real-case study.     

Impact of forecasting methods on variance ratio in order-up-to level policy

This paper considers the impact of forecasting methods on the bullwhip effect for a simple replenishment system in which a first-order autoregressive process describes the customer demand and an order-up-to inventory policy characterizes the replenishment decision. The impact of exponential smoothing and minimum mean squared error forecasting is measured for both the bullwhip effect and inventory variances. Previous similar studies have focused on investigating the impact of forecasting methods on bullwhip effect. However, little research has been carried out to explore the impact of forecasting methods for both bullwhip effect and inventory variances. Through simulation experiments, it has been found that depending on the structure of the demand process, the appropriate selection of forecasting technique can reduce, or even eliminate (i.e., “dewhip”) the bullwhip effect. However, in terms of inventory variances it has been shown that the inventory variances for the exponential smoothing are greater than the minimum mean squared error forecasting method and that gap increases as lead time increases. These findings will help companies to choose the appropriate forecasting technique depending on the nature of demand. These guidelines can help companies to reduce the bullwhip effect and inventory variances across supply chain.     

Economic order quantity for deteriorating items with time discounting

In this paper, an economic order quantity model for deteriorating items with time discounting has been developed for varying demand pattern over a fixed planning horizon. Optimal solutions with complete backlogging and without backlogging are established and has proven that the total variable cost is convex. The main contribution of this paper is based on the assumption of the demand which is the linear function of the instantaneous stock level I(t). In this paper, a new type of demand has been considered which will help us to obtain qualitative insights without much analytical complexity. Optimal solutions of the proposed models are derived and effects of deterioration on the inventory replenishment policies are studied with the help of numerical examples.     

Inventory replenishment and delivery planning in a two-level supply chain with compound Poisson demands

This paper presents a model for integrating inventory replenishment and delivery planning in a two-level supply chain consisting of a supplier and a retailer. The supplier is authorized to manage the inventory level of the retailer by using the information on demands from final customers and the inventory level of the retailer. The problem considered here is to determine order-up-to levels of the supplier and the retailer simultaneously for the objective of minimizing the expected long-run average cost, which is composed of replenishment cost at the supplier, delivery cost to the retailer, and inventory holding costs at both members. We develop a renewal theoretic optimization model for a case of compound Poisson demands with distribution-free order quantities and present an approximation method for obtaining a solution of the problem. In addition, a closed-form solution is derived for the problem with a special case of compound Poisson demands, in which demand quantities follow an exponential distribution. A series of simulation tests show that the solutions obtained from the approximated cost functions are reasonably good.     

Scheduling and replenishment plan for an integrated deteriorating inventory model with stock-dependent selling rate

An integrated approach is used to clarify the critical issues of scheduling and replenishment planning in an advanced inventory system under stock-dependent selling rate environment. This is because integration removes the barriers between enterprises and improves overall performance. A close collaboration such as just-in-time (JIT) operations also improves product quality of the supply chain. Different from the single-stage inventory model, this study develops an integrated two-stage production-inventory deteriorating model for the buyer and the supplier with stock-dependent selling rate, as well as considering imperfect items and JIT multiple deliveries. Our paper proposes a significant method using a time-weighted-inventory approach to analyze the supplier’s saw-tooth holding cost. We derive the optimal number of inspection, optimal deliveries and the optimal delivery-time interval. A numerical example is also presented to illustrate the theory. The results show that the fixed demand rate, the holding cost and the unit inspection cost are critical in the management of the deteriorating inventory model.     

General bounds for the optimal value of retailers’ reorder point in a two-level inventory control system with and without information sharing

In this study, an inventory system consisting of a single product, one supplier, and multiple identical retailers is considered. Each retailer replenishes inventory from the supplier according to the well known (R,Q) policy. Transit times are constant and retailers face independent Poisson demand. The supplier utilizing the retailers' information in decision making for replenishment policy with a given order size starts with m initial batches (of size Q) and places an order in a batch of size Q to an outside source when a new order is placed. In this inventory system, excess demand is backordered, delayed orders are satisfied on a first-come first-serve basis, and no partial shipment is allowed. By partitioning the cost function of this system, general upper and lower bounds for the optimal value of R are determined. Based on several numerical examples, it is shown that these bounds (especially the lower bound) allow the optimal reorder point to be found more effectively with a shorter solving time.     

模糊环境下含缺陷率且允许缺货的经济生产批量模型

鉴于实际生产库存管理中的产品缺陷问题,研究了允许缺货情况下含确定缺陷率和模糊缺陷率的经济生产批量问题.根据产品检验速率的不同,建立了两种含LR型模糊缺陷率、模糊需求、模糊缺货费、模糊检验费、模糊存储费和模糊订货费的经济生产批量模型.运用符号距离,将模糊模型转化为确定模型,进而确定了其最优生产策略.通过理论分析,揭示了模糊与经典经济生产批量模型的关系.结合算例,分析了产品缺陷率的模糊性和检验速率对最优生产量和最小成本的影响.     

Bringing order [replenishment process control]

The importance of replenishment management in "make to stock" businesses is often overlooked in demand management studies in favour of forecast management. The real issue in replenishment strategy is addressing the fundamental challenge between holding enough inventory to protect future sales versus reducing inventory to reduce costs and enhance productivity. It is likely that replenishment lead-time will be greater than is desirable, vendors will be unreliable and forecasts will in most cases be wrong. Thus, in this paper, the author urges manufacturers to take control of the replenishment process.     

Optimal replenishment policies for deteriorating control wafers inventory

This paper considers a control wafers replenishment problem with inventory deterioration. In the process, control wafers begin to deteriorate after the pre-disposition. The objective of this research is to minimize the total cost of control wafers, where the cost includes ordering cost, holding cost and purchase cost. We first formulate the control wafers inventory problem as a dynamic programming model. We then transform the control wafers’ inventory problem into the mixed 0–1 linear programming model. An illustrative example with four cases is used to illustrate the practicality of these models, and sensitivity analysis is applied to understand the impact of parameters to these models. The results demonstrate that the proposed mixed 0–1 linear programming model is an effective tool for determining the replenishment of control wafers for multi-periods.     

A method to exchange the demand of products for cost improvement

In a multiproduct manufacturing environment, the actual demands of various products are either available, or these are expected. There are situations when demand of a product can be substituted with that of another. In the context of cyclic manufacture, all the items are produced in an optimal cycle time, and the production facility runs at certain cost level. The total cost consists of the facility setup cost, inventory carrying costs, and the manufacturing time cost for the basic case. The total cost is optimized. For the purpose of total cost improvement, a method is presented in which the demand of a product is exchanged with that of another item in the group. The basic model without backorders is analyzed first. Then, it is extended for an inclusion of shortages that are either completely backlogged or partially. In addition to the cost components discussed before, shortage costs are included in the total cost for this case. Finally, after a discussion of idle time costs, these are also included briefly in the formulation of the total cost. The proposed methods are useful for implementation in a variety of industrial or business situations in the context of internal benchmarking or gradual improvement.     

An integrated vendor–buyer inventory model with imperfect items and planned back orders

In this paper, we develop a mathematical model to determine an integrated vendor–buyer inventory policy, where the vendor’s production process is imperfect and produces a certain number of defective items with a known probability density function. The vendor prepares for the repeating flow of orders of size $ {Q_{\mathrm{P}}}=nQ $ from the buyer by producing items in batches of size Q _P and planning to have each batch delivered to the buyers in n deliveries, each with a lot of Q units. Once the buyer receives the items, a 100 % screening process is conducted. We assume the screening process and demand take place simultaneously. We also assume that shortages are allowed and are completely back ordered. The objective is to minimize the total joint annual costs incurred by the vendor and the buyer. The expected annual integrated total cost is derived and a solution procedure is provided to find the optimal solution. Numerical examples show that the integrated model gives an impressive cost reduction in comparison to an independent decision by the buyer. The results also show that even though there is a cost associated with each back order, it is profitable for the company to have planned back orders if customers are willing to wait for the next delivery when a shortage occurs.     

Integrated vendor–buyer cooperative inventory model with controllable lead time, ordering cost reduction, and service-level constraint

In this study, an integrated vendor–buyer inventory model is proposed. The vendor produces a product in a batch environment and delivers it to a buyer facing normally distributed demand. In the current study, several assumptions are used that the combination of these assumptions has not been studied in previous papers. Here is the list of these assumptions: service-level constraint instead of shortage cost is used; ordering cost reduction is allowed, and decreasing lead time by a cost dependent on two factors including shortened lead time and ordering quantity is considered. An algorithm is developed to obtain the optimal solution of the proposed model. A numerical example is included to illustrate the results of the model. Also, the effects of assumptions used in this paper are evaluated and discussed.     

A replenishment policy for perishable products with non-linear holding cost under stochastic supply lead time

The development and application of inventory models for deteriorating items is one of the main concerns of subject matter experts. The inventory models developed in this field have focused mainly on supply chains under the assumption of constant lead time. In this study, we develop an inventory model for a main class of deteriorating items, namely perishable products, under stochastic lead time assumption. The inventory system is modeled as a continuous review system (r, Q). Demand rate per unit time is assumed to be constant over an infinite planning horizon and the shortages could be backordered completely. For modeling the deterioration process, a non-linear holding cost is considered. Taking into account the stochastic lead time as well as a non-linear holding cost makes the mathematical model more complicated. We customize the proposed model for a uniform distribution function that could be tractable to solve optimally by means of an exact approach. We then solve an example taken from the literature to demonstrate the applicability and effectiveness of the proposed model. Finally, by doing several sensitivity analyses for the key parameters of the model, some managerial insights are proposed.     

A multi-product multi-period inventory control problem under inflation and discount: a parameter-tuned particle swarm optimization algorithm

In this paper, a seasonal multi-product multi-period inventory control problem is modeled in which the inventory costs are obtained under inflation and all-unit discount policy. Furthermore, the products are delivered in boxes of known number of items, and in case of shortage, a fraction of demand is considered backorder and a fraction lost sale. Besides, the total storage space and total available budget are limited. The objective is to find the optimal number of boxes of the products in different periods to minimize the total inventory cost (including ordering, holding, shortage, and purchasing costs). Since the integer nonlinear model of the problem is hard to solve using exact methods, a particle swarm optimization (PSO) algorithm is proposed to find a near-optimal solution. Since there is no bench mark available in the literature to justify and validate the results, a genetic algorithm is presented as well. In order to compare the performances of the two algorithms in terms of the fitness function and the required CPU time, they are first tuned using the Taguchi approach, in which a metric called “smaller is better” is used to model the response variable. Then, some numerical examples are provided to demonstrate the application and to validate the results obtained. The results show that, while both algorithms have statistically similar performances, PSO tends to be the better algorithm in almost all problems.     

Optimal production run length and maintenance schedule for a deteriorating production system

This study considers manufacturing cost, inventory holding cost, system setup and maintenance costs, restoration cost, and warranty cost to a deteriorating production system whose state can be classified into in-control or out-of-control state at any time. This study develops a framework of simultaneous determination of optimal production run length and maintenance schedule and shows that there exists a unique optimal production run length and scheduled maintenance policy that minimize the expected total cost per item. The mathematical conditions to the optimal production run length and scheduled maintenance policy for a production cycle are deduced.     

The economic lot scheduling problem with deteriorating items and shortage: an imperialist competitive algorithm

This paper addresses an economic lot scheduling problem (ELSP) for manufacturing environments regarding slack costs and deteriorating items using the extended basic period approach under Power-of-Two (PoT) policy. The purpose of this research is to determine an optimal batch size for a product and minimizing total related costs to such a problem. The cost function consists of three components, namely, setup cost, holding cost includes deteriorating factor, and slack cost. The ELSP is concerned with the scheduling decision of n items and lot sizing. Avoiding schedule interference is the main problem in ELSP. The used PoT policy ensures that the replenishment cycle of each item to be integer and this task reduces potential schedule interferences. Since the ELSP is shown as an NP-hard problem, an imperialist competitive algorithm is employed to provide good solutions within reasonable computational times. Computational results show that the proposed approach can efficiently solve such complicated problems.     

Design of a just-in-time periodic material supply system for the assembly lines and an application in electronics industry

The purpose of the paper is the development of a mathematical model and a heuristic approach where the routes are constructed and the service period is determined for the design of an internal milk-run material supply system. The material supply by this system occurs on a just-in-time basis from a central warehouse to several stations of an assembly line. The objective of the proposed mathematical model is the minimization of the total material handling and inventory holding cost. Besides, the proposed heuristic approach intends to construct routes based on an initial service period value and attempts to improve the solution by considering different period values. The most suitable solution is decided on the basis of the least total material handling and WIP/inventory holding cost. The application of the proposed heuristic in a TV assembly plant demonstrates the utility of it to the real practice.     

通货膨胀环境下需求依赖库存的经济订货批量模型

为考虑通货膨胀和货币时间价值对库存的影响,研究了通货膨胀的条件下需求受库存水平影响且允许短缺发生的经济订货批量问题,其中通货膨胀率由内部通货膨胀率与外部通货膨胀率两部分组成。以系统成本最小化为目标,建立了四个不同补货策略下的仿真模型,并提供了寻求模型整体最优解的简单方法。最后,通过实例对这四个模型进行了比较,同时分析了参数变化对模型最优解的影响。