A periodic review policy with quality improvement, setup cost reduction, backorder price discount, and controllable lead time

This paper explores a periodic review inventory model under stochastic demand. The setup (or ordering) cost and the lead time are controllable. The model considers an imperfect production process, whose quality can be improved by means of an investment. A backorder price discount to motivate customers to wait for backorders is included. The demand in the protection interval is first assumed Gaussian; then, the distribution-free approach is adopted. The objective is to determine the review period, the setup cost, the quality level, the backorder price discount, and the length of lead time that minimize the long-run expected total cost per time unit. A solution method for each case is presented. Numerical experiments show that substantial savings can be achieved if the quality level, the setup cost and the lead time are controlled, and if a backorder price discount is applied. A sensitivity analysis is finally carried out

Periodic review inventory policy with variable ordering cost, lead time, and backorder rate

In this paper, a stochastic periodic review inventory model is developed. The backorder rate (backorder price discount), ordering cost (safety stock), lead time, and review period are treated as decision variables. The ordering cost and lead time can be controlled by using capital investment and crashing cost, respectively. It is assumed that shortages are allowed and partially backlogged. If an item is out of stock, the supplier may offer a negotiable price discount to the loyal, tolerant and obliged customers to pay off the inconvenience of backordering. Furthermore, it is assumed that the protection interval demand follows a normal distribution. Our objective is to develop an algorithm to determine the optimal decision variables, so that the total expected annual cost incurred has a minimum value. Finally, a numerical example is presented to illustrate the solution procedure, and sensitivity analysis is carried out to analyze the proposed model. The numerical results show that a significant amount of savings can be obtained by making decisions with capital investment in reducing ordering cost

Integrated supply chain inventory model with quality improvement involving controllable lead time and backorder price discount

For the past four decades the integrated vendor and buyer supply chain inventory model has been an interesting topic, but quality improvement of defective items in the integrated inventory model with backorder price discount involving controllable lead time has been rarely discussed. The aim of this paper is to minimize the total related cost in the continuous review model by considering the order quantity, reorder point, lead time, process quality, backorder price discount and number of shipment as decision variables. Moreover, we assume that an investment function is used to improve the process quality. The lead time demand follows a normal distribution. In addition, the buyer offers backorder price discount to motivate the customers for possible backorders. There are some defective items in the arrival lot, so its treatment is also taken in account in this paper. We develop an iterative procedure for finding the optimal values of decision variables and numerical example is presented to illustrate the solution procedure. Additionally, sensitivity analysis with respect to major parameters is also carried out

[[alternative]]Ordering Strategy of the Inventory System for Considering the Effect of Controllable Lead Time, Time Value of Money and Inflation

計畫編號：NSC91-2416-H032-005研究期間：200208~200307研究經費：394,000[[sponsorship]]行政院國家科學委員

Optimal consignment stocking policies for a supply chain under different system constraints

The research aims are to enable the decision maker of an integrated vendor-buyer system under Consignment Stock (CS) policy to make the optimal/sub-optimal production/replenishment decisions when some general and realistic critical factors are considered. In the system, the vendor produces one product at a finite rate and ships the outputs by a number of equal-sized lots within a production cycle. Under a long-term CS agreement, the vendor maintains a certain inventory level at the buyer’s warehouse, and the buyer compensates the vendor only for the consumed products. The holding cost consists of a storage component and a financial component. Moreover, both of the cases that the unit holding costs may be higher at the buyer or at the vendor are considered. Based upon such a system, four sets of inventory models are developed each of which considers one more factor than the former. The first set of models allows a controllable lead-time with an additional investment and jointly determines the shipping size, the number of shipments, and the lead time, that minimize the yearly joint total expected cost (JTEC) of the system. The second set of models considers a buyer’s capacity limitation which causes some shipments to be delayed so that the arrival of these shipments does not cause the buyer’s inventory to go beyond its limitation. As a result, the number of delayed shipments is added as the fourth decision variable. A variable demand rate is allowed in the third set of models. Uncertainty caused by the varying demand are controlled by a safety factor, which becomes the fifth decision variable. Finally, the risk of obsolescence of the product is considered in the fourth model. The first model is solved analytically, whereas the rest are not, mainly because of the complexity of the problem and the number of variables being considered. Three doubly-hybrid meta-heuristic algorithms that combine two different hybrid meta-heuristic algorithms are developed to provide a solution procedure for the rest of models. Numerical experiments illustrate the solution procedures and reveal the effects of the buyer’s capacity limitation, the effects of the variable demand rate, and the effects of the risk of obsolescence, on the system. Furthermore, sensitivity analysis shows that some of the system parameters (such as the backorder penalty, the extra space penalty, the ratio of the unit holding cost of the vendor over that of the buyer) are very influential to the joint system total cost and the optimal solutions of the decision variables

Reducing lead time risk through multiple sourcing: the case of stochastic demand and variable lead time

This paper studies a buyer sourcing a product from multiple suppliers under stochastic demand. The buyer uses a (Q, s) continuous review, reorder point, order quantity inventory control system to determine the size and timing of orders. Lead time is assumed to be deterministic and to vary linearly with the lot size, wherefore lead time and the associated stockout risk may be influenced by varying the lot size and the number of contracted suppliers. This paper presents mathematical models for a multiple supplier single buyer integrated inventory problem with stochastic demand and variable lead time and studies the impact of the delivery structure on the risk of incurring a stockout during lead time

Static and dynamic inventory models under inflation, time value of money and permissible delay in payment

In this research a number of mathematical models were developed for static and dynamic deterministic single-item inventory systems. Economic factors such as inflation, time value of money and permissible delay in payment were considered in developing the models. Nonlinear optimization techniques were used to obtain the optimal policies for the systems.;First, a static single-item inventory model was considered in which shortages are allowed and a delay is permitted in payment. In this case, suppliers allow the customers to settle their accounts after a fixed delay period during which no interest is charged.;An extension of the model was then considered in which all cost components of the model are subject to inflation and discounting, with constant rates over the planning horizon. The mathematical model of the system was developed and a nonlinear optimization technique, Hooke and Jeeves search method, was used to obtain the optimal policies for the system.;A dynamic deterministic single-item inventory model was also considered in which the demand was assumed to be a linear function of time. Suppliers allow for a delay in payment and the cost components are subject to inflation and discounting with constant rates and continuous compounding. The Golden search technique was used to obtain the optimum length of replenishment cycle such that the total cost is minimized.;Computer applications using Visual Basic and Mathematics were developed and several numerical example were solved

Benefits and challenges with coordinated inventory control at Volvo Parts

Coordinated inventory control is a concept within inventory management where decisions are based on stock and demand situations throughout a whole system of interconnected warehouses and inventories, and where control parameters are simultaneously determined and set at all installations. This thesis is a part of a larger research collaboration project in coordinated inventory control where NGiL (Next Generation Innovative Logistics), a Lund based research institute, and Volvo Parts AB in Gothenburg participate. Volvo Parts handles the aftermarket distribution, sales and related services for the Volvo Group companies and has centrally controlled complex multi-level warehouse structures and routines. These warehouse structures are well suited for a coordinated inventory control approach. A new multi-level inventory control model has been developed by NGiL especially for the Volvo Parts supply chain in Europe. The model utilizes advanced mathematical concepts to mimic Volvo Parts inventory systems consisting of several dealers and warehouses on a market. The model optimizes the reorder points at all locations with the aim of minimizing the total costs of the system while still maintaining or increasing today’s service to end customers. The purpose of this thesis is to prepare for this pilot study by analyzing the information systems, processes, structures and routines at Volvo Parts, design methods for extraction and calculation of the necessary parameters, select an appropriate market and to perform a selection of suitable spare parts and accessories to be included in the pilot study. A suitable market for the pilot study and a method to select and classify 100 parts with all necessary parameters are the main results of the thesis. The study is performed as an action research project, meaning that the authors are stationed at Volvo Parts headquarters in Gothenburg and observe the daily work, perform the necessary data extractions from the IT systems themselves and conduct interviews on a daily basis. The gathered data is a combination of primary and secondary quantitative data from the IT systems and calculations, as well as a lot of primary qualitative data from interviews and observations. The authors also function as mediators between NGiL researchers and Volvo Parts personnel. The developed model is concluded to be a good representation of the reality of Volvo Parts’ supply chain on the selected market Spain, and the authors do not see any large obstacles in a generalization to other Volvo Parts markets with the same structure or even other companies. The one major discrepancy between the NGiL model and current Volvo Parts control methods is how service levels are measured and how goals on these service levels are achieved. We have also performed a simulation study for some of the selected parts and found that the potential for cost reductions is significant and that the optimized solution fulfills target service levels in almost all cases. We also found out that there are no clear correlations or patterns between the cost reduction and any of the part characteristics that were studied, implying that a larger simulation study or a real life pilot study is necessary in order to further investigate the full potential of the NGiL model

Application of Optimization in Production, Logistics, Inventory, Supply Chain Management and Block Chain

The evolution of industrial development since the 18th century is now experiencing the fourth industrial revolution. The effect of the development has propagated into almost every sector of the industry. From inventory to the circular economy, the effectiveness of technology has been fruitful for industry. The recent trends in research, with new ideas and methodologies, are included in this book. Several new ideas and business strategies are developed in the area of the supply chain management, logistics, optimization, and forecasting for the improvement of the economy of the society and the environment. The proposed technologies and ideas are either novel or help modify several other new ideas. Different real life problems with different dimensions are discussed in the book so that readers may connect with the recent issues in society and industry. The collection of the articles provides a glimpse into the new research trends in technology, business, and the environment