An inventory reservation problem with nesting and fill rate-based performance measures

In many inventory settings companies wish to provide customer-differentiated service levels. These may, for example, be motivated by differences in the perceived customer lifetime value or by specific contractual agreements. One approach to provide differentiated service levels is to reserve some portion of the available inventory exclusively for specific customer classes. Existing approaches to inventory reservation are typically based on the assumption that a company can assign a customer specific revenue or penalty cost to any order or unit of demand filled or unfulfilled. In practice, however, it is usually extremely difficult to accurately estimate (especially long term) monetary implications of meeting or not meeting customer demand and corresponding service level requirements. The research presented in this paper addresses the problem of setting appropriate inventory reservations for different customer classes based on fill rate-based performance measures. We model a single period inventory reservation problem with two customer classes and nesting. We develop exact expressions for two conflicting performance measures: (1) the expected fill rate of high priority customers and (2) the expected loss in the system fill rate induced by inventory reservation. With these expressions a decision maker can analyze the tradeoff between the loss in overall system performance and the higher expected fill rates for prioritized customers. We provide analytical insights into the effects of nesting and the impact of relevant problem parameters on these two performance measures. The analytical insights are illustrated and highlighted through a set of numerical examples. Although we limit our analysis to a single period inventory reservation problem, we expect that our results can be utilized in a wide range of problem settings in which a decision maker has to ration a perishable resource among different classes of customers.     

An integrated production–distribution model for the dynamic location and allocation problem with safety stock optimization

The design and management of a multi-stage production–distribution system is one of the most critical problems in logistics and in facility management. Companies need to be able to evaluate and design different configurations for their logistic networks as quickly as possible. This means coordinating the entire supply chain effectively in order to minimize costs and simultaneously optimize facilities location, the allocation of customer demand to production/distribution centers, the inbound and outbound transportation activities, the product flows between production and/or warehousing facilities, the reverse logistics activities, etc.Full optimization of supply chain is achieved by integrating strategic, tactical, and operational decision-making in terms of the design, management, and control of activities. The cost-based and mixed-integer programming model presented in this study has been developed to support management in making the following decisions: the number of facilities (e.g. warehousing systems, distribution centers), the choice of their locations and the assignment of customer demand to them, and also incorporate tactical decisions regarding inventory control, production rates, and service-level determination in a stochastic environment. This paper presents an original model for the dynamic location–allocation problem with control of customer service level and safety stock optimization. An experimental analysis identifies the most critical factors affecting the logistics cost, and to finish, an industrial application is illustrated demonstrating the effectiveness of the proposed optimization approach.     

Modelling consumer-directed substitution

We discuss the challenges and difficulties arising when approaching and modelling the consumer-directed substitution problem in quick response supply chains. Further, we propose heuristic solutions suited for large problems with complex uncertainty and dependency patterns. Despite the single-period newsvendor model we use, our substitution process is an approximation of the dynamic product choice. To ensure consistency with regard to the information used to establish substitution fractions and information available at the time of optimisation, substitution fraction estimation and inventory/assortment optimisation are discussed simultaneously. The decision-independent substitution preferences applied here do not require inventory or sales transaction data, but reflect understanding on the demand driver attributes. This approach, in turn, leads to increased robustness in assortment planning. Factual substitution is an outcome of the optimisation process, constrained by the available substitutes and unfulfilled demand.Despite being unable to fully describe the dependencies among the substitute choice possibilities, our substitution approach, together with the modelling process, allows handling the most important dependencies, such as negatively correlated substitute choice possibilities and positively/negatively correlated first and second choice possibilities.     

Exact and approximate calculation of the cycle service level in periodic review inventory policies

The parameters of stock policies are usually determined to minimize costs while satisfying a target service level. In a periodic review policy the time between reviews can be selected to minimize costs while the order-up-to-level is based on the fulfilment of a target service level. Generally, the calculation of this service measurement is obtained using approximations based on an additional hypothesis related to the demand pattern. Previous research has shown that there is a substantial difference between exact and approximate calculations in some general circumstances, so in these cases the service level is not accomplished or the stock level is overestimated. Although an exact calculation of CSL was developed in previous work, the computational effort required to apply it in practical environments leads to the proposal of two approximate methods (PI and PII) that, with the classic approximation, are analysed and evaluated in this paper. This analysis points out the risks of using the classic approximation and leads one to suggest PII as the most suitable and accurate enough procedure to compute the CSL straightforwardly in practice. Additionally, a heuristic approach based on PII is proposed to accept or reject an inventory policy in terms of fulfilling a given target CSL. This paper focuses on uncorrelated, discrete and stationary demand with a known distribution pattern and without backlog.     

Competition under capacitated dynamic lot-sizing with capacity acquisition

Lot-sizing and capacity planning are important supply chain decisions, and competition and cooperation affect the performance of these decisions. In this paper, we look into the dynamic lot-sizing and resource competition problem of an industry consisting of multiple firms. A capacity competition model combining the complexity of time-varying demand with cost functions and economies of scale arising from dynamic lot-sizing costs is developed. Each firm can replenish inventory at the beginning of each period in a finite planning horizon. Fixed as well as variable production costs incur for each production setup, along with inventory carrying costs. The individual production lots of each firm are limited by a constant capacity restriction, which is purchased up front for the planning horizon. The capacity can be purchased from a spot market, and the capacity acquisition cost fluctuates with the total capacity demand of all the competing firms. We solve the competition model and establish the existence of a capacity equilibrium over the firms and the associated optimal dynamic lot-sizing plan for each firm under mild conditions.     

Ordering and pricing policies in a manufacturing and distribution supply chain for fashion products

In the paper, we develop a model of manufacturing and distribution supply chains that are operating to meet price-sensitive random demand for products with short life cycles such as fashion products. Two specific scenarios are considered. The manufacturer-controlled scenario is one where the distributor shares price-sensitive random demand with the manufacturer, and the manufacturer controls the supply chain stocking decisions and bears the risk of overstocking costs. The distributor-controlled scenario works in the opposite direction. Prevailing wisdom suggests that the manufacturer should control supply chain decisions (e.g., via vendor-managed inventory). Our results indicate that such an arrangement is against the interest of a distributor selling short life-cycle products. Furthermore, we find that the total supply chain profit is generally higher when the distributor controls the supply chain stocking decisions and bears the risk of overstocking costs.     

A local search algorithm for the optimization of the stochastic economic lot scheduling problem

This paper describes a model for the stochastic economic lot scheduling problem (SELSP) and a Local Search heuristic to find close to optimal solutions to this model. The SELSP considers multiple products, which have to be scheduled on a single facility with limited capacity and significant setup times and costs. The demand is modeled as a stationary compound renewal process. The objective is to find a schedule that minimizes the long-run average costs for setups and inventories while satisfying a given fill rate. We use a cyclic scheduling approach in which the individual cycle time of each product is a multiple of some basic period (fundamental cycle).For the deterministic version of the SELSP, efficient heuristics have been developed which guarantee the feasibility of the solution by adding an additional constraint to the problem. In our case this is not sufficient, because for the calculation of the average inventory levels and fill rates we need to develop a schedule with detailed timing of the lots. We present an efficient heuristic for this scheduling problem, which can also be used to check the feasibility of the solution. Thereby, the most time-consuming step (the calculation of average inventory levels and fill rates) is only performed for a limited set of candidates.The algorithm was tested on deterministic benchmark problems from literature and on a large set of stochastic instances. We report on the performance of the heuristic in both cases and try to identify the main factors influencing the objective.     

The performance of two popular service measures on management effectiveness in inventory control

Service is one of the inventory managers' concerns and is frequently incorporated into the ordering decisions. Since there are multiple measures of service available for evaluating the efficiency of an inventory system, a comparative study is necessary and has not been addressed in the literature. This paper evaluates two popular service measures, which are the probability of no stockout during lead time and the fill rate, in the context of continuous inventory systems. The performance of the two measures is examined by evaluating the tradeoff among the cost, the level of service, and the inventory turnover ratio.     

Introduction to design and analysis of production systems

In a two-party VMI channel, the vendor operates the basic stocking and delivery functions and makes inventory replenishment decisions while the retailer is responsible for customer acquisition and in-store services. This paper focuses on such retail channel and proposes an analytical model for the partners in supply channel to determine the inventory policy with the objective of optimizing system net profit. The model explicitly incorporates issues from both the vendor and the retailer in order to derive a policy for mutual benefits. To illustrate and obtain insights from the proposed solution procedure, we devise a set of numerical analyses based on various scenarios. Factors such as shelf-space-dependent demand, shelf-space capacity, demand pattern, logistics characteristics, and disparity between holding costs of the warehouse and the retail store are also investigated.     

Channel coordination with the newsvendor model using asymmetric information

In this paper, after surveying short-term two-echelon supply channel coordination methods, we present an extended version of the newsvendor model in which the supplier has to fulfil all demand of the customer, even if this calls for an additional setup of production. Given uncertain demand forecast, the solution is an optimal production quantity that minimises the expected total cost including setup, inventory holding and obsolete inventory costs. Then, the model is studied in a decentralised setting where the customer has private information about the demand forecast, while the supplier knows the various cost factors. We suggest such a coordination protocol and payment scheme that provides both partners the right incentive for minimising the total cost: the customer is interested in sharing her unbiased demand forecast and uncertainty, while the supplier's rational decision concurs with the overall optimum. Hence, local decisions based on asymmetric information coordinate the channel in the global sense. The results are also demonstrated by taking some real-life test cases from an industrial study that motivated our work.     

Production planning and inventory allocation of a single-product assemble-to-order system with failure-prone machines

We consider the optimal production and inventory allocation of a single-product assemble-to-order system with multiple demand classes and lost sales. Each component is replenished by a dedicated machine that is subjected to unpredictable breakdowns. We find that the machine state not only influences the production and allocation decisions on its own component but also influences the decisions on the other components. Specifically, the optimal component production policy is a base-stock policy with the base-stock level non-decreasing in the inventory levels of the other components and the states of the other machines. The optimal component allocation policy is a rationing policy with the rationing level non-increasing in the inventory levels of the other components, the states of the other machines, and its own machine state. We use an exponential distribution to approximate the distribution of the total processing times and propose two heuristic policies to address the production and allocation decisions. The importance of taking machine failures into consideration is revealed through computational experiments.     

An efficient hybrid genetic algorithm for the multi-product multi-period inventory routing problem

The inventory routing problem (IRP) addressed in this study is a many-to-one distribution network consisting of an assembly plant and many distinct suppliers where each supplies a distinct product. We consider a finite horizon, multi-periods, multi-suppliers and multi-products where a fleet of capacitated homogeneous vehicles, housed at a depot, transport products from the suppliers to meet the demand specified by the assembly plant in each period. The demand for each product is deterministic and time varying. A mathematical formulation of the problem is given and CPLEX 9.1 is run for a finite amount of time to obtain lower and upper bounds. A hybrid genetic algorithm, which is based on the allocation first route second strategy and which considers both the inventory and the transportation costs, is proposed. In addition to a new set of crossover and mutation operators, we also introduce two new chromosome representations. Several medium and small sized problems are also constructed and added to the existing data sets to show the effectiveness of the proposed approach.     

A discounted cash flow approach to the base stock inventory model

A widespread approach to inventory modelling is to associate costs with measures of system performance and determine the control policy which minimises the long run average cost per unit time. This type of approach ignores the impact of a control policy on the timing of the cash flows associated with payments to suppliers and revenue streams from customers. The approach in this paper is to concentrate on cash flows and determine the control policy which maximises the expected net present value of the cash flows associated with a demand, valued at the time when that demand occurs. There is a Poisson demand process, a fixed lead time, unsatisfied demand is backordered and the system is controlled using a base stock policy. A solution procedure is given and a comparison is made with an equivalent simple interest model and with the standard cost model with linear holding and shortage costs.     

AN INVENTORY MODEL FOR DETERIORATING ITEMS WITH STOCK-DEPENDENT DEMAND UNDER THE CONDITIONS OF INFLATION AND TIME-VALUE OF MONEY

In this paper, we incorporate the effects of inflation and time-value of money in inventory decision making when demand, at each time moment rather than being constant, is considered to be dependent upon current stock level. In addition, the shortages are neither completely backlogged nor completely lost assuming the backlogging rate to be linearly dependent on the amount of demand backlogged. We shall be concerned with finding the optimal number of replenishments and service rate to minimize the total relevant costs over a finite planning horizon. Numerical examples are presented to illustrate the proposed models.     

A network approach to modeling the multi-echelon spare-part inventory system with backorders and interval-valued demand

A multi-echelon inventory system implies the existence of a hierarchy of stocking locations, and the dependence and interaction between them. We consider a multi-echelon, spare-part inventory management problem with outsourcing and backordering. The problem is characterized by deterministic repair time/cost, and supply and demand that lie within prescribed intervals and that vary over time. The objective is to minimize the total inventory and transportation costs. We develop a network model for problem analysis and present a network flow algorithm for solving the problem. We prove that the Wagner-Whitin property, known for the lot-sizing problem, can be extended to the spare-part inventory management problem under study.     

A master production scheduling procedure for stochastic demand and rolling planning horizons

The problem of interest is a one product, uncapacitated master production schedule (MPS) in which decisions are made under rolling planning horizons. Demand is stochastic and time varying, and effectiveness is measured by inventory holding, production setup, and backorder costs.Typically, in both the research literature and the business practice the stochastic nature of the problem is modeled in an ad hoc fashion. The stochastic MPS problem is usually solved by adding safety stock to production quantities obtained from a deterministic lot-sizing algorithm. Here, the stochastic nature of the problem is explicitly considered, as an optimal algorithm for solving the static probabilistic dynamic lot-sizing problem is adapted to rolling planning horizons. The resulting algorithm is found to dominate traditional approaches over a wide variety of experimental factors, reducing total costs by an average of 16% over traditional methods.     

Multi-item dynamic lot-sizing with delayed transportation policy

We optimize ordering and inbound shipment decisions for a manufacturer that sources multiple items from a single supplier. The objective is to satisfy the requirements in the production plan with minimum transportation and inventory holding costs over a multi-period planning horizon. Transportation costs are charged to the manufacturer on a per truck shipment basis. We investigate the option of delaying a less-than-full truckload shipment to the next period, by utilizing the safety stocks as needed. We analyze the impact of delaying shipments on both cost and service levels in stochastic environments through experiments with data from a bus manufacturer. The results indicate that the proposed policy reduces both holding and transportation costs without creating much stock-out risk.     

Inventory decisions for substitutable products with stock-dependent demand

We study a retailer’s inventory policy for two products. The products are substitutable and have inventory dependent demand, so a higher inventory level of a product increases its sales. We model the joint effect of demand stimulation and product substitution on inventory decisions by considering a single-period, stochastic demand setting. We provide the first order optimality conditions for the profit maximizing order quantities and interpret them using marginal analysis. We also consider two heuristic solutions that separately account for either demand stimulation or product substitution. Our numerical analysis reveals that the optimal policy by appropriately using sales information that quantifies substitution and demand stimulation can produce significantly higher profits. The profit benefits are lessened under certain circumstances, such as when the two products have similar critical fractile values, suggesting that in such instances the heuristics may be used effectively.     

A multiple objective particle swarm optimization approach for inventory classification

This paper presents a particle swarm optimization approach for inventory classification problems where inventory items are classified based on a specific objective or multiple objectives, such as minimizing costs, maximizing inventory turnover ratios, and maximizing inventory correlation. In addition, this approach determines the best number of inventory classes and how items should be categorized for the desired objectives at the same time. Experiments are employed to determine the best combination of algorithm parameter values. Extensive numerical studies are conducted and results are compared to other known classification methods. The performance of the algorithm on a practical case is also presented.     

Timing production in LP models in a rolling schedule

We consider an arbitrary supply chain structure under demand uncertainty. We look at a setting where the supply chain planning is executed periodically and where the demand of end items in subsequent periods is stochastic. In contrast to other linear programming-based approaches, we assume constant planned lead times. In this paper we discuss the timing of production during the planned lead times of items. If production starts immediately, the work-in-process inventory costs are higher, but producing later will result in higher safety stocks. We look at the influence of the demand variation, the planned lead time of the items, the utilization rate of resources, and the added value when merging items, on the inventory costs. The results indicate that, for higher utilization rates, producing early is more suitable.