Joint replenishment model with substitution

When products are coupled to the same cycle, the joint replenishment model (JRM) is used to determine optimal inventory levels, where the amount to order (for each item) is designed to minimize the joint holding and ordering costs based on a given demand. JRM studies assume that there is no substitution between items. However, this assumption is unrealistic in some settings where substitution cannot be ignored. This paper combines the separate works on substitution and joint replenishment and proposes a solution procedure for solving the joint replenishment model with substitution (JRMS) for two products within the framework of the classical economic order quantity model. We determine the optimal order quantities for each product taking into consideration substitution between them so that demand is partially met and the total cost associated with the delivery, holding, and shortage of the products is minimized. We also provide an extensive scenario analysis and draw insights. In particular, we shed some light on the role of substitution in reducing the fixed cost. We show that JRMS can result in substantial cost savings compared to the ordinary JRM.     

Joint replenishment of multi retailer with variable replenishment cycle under VMI

In the recent article, Darwish and Odah (2010) develop a scheme that allows for identical replenishment cycles for all the retailers, in the context of a single vendor supplying a group of retailers under VMI partnership. This paper proposes an alternative replenishment scheme allowing for different replenishment cycles for each retailer. An example has been shown to illustrate the cost savings under the proposed model.     

Inventory replenishment model: lot sizing versus just-in-time delivery

Motivated by a practical industrial problem where a manufacturer stipulates a minimum order from each buyer but where a local dealer promises the buyer a just-in-time delivery with a slightly higher unit cost, this paper uses a dynamic lot-sizing model with a stepwise cargo cost function and a minimum order amount constraint to help the buyer select the supplier with minimum total cost.     

An optimal replenishment policy for deteriorating items with time-varying demand and partial backlogging

Recently, Papachristos and Skouri developed an inventory model in which unsatisfied demand is partially backlogged at a negative exponential rate with the waiting time. In this article, we complement the shortcoming of their model by adding not only the cost of lost sales but also the non-constant purchase cost.     

A joint optimisation model for inventory replenishment,product assortment,shelf space and display area allocation decisions

In this paper, we propose an optimisation model to determine the product assortment, inventory replenishment, display area and shelf space allocation decisions that jointly maximize the retailer’s profit under shelf space and backroom storage constraints. The variety of products to be displayed in the retail store, their display locations within the store, their ordering quantities, and the allocated shelf space in each display area are considered as decision variables to be determined by the proposed integrated model. In the model formulation, we include the inventory investment costs, which are proportional to the average inventory, and storage and display costs as components of the inventory costs and make a clear distinction between showroom and backroom inventories. We also consider the effect of the display area location on the item demand. The developed model is a mixed integer non-linear program that we solved using LINGO software. Numerical examples are used to illustrate the developed model.     

Long-term inventory policy-making through fuzzy decision-making models

The inventory policy, meant as a replenishment rule, has a considerable impact on most firms. The paper considers the determination of optimal inventory policy of firms from a global viewpoint of top management. The inventory is represented as a fuzzy system with the fuzzy inventory level as the output, the fuzzy replenishment as the input and fuzzy demand. The control problem is formulated in terms of decision-making in a fuzzy environment with fuzzy constraints imposed on replenishments, a fuzzy goal for preferable inventory levels to be attained and the fuzzy decision as the intersection of fuzzy constraints and the fuzzy goal at subsequent stages. The planning horizon is infinite. The problem is to find an optimal time-invariant strategy relating the optimal replenishments to the current inventory levels, maximizing the membership function of fuzzy decision. The existence of such a strategy is proved and an algorithm for its determination is given. The optimal time-invariant strategy obtained is represented as a fuzzy conditional statement equated with a fuzzy relation which is the firm's optimal fuzzy replenishment rule.     

A (Q, R) inventory replenishment model with two delivery modes

Although splitting shipments across multiple delivery modes typically increases total shipping costs as a result of diseconomies of scale, it may offer certain benefits that can more than offset these costs. These benefits include a reduction in the probability of stockout and in the average inventory costs. We consider a single-stage inventory replenishment model that includes two delivery modes: a cheaper, less reliable mode, and another, more expensive but perfectly reliable mode. The high-reliability mode is only utilized in replenishment intervals in which the lead time of the less-reliable mode exceeds a certain value. This permits substituting the high-reliability mode for safety stock, to some degree. We characterize optimal replenishment decisions with these two modes, as well as the potential benefits of simultaneously using two delivery modes.     

Inflation and the optimal inventory replenishment schedule within a finite planning horizon

The subject of this paper is the problem of finding the optimal replenishment schedule for an inventory, subject to time-dependent demand and deterioration, within a finite time planning horizon. It is shown that taking inflation into account has a profound effect on the solution of the problem. For instance, there is a critical number of replenishment periods, in excess of which the optimal schedule is characterized by the inclusion of token orders at the end of the planning horizon. This and other conclusions, obtained via a careful mathematical analysis of the problem, rectify those of earlier studies.     

An EOQ model for perishable products with discounted selling price and stock dependent demand

A single item economic order quantity model is considered in which the demand is stock dependent. After a certain time the product starts to deteriorate and due to visualization effect and other aspects of deterioration the demand becomes constant. In that situation a discount on selling price provides significant increment in demand rate. In this paper we investigate how much discount on selling price may be given during deterioration to maximize the profit per unit time and whether a pre-deterioration discount affects the unit profit or not. A mathematical model is developed incorporating both pre- and post deterioration discounts on unit selling price, where analytical results reveal some important characteristics of discount structure. A numerical example is presented and sensitivity analysis of the model is carried out.     

Optimal replenishment policies for deteriorating items with stock sensitive demand under two-level trade credit and limited capacity

Recently, Min et al. [18] established an inventory model for deteriorating items under stock-dependent demand and two-level trade credit and obtained the optimal replenishment policy. Their analysis imposed a terminal condition of zero ending-inventory. However, with a stock-dependent demand, it may be desirable to order large quantities, resulting in stock remaining at the end of the cycle, due to the potential profits resulting from the increased demand. As a result, to make the theory more applicable in practice, we extend their model to allow for: (1) an ending-inventory to be nonzero, (2) a maximum inventory ceiling to reflect the facts that too much stock leaves a negative impression on the buyer and the amount of shelf/display space is limited.     

Inventory models with lateral transshipments: A review

Lateral transshipments within an inventory system are stock movements between locations of the same echelon. These transshipments can be conducted periodically at predetermined points in time to proactively redistribute stock, or they can be used reactively as a method of meeting demand which cannot be satisfied from stock on hand. The elements of an inventory system considered, e.g. size, cost structures and service level definition, all influence the best method of transshipping. Models of many different systems have been considered. This paper provides a literature review which categorizes the research to date on lateral transshipments, so that these differences can be understood and gaps within the literature can be identified.     

Optimal dynamic pricing and inventory control with stock deterioration and partial backordering

This paper studies the optimal dynamic pricing and inventory control policies in a periodic-review inventory system with fixed ordering cost and additive demand. The inventory may deteriorate over time and the unmet demand may be partially backlogged. We identify two sufficient conditions under which (s,S,p) policies are optimal.     

Inventory systems with stochastic demand and supply: Properties and approximations

We model a retailer whose supplier is subject to complete supply disruptions. We combine discrete-event uncertainty (disruptions) and continuous sources of uncertainty (stochastic demand or supply yield), which have different impacts on optimal inventory settings. This prevents optimal solutions from being found in closed form. We develop a closed-form approximate solution by focusing on a single stochastic period of demand or yield. We show how the familiar newsboy fractile is a critical trade-off in these systems, since the optimal base-stock policies balance inventory holding costs with the risk of shortage costs generated by a disruption.     

Integrated inventory models considering permissible delay in payment and variant pricing strategy

The allocation of cost savings is very important for the success of the joint relationship between the buyer and vendor in supply chain management. This paper develops integrated models with permissible delay in payments for determining the optimal replenishment time interval and replenishment frequency. In addition, the variant pricing strategy is employed to obtain both sides’ cost savings in order to entice buyers to join long-term cooperative relationships. A simple solution algorithm is presented to allocate the cost savings in the integration model, and a numerical example is used to demonstrate the feasibility of the proposed integration models.     

The newsvendor problem: Review and directions for future research

In this paper, we review the contributions to date for analyzing the newsvendor problem. Our focus is on examining the specific extensions for analyzing this problem in the context of modeling customer demand, supplier costs, and the buyer risk profile. More specifically, we analyze the impact of market price, marketing effort, and stocking quantity on customer demand; how supplier prices can serve as a coordination mechanism in a supply chain setting; integrating alternative supplier pricing policies within the newsvendor framework; and how the buyer’s risk profile moderates the newsvendor order quantity decision. For each of these areas, we summarize the current literature and develop extensions. Finally, we also propose directions for future research.     

Supply chain models for an assembly system with preprocessing of raw materials: A simple and better algorithm

Recently, Rahman and Sarker [1] formulated a nonlinear cost function to include the costs of inventories, ordering, shipping and deliveries for a manufacturing system where raw materials enter into the assembly line from two different channels. In order to find the best integer solutions to the variables, they proposed an algorithm that uses the branch and bound concept. The authors claim that their algorithm finds an optimal solution. In this paper, we present a simple and better heuristic algorithm that provides better solutions with a lower number of evaluations than Rahman and Sarker’s algorithm.     

Cooperation and game-theoretic cost allocation in stochastic inventory models with continuous review

We study cooperation strategies for companies that continuously review their inventories and face Poisson demand. Our main goal is to analyze stable cost allocations of the joint costs. These are such that any group of companies has lower costs than the individual companies. If such allocations exist they provide an incentive for the companies to cooperate.     

Inventory management of multiple items with irregular demand: A case study

We present the case of a Greek commercial enterprise facing the problem of managing the inventories of thousands of different items, supplied by more than 20 European and Asian manufacturers and sold to a large number of different-type customers. A key feature of the problem is that the demand for the vast majority of items is intermittent and lumpy, thus not allowing the use of the usual normal or Poisson distributions. The paper describes the solutions given to several practical problems in the course of developing an easy-to-use yet effective and all-encompassing inventory control system. Emphasis is placed on the accurate modeling of demand by means of a gamma distribution with a probability mass at zero or a package Poisson distribution for very-slow-moving items. Using those models and simple quantitative tools we develop an efficient procedure for approximate but quite accurate determination of the base stock levels that achieve the desired fill rates in the proposed periodic review system. We briefly describe the computerized implementation of the new system and the very encouraging results.     

An integrated production and inventory model to dampen upstream demand variability in the supply chain

We consider a two-echelon supply chain: a single retailer holds a finished goods inventory to meet an i.i.d. customer demand, and a single manufacturer produces the retailer’s replenishment orders on a make-to-order basis. In this setting the retailer’s order decision has a direct impact on the manufacturer’s production. It is a well known phenomenon that inventory control policies at the retailer level often propagate customer demand variability towards the manufacturer, sometimes even in an amplified form (known as the bullwhip effect). The manufacturer, however, prefers to smooth production, and thus he prefers a smooth order pattern from the retailer. At first sight a decrease in order variability comes at the cost of an increased variance of the retailer’s inventory levels, inflating the retailer’s safety stock requirements. However, integrating the impact of the retailer’s order decision on the manufacturer’s production leads to new insights. A smooth order pattern generates shorter and less variable (production/replenishment) lead times, introducing a compensating effect on the retailer’s safety stock. We show that by including the impact of the order decision on lead times, the order pattern can be smoothed to a considerable extent without increasing stock levels. This leads to a situation where both parties are better off.     

A genetic algorithm for a single product network design model with lead time and safety stock considerations

We consider a two-stage supply chain with a production facility that replenishes a single product at retailers. The objective is to locate distribution centers in the network such that the sum of facility location, pipeline inventory, and safety stock costs is minimized. We explicitly model the relationship between the flows in the network, lead times, and safety stock levels. We use genetic algorithms to solve the model and compare their performance to that of a Lagrangian heuristic developed in earlier work. A novel chromosome representation that combines binary vectors with random keys provides solutions of similar quality to those from the Lagrangian heuristic. The model is then extended to incorporate arbitrary demand variance at the retailers. This modification destroys the structure upon which the Lagrangian heuristic is based, but is easily incorporated into the genetic algorithm. The genetic algorithm yields significantly better solutions than a greedy heuristic for this modification and has reasonable computational requirements.