A vendor managed inventory supply chain with deteriorating raw materials and products

Fast deteriorating raw materials such as raw milk, fruit and vegetables are commonly used to produce slowly deteriorating finished products such as milk powders, cheeses, and pastas. This paper studies a Vendor Managed Inventory (VMI) type supply chain where the manufacturing vendor decides how to manage the system-wide inventories of its fast deteriorating raw material and its slowly deteriorating product. The decision variables are a common replenishment cycle of the product and the replenishment frequency of the raw material. We assume the deteriorating rates are known constants and every retailer's demand is deterministic. We develop an integrated model to calculate the total inventory and deterioration cost for such a system. We prove the convexity of the cost functions, and based on this a golden search algorithm is developed to find the optimal solution of the model. Our numerical results show that the deteriorating rate of the product may increase the total cost by more than 40% compared to the zero-deteriorating rate, while the deteriorating raw material has less impact on the total cost (commonly less than 5% in our numerical examples). This indicates that more attention should be paid to the product than the raw material. Further, an increase in the number of retailers can make the replenishment frequency of the raw material increase significantly but the common replenishment cycle of the product decreases a little. This indicates that adding a new retailer would not be felt strongly by the other retailers but would be felt by the supplier of the raw material.     

Generalized single-vendor multi-buyer integrated inventory supply chain models with a better synchronization

Researchers have synchronized both the single-vendor single-buyer and the single-vendor multi-buyer integrated inventory supply chains by transferring the lot either only with equal-sized or only with unequal-sized sub-lot (batches). However, synchronization by transferring the lot with unequal and/or equal-sized batches (combination of unequal and equal sized batches along with the previous two cases), though available in the former case, the latter one lacks it. Accumulating the inventory in each of the vendor and the buyers, here we develop a generalized single-vendor multi-buyer supply chain model individually by extending the idea of such synchronization, and present logical development of their minimal cost solution techniques. Thereafter, we highlight theoretically the uniqueness of the present techniques by showing the best available methods as their special cases. Special cases are validated with the solutions of some numerical problems. Then their comparative studies with recently developed techniques on two numerical problems are carried out to show significant cost reductions.     

An improved algorithm and solution on an integrated production-inventory model in a three-layer supply chain

Ben-Daya et al. (2010) established a joint economic lot-sizing problem (JELP) for a three-layer supply chain with one supplier, one manufacturer, and multiple retailers, and then proposed a heuristic algorithm to obtain the integral values of four discrete variables in the JELP. In this paper, we first complement some shortcomings in Ben-Daya et al. (2010), and then propose a simpler improved alternative algorithm to obtain the four integral decision variables. The proposed algorithm provides not only less CPU time but also less total cost to operate than the algorithm by Ben-Daya et al. (2010). Furthermore, our proposed algorithm can solve certain problems, which cannot be solved by theirs. Finally, the solution obtained by the proposed algorithm is indeed a global optimal solution in each of all instances tested.     

An iterative approach to item-level tactical production and inventory planning

In this paper, we propose an iterative approach to jointly solve the problems of tactical safety stock placement and tactical production planning. These problems have traditionally been solved in isolation, even though both problems operate in the same decision making space and the outputs of one naturally serve as the inputs to the other. For simple supply chain network structures, two stages and one or many products, we provide sufficient conditions to guarantee the iteration algorithm’s termination. Through examples, we show how the algorithm works and prove its applicability on a realistic industrial-scale problem.     

Conceptual modelling for supply chain inventory visibility

Visibility becomes increasingly important for companies that seek to globalise their supply chains due to the increasing complexity involved. This paper contributes to the research on Supply Chain Visibility (SCV) from an inventory perspective with a focus on inventory visibility, which is a critical part of SCV. The characteristics of Inventory Visibility (IV), which are inherited from SCV, are conceptually analysed. A theoretical model in terms of atom, single, and compound visibility, is developed based on the characteristics identified. A method for objectively measuring IV is presented together with a case example to demonstrate its convenience and usefulness.     

Integrated inventory model for deteriorating items under a multi-echelon supply chain environment

As the industrial environment becomes more competitive, supply chain management has become essential. The objective of this research is to develop a multi-echelon inventory model for a deteriorating item and to derive an optimal joint total cost from an integrated perspective among the supplier, the producer, and the buyer. A computer code is developed to derive the optimal solution. A numerical example is given to illustrate the model. This paper shows that the integrated approach strategy results in the lowest joint total cost as compared with the independent decision approaches.     

An inventory model with non-resuming randomly interruptible lead time

We assume that an unreliable supplier in a single-item stochastic inventory system alternates randomly between two possible states (i.e., available and unavailable), following a two-state continuous-time homogeneous Markov chain. For a compound Poisson stream of demands and Erlang lead times, our model considers the scenario where the processing of the outstanding order (if any) is interrupted at every supplier's transition epoch from the available to the unavailable state, and is restarted from the outset upon the supplier's regaining its available state. We derive the stationary distribution of the on-hand inventory under a continuous-review policy and provide some numerical results.     

An inventory model with deteriorating items under inflation when a delay in payment is permissible

This study develops an inventory model for initial-stock-dependent consumption rate when a delay in payment is permissible. In the inventory model, shortages are not allowed. The effect of the inflation rate, deterioration rate, initial-stock-dependent consumption rate and delay in payment are discussed. In the study, mathematical models are also derived under two different circumstances, i.e., Case I: The credit period is less than or equal to the cycle time for settling the account; and Case II: The credit period is greater than the cycle time for settling the account. Besides, expressions for an inventory system's total cost are derived for these two cases. Moreover, a computational procedure and GINO (Lasdon et al., ACM Transactions Mathematical Software 4 (1978) 34–50) are proposed to obtain the optimal order size and cycle time. The results can help managers determine the optimal total cost. Finally, a numerical example demonstrates the applicability of the proposed model.     

Optimal economic ordering policy with deteriorating items under different supplier trade credits for finite horizon case

This paper develops and solves a general finite horizon trade credit economic ordering policy for an inventory model with deteriorating items under inflation and time value of money when shortages are not allowed. The time horizon is divided into different cycles each of which has its own demand rate and its own trade credit period offered from the supplier to his retailer so that the retailer should pay his supplier before or after the end of the permissible trade credit of that cycle. Up to the end of the trade credit of a cycle, the retailer is free of charge, but he is charged on an interest for those items not being sold before this end. The retailer can also earn the interest of the money from the generated sales revenue in any cycle by depositing such revenue into an interest bearing account. The objective of the retailer is then to minimize his net total relevant costs. A closed form of this net total cost is derived and the resulting model is solved. Then rigorous mathematical methods are used to show that, under some seemingly possible conditions, there exist a unique vector of the relevant decision variables that solve the underlying inventory system. A numerical example which shows the applicability of the theoretical results is given.     

A heuristic for balancing the inventory level of different locations through lateral shipments

Solving transshipment problems to optimality is difficult, unless several simplifying hypotheses are assumed (such as unit-sized customer demands and replenishments, negligible replenishment lead time, etc.). For this reason, some heuristics have been recently proposed in order to provide rules, which incorporate relevant factors of the problem, to find conditions under which it makes sense to transship a certain number of units from one retailer to another. Most of these studies concern emergency transshipment, which means that shipments between locations can occur only when a shortage happens, and shipments are assumed to be fast enough to satisfy the location in shortage. When this assumption is not feasible, as in many real cases, transshipments between locations have to be performed before a shortage happens. The paper addresses this case, which can be named ‘preventive’ transshipment, where the inventory level of different locations at the same echelon is balanced through lateral shipments, before a shortage happens. A heuristic for deciding on transshipment policy (when to transship and how much), trying to minimise overall expected costs, is presented. A simulation study considering different scenarios is performed and results confirm the effectiveness of the heuristic.     

An inventory control model with consideration of remanufacturing and product life cycle

This paper investigates inventory control policies in a manufacturing/remanufacturing system during the product life cycle, which consists of four phases: introduction, growth, maturity, and decline. Both demand rate and return rate of products are random variables with normal distribution; the mean of the distribution varies according to the time in the product life cycle. Closed-form formulas of optimal production lot size, reorder point, and safety stock in each phase of the product life cycle are derived. A numerical example is presented with sensitivity analysis. The result shows that different inventory control policies should be adopted in different phases of the product life cycle. It is also found that the optimal production lot size and reorder point are not sensitive to the phase length and the demand changing rate.     

Managers’ view of a new inventory paradigm

The significance of inventories in business operations have never been denied. The actual role of inventories, however, is changing over time, as required by the business environment. This paper provides empirical background to the thesis, which says that the role of inventories in the “Golden Era” of inventory research, which was in the 1950s, was significantly different from that of today because of fundamental changes in business. This development requires new approaches in research as well.After a summary of the antecedents, the results of a survey are analysed, and they support the above thesis. The lack of difference between the inventory performance measured by the turnover rate of those companies, whose managers accept and those who deny the birth of the new paradigm calls attention to the need for the elaboration of a more complex inventory performance measurement.     

Lead time reduction strategies in a single-vendor-single-buyer integrated inventory model with lot size-dependent lead times and stochastic demand

This paper studies alternative methods for reducing lead time and their impact on the safety stock and the expected total costs of a (Q,s) continuous review inventory control system. We focus on a single-vendor-single-buyer integrated inventory model with stochastic demand and variable, lot size-dependent lead time and assume that lead time consists of production and setup and transportation time. As a consequence, lead time may be reduced by crashing setup and transportation time, by increasing the production rate, or by reducing the lot size. We illustrate the benefits of reducing lead time in numerical examples and show that lead time reduction is especially beneficial in case of high demand uncertainty. Further, our studies indicate that a mixture of setup time and production time reduction is appropriate to lower expected total costs.     

Inventory model for an inventory system with time-varying demand rate

The standard inventory problems of the multi-period have been modeled under different situations. Specifically we have considered the demand subjects of a continuous distribution and a discrete distribution, and whether the demand of each period is unchanged or not. A method to get an economic order quantity in inventory systems with discrete and unchanged demand was presented in a previous paper, and this method has been generalized to an inventory model with varying continuous demand. However, it was not achieved due to there being many classified cases in the general situations. In this article the above method is discussed in the case discrete demand to determine whether it increases or decreases from period to period. A theoretical method is presented by using previous results and some examples are given which suggest how the concept can handle on inventory system. In order to make the decision, an algorithm is also presented under some conditions, and examples are shown by using the computer software program, Mathematica, which helps to explain the findings. In general cases, we view the optimal policy in the inventory problems in only a few periods.     

A serial mixed produce-to-order and produce-in-advance inventory model with multiple retailers

We formulate a general mixed produce-to-order and produce-in-advance inventory model having multiple stocking echelons and multiple retailers. We show that the problem to find an optimal inventory policy for such a model with a uniform or a normal demand distribution can be reduced to a general constrained optimization problem.     

German inventory to sales ratios 1971-2005—An empirical analysis of business practice

The purpose of this study is to test empirically for the first time the general hypothesis that inventory to sales ratios have decreased over time in the German economy. Although inventory reduction has been a prevalent topic in the production and operations management literature, there is a lack of empirically confirmed answers to questions. They are as follows: Have inventories in German firms decreased overall during the past decades? What sectors of German industry are leading (lagging behind) inventory reduction? Has inventory reduction developed differently for raw materials, work-in-process, or finished goods? In which periods was marginal inventory reduction greatest? To the best of our knowledge, this empirical study is the first to broadly investigate inventory development from the 1970s until the present for a major European economy, Germany, and will provide the first answers to the research questions stated above using aggregate industry-level data provided by the Deutsche Bundesbank. We show that inventory levels decreased overall in many sectors of German industry. This reduction was mainly marked for raw materials and finished goods, particularly for the second-half of the time frame investigated.     

Environmentally responsible inventory models: Non-classical models for a non-classical era

Mathematical models of inventory typically include the three inventory associated costs of surplus, shortage and ordering. These classic inventory models are then analysed so as to choose inventory parameters that usually minimise the total cost of operating the inventory system being investigated.Unfortunately, classic inventory models do not provide a meaningful basis for analysing many real and increasingly important practical inventory problems and situations. It is therefore not surprising that over recent years, several authors have discussed these issues in broad terms and suggested that a new paradigm needs to be developed.This paper develops some specific aspects of this discussion. In particular, the paper identifies a range of inventory problems that are not covered appropriately by traditional inventory analysis. One of these is to design responsible inventory systems, i.e. systems that reflect the needs of the environment. The paper then examines the importance of inventory planning to the environment in greater detail. For example, packaging is important, not only because of its costs and the protection that it provides to the inventory items, but also because of its eventual effects on the environment in terms of the use of resources and potential landfill. For similar reasons, waste, which can result from poor inventory management, is highly important. The location of stores is important because location affects transport costs. Thus the influence of the secondary aspects of most inventory models; packaging, waste and location are important but, even more important are the inter-relations with the total system. In particular, the location of the manufacturing plants and the effect that inventory planning has on the logistics chain, potentially have considerable environmental implications. Inventory is part of a wider system.However, until the cost charged for an activity reflects the true environmental cost of that activity, it is likely that decisions will be made on the basis of erroneous data. In that situation, we are faced with either determining the environmental cost of specific actions or to use environmental costs that are somewhat contrived; in which case it may be more sensible to use very different performance measures and models. The paper discusses these ideas and ways in which inventory policies may reassure us with our environmental concerns.     

A perishable inventory model with Markovian renewal demands

In the inventory model, people usually assume that the inter-demand time is independently identical distributed which may not be true in reality. Here we study an (s,S) continuous review model for items with an exponential random lifetime and a general Markovian renewal demand process. By constructing Markovian renewal equations, we derive the mean and the variance of the reorder cycle time and lead to a simple expression for the total expected long run cost rate. The numerical results illustrate the system behavior and lead to managerial insights into controlling such inventory systems.     

An investigation of setup instability in non-stationary stochastic inventory systems

In stochastic inventory systems unfolding uncertainties in demand lead to the revision of earlier replenishment plans which in turn results in an instability or so-called system nervousness. In this paper, we provide the grounds for measuring system nervousness in non-stationary demand environments, and gauge the stability and the cost performances of (R,S) and (s,S) inventory policies. Our results reveal that, both the stability and the cost performance of inventory policies are affected by the demand pattern as well as the cost parameters, and the (R,S) policy has the potential to replace the cost-optimal (s,S) policy for systems with limited flexibility.