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In paper (2004) Chang studied an inventory model under a situation in which the supplier provides the purchaser with a permissible delay of payments if the purchaser orders a large quantity. Tripathi (2011) also studied an inventory model with time dependent demand rate under which the supplier provides the purchaser with a permissible delay in payments. This paper is motivated by Chang (2004) and Tripathi (2011) paper extending their model for exponential time dependent demand rate. This study develops an inventory model under which the vendor provides the purchaser with a credit period; if the purchaser orders large quantity. In this chapter, demand rate is taken as exponential time dependent. Shortages are not allowed and effect of the inflation rate has been discussed. We establish an inventory model for deteriorating items if the order quantity is greater than or equal to a predetermined quantity. We then obtain optimal solution for finding optimal order quantity, optimal cycle time and optimal total relevant cost. Numerical examples are given for all different cases. Sensitivity of the variation of different parameters on the optimal solution is also discussed. Mathematica 7 software is used for finding numerical examples.

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This paper explains a model for analyzing and measuring the propagation of order amplifications (i.e. bullwhip effect) for a single-product supply network topology considering exogenous uncertainty and linear and time-invariant inventory management policies for network entities. The stream of orders placed by each entity of the network is characterized assuming customer demand is ergodic. In fact, we propose an exact formula in order to measure the bullwhip effect in the addressed supply network topology considering the system in Markovian chain framework and presenting a matrix of network member relationships and relevant order sequences. The formula turns out using a mathematical method called frequency domain analysis. The major contribution of this paper is analyzing the bullwhip effect considering exogenous uncertainty in supply networks and using the Fourier transform in order to simplify the relevant calculations. We present a number of numerical examples to assess the analytical results accuracy in quantifying the bullwhip effect.

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In this paper, the study deals with the lead time and setup reduction problem in the vendor-purchaser integrated inventory model. The cost of capital (i.e., opportunity cost) is one of the key factors in making the inventory and investment decisions. Lead time is an important element in any inventory system. The proposed model is presents an integrated inventory model with controllable lead time with setup cost reduction for defective and non defective items under investment for quality improvement. In this analysis, the proposed model, we assumed that the setup cost and process quality is logarithmic function. Setup cost reduction for defective and non defective items, is the main focus for the proposed model. The objective of the proposed model is to minimize the total cost of both the vendor-purchaser. The mathematical model is derived to investigate the effects to the optimal decisions when investment strategies in setup cost reductions are adopted. This paper attempts to determine optimal order quantity, lead time, process quality and setup cost reduction for production system such that the total cost is minimized. A solution procedure is developed to find the optimal solution and numerical examples are presented to illustrate the results of the proposed models.

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This paper presents an inventory model for deteriorating items in which shortages are allowed. It is assumed that the production rate is proportional to the demand rate and greater than demand rate. The inventory model is developed by considering four different circumstances. The optimal of the problem is obtained with the help of Mathematica 7 software. Numerical examples are given to illustrate the model for different parameters. Sensitivity analysis of the model has been developed to examine the effect of changes in the values of the different parameters for optimal inventory policy. Truncated Taylor’s series is used for finding closed form optimal solution.

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This study considers an EOQ inventory model with advance payment policy in a fuzzy situation by employing two types of fuzzy numbers that are trapezoidal and triangular. Two fuzzy models are developed here. In the first model the cost parameters are fuzzified, but the demand rate is treated as crisp constant. In the second model, the demand rate is fuzzified but the cost parameters are treated as crisp constants. For each fuzzy model, we use signed distance method to defuzzify the fuzzy total cost and obtain an estimate of the total cost in the fuzzy sense. Numerical example is provided to ascertain the sensitiveness in the decision variables about fuzziness in the components. In practical situations, costs may be dependent on some foreign monetary unit. In such a case, due to a change in the exchange rates, the costs are often not known precisely. The first model can be used in this situation. In actual applications, demand is uncertain and must be predicted. Accordingly, the decision maker faces a fuzzy environment rather than a stochastic one in these cases. The second model can be used in this situation. Moreover, the proposed models can be expended for imperfect production process.

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In this study, a vendor-managed inventory model is developed for a single-vendor multiple-retailer single-warehouse (SV-MR-SV) supply chain problem based on the economic order quantity in which demands are stochastic and follow a uniform probability distribution. In order to reduce holding costs and to help balanced on-hand inventory cost between the vendor and the retailers, it is assumed that all inventory is held at a central warehouse with the lowest cost among the parties. The capacity of the central warehouse is limited. The objective is to find the warehouse replenishment frequency, the vendor\'s replenishment frequency, the order points, and the order quantities of the retailers such that the total inventory cost of the integrated supply chain is minimized. The proposed model is a mixed integer nonlinear programming problem (MINLP); hence, a genetic algorithm (GA) is utilized to solve this NP-hard problem. The parameters of the GA are calibrated using the Taguchi method to find better solutions. Some numerical illustrations are solved at the end to demonstrate the applicability of the proposed methodology and to evaluate the performance of the solution method.

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Accidents and natural disasters and crises coming out of them indicate the importance of an integrated planning to reduce their effected. Therefore, disaster relief logistics is one of the main activities in disaster management. In this paper, we study the response phase of the disaster management cycle and a bi-objective model has been developed for relief chain logistic in uncertainty condition including uncertainty in traveling time an also amount of demand in damaged areas. The proposed mathematical model has two objective functions. The first one is to minimize the sum of arrival times to damaged area multiplying by amount of demand and the second objective function is to maximize the minimum ratio of satisfied demands in total period in order to fairness in the distribution of goods. In the proposed model, the problem has been considered periodically and in order to solve the mathematical model, Global Criterion method has been used and a case study has been done at South Khorasan.

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The purpose of this article is to investigate a two-echelon supply chain inventory problem consisting of a single-vendor and a single-buyer with controllable lead time and investment for quality improvements. This paper presents an integrated vendor-buyer inventory model in order to minimize the sum of the ordering cost, holding cost, setup cost, investment for quality improvement and crashing cost by simultaneously optimizing the optimal order quantity, process quality, lead time and number of deliveries the vendor to the buyer in one production run with the objective of minimizing total relevant cost. Here the lead-time crashing cost has been assumed to be an exponentially function of the lead-time length. The main contribution of proposed model is an efficient iterative algorithm developed to minimize integrated total relevant cost for the single vendor and the single buyer systems with controllable lead time reduction and investment for quality improvements. Graphical representation is also presented to illustrate the proposed model. Numerical examples are presented to illustrate the procedures and results of the proposed algorithm. Matlab coding is also developed to derive the optimal solution and present numerical examples to illustrate the model.

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The study determined optimum inventory levels for various bakery resources using the bread supply chain network in Onitsha City. Structured questionnaires were administered among bakery factories. The optimum design achieved through the optimization model was compared with the existing systems. Analysis of 90 bakeries with a combined capacity of 3960 revealed that total money N 564,408,477.28 is spent on energy annually. Of this amount, 66.75% is expended annually to meet diesel requirements, while firewood and petrol account for 22.57% and 10.66%, respectively. The results of the ABC analysis show that flour ranks as class A with over 78%, followed by sugar at 13%, whilst the remainder of the ingredients constitutes 9%. High operating costs was identified as a major factor militating against the growth of the sector. Consequently, baked bread is expensive and remuneration is very poor, making the industry less attractive. The implementation of optimization practice adds value leading to savings amounting to N 6,957.51, thus enhancing the supply chain competiveness. The annual supply chain performance measured by inventory turnover shows a frequency of 73 inventory turns. Since the bakeries contribute to ensuring food security, these findings, if implemented, will assuage the rising food insecurity in the nation.

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This paper deals with a deterministic inventory model for deteriorating items under the condition of permissible delay in payments with constant demand rate is a function of time which differs from before and after deterioration for a single item. Shortages are allowed and completely backlogged which is a function of time. Under these assumptions, this paper develops a retailer\'s model for obtaining an optimal cycle length and ordering quantity in deteriorating items of an inventory model. Thus, our objective is retailer\'s cost minimization problem to nd an optimal replenishment policy under various parameters. The convexity of the objective function is derived and the numerical examples are provided to support the proposed model. Sensitivity analysis of the optimal solution with respect to major parameters of the model is included and the implications are discussed.

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This study develops a inventory model to determine ordering policy for deteriorating items with shortages under markovian inflationary conditions. Markov processes include process whose future behavior cannot be accurately predicted from its past behavior (except the current or present behavior) and which involves random chance or probability. Behavior of business or economy, flow of traffic, progress of an epidemic, all are examples of Markov processes. Since the far previous inflation rate don’t have a great impact on the current inflation rate, so, It is logical to consider changes of the inflation rate as a markov process. In addition, It is assumed that the cost of the items changes as a Continuous – Time - Markov Process too. The inventory model is described by differential equations over the time horizon along with the present value method. The objective is minimization of the expected present value of costs over the time horizon. The numerical example and a sensitivity analysis are provided to analyze the effect of changes in the values of the different parameters on the optimal solution.

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This work investigates the effect of different inventory policies of a supply chain model using the system dynamics approach which belongs to the class of Vendor Managed Inventory (VMI), automatic pipeline, inventory and order based production control systems (VMI-APIOBPCS). This work helps management to investigate the effect of different policies such as adding the VMI system or third party logistic (TPL) on the whole cost of the supply chain. To this end, this work applies system dynamics in supply chain with two supplier and one retail channel which consists of VMI system. Moreover, this work studies the performance of the proposed model via three metrics: Bullwhip effect; satisfaction of the end-customer; the amount of the whole inventory of chain.

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This study examines inventory management practices of flour milling manufacturing firms and their effects on operational performance. Five flour milling manufacturing firms in Lagos were used for this study. Structured questionnaire was the major instrument for the collection of relevant primary data while descriptive statistics such as mean and standard deviation was deployed to analyzing the data gathered. The results obtained showed that exception of the large manufacturing companies, most of the medium-sized flour milling firms adopts different inventory management strategies from the scientific and best practice models. Their inventory management strategies and policies were rather based on factors such as changing level of customer demand, prevailing industry practices, forecast estimates and guesses, and available production capacity. Findings also revealed significant differences between the effective management of inventory and optimal operating performance. For instance, while firms that adopt best practice inventory management approaches reported efficiency in capacity utilization, increased service level, and reduced lead time, others with different strategies had minimal utilization of material resources. There is need for flour manufacturing firms to implement scientific inventory management models to adequately handle material shortages, product stock outs situations, component pile up and their associated penalties.

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Considered supply chain in this article consists of one vendor and multiple retailers where the vendor applies vendor managed inventory. Considering vendor as a leader and retailers as followers, Stackelberg game theory is applied for modeling and analyzing this system. A general mixed integer nonlinear model is developed which can optimizes the performance of the system under revenue sharing contract, wholesale price contract and centralized structure. Based on this model, we numerically analyzed the performance of revenue sharing contract in the considered supply chain and four states for revenue sharing contract are analyzed at the end. Moreover, in each state, performance of the system under revenue sharing contract is compared with the performance of the system under wholesale price contract and centralized structure.

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In this paper, an EOQ model is developed for a deteriorating item with quadratic time dependent demand rate under trade credit. Mathematical models are also derived under two different situations i.e. Case I; the credit period is less than the cycle time for settling the account and Case II; the credit period is greater than or equal to the cycle time for settling the account. The numerical examples are also given to validate the proposed model. Sensitivity analysis is given to study the effect of various parameters on ordering policy and optimal total profit. Mathematica 7.1 software is used for finding optimal numerical solutions.

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This paper, considers the supplier selection in three echelon supply chain with Vendor Managed Inventory (VMI) strategy under price dependent demand condition. As there is a lack of study on the supplier selection in VMI literature, this paper presents a VMI model in supply chain including multi supplier, one distributer and multi retailer that distributer selects suppliers. Two class models (traditional vs. VMI) are presented and we compare them to study the impact of VMI on supply chain and supplier selection. As the proposed model is a NP-hard problem, a meta-heuristics namely Harmony Search is employed to optimize the proposed models. We show that how the VMI system can effect on supplier selection and can change the set of selected suppliers. Finally the conclusion and further studies are presented