An Inventory Model for Deteriorating Commodity under Stock Dependent Selling Rate

Economic order quantity (EOQ) is one of the most important inventory policy that have to be decided in managing an inventory system. The problem addressed in this paper concerns with the decision of the optimal replenishment time for ordering an EOQ to a supplier. This Model is captured the affect of stock dependent selling rate and varying price. We developed an inventory model under varying of demand-deterioration-price of commodity when the relationship of supplier-grocery-consumer at stochastic environment. The replenishment assumed instantaneous with zero lead time. The commodity will decay of quality according to the original condition with randomize characteristics. First, the model is addressed to solve a problem phenomenon how long is the optimum length of cycle time. Then, an EOQ of commodity to be ordered by will be determined by model. To solve this problem, the first step is developed a mathematical model based on reference’s model, and then solve the model analytically. Finally, an inventory model for deteriorating commodity under stock dependent selling rate and considering selling price was derived by this research. Keywords: deterioration commodity, expected profit, optimal replenishment time stock dependent selling rate

Efficient inventory control for imperfect quality items

In this paper, we present a general EOQ model for items that are subject to inspection for imperfect quality. Each lot that is delivered to the sorting facility undertakes a 100 per cent screening and the percentage of defective items per lot reduces according to a learning curve. The generality of the model is viewed as important both from an academic and practitioner perspective. The mathematical formulation considers arbitrary functions of time that allow the decision maker to assess the consequences of a diverse range of strategies by employing a single inventory model. A rigorous methodology is utilised to show that the solution is a unique and global optimal and a general step-by-step solution procedure is presented for continuous intra-cycle periodic review applications. The value of the temperature history and flow time through the supply chain is also used to determine an efficient policy. Furthermore, coordination mechanisms that may affect the supplier and the retailer are explored to improve inventory control at both echelons. The paper provides illustrative examples that demonstrate the application of the theoretical model in different settings and lead to the generation of interesting managerial insights

Quadratic Approximation of the Newsvendor Problem with Imperfect Quality

The paper presents a newsvendor problem in a fuzzy environment by introducing product quality as a fuzzy variable, and product demand as a probability distribution in an economic and supply chain management environment. In order to determine the optimal order quantity, a methodology is developed where the solution is achieved using a fuzzy ranking method combined with a quadratic programming problem approximation. Numerical examples are provided and compared in both situations, namely fuzzy and crisp. The results of these numerical examples show that the decision maker has to order a higher quantity when product quality is a fuzzy variable. The model can be useful for real world problems when historical data are not available

Agribusiness supply chain risk management: A review of quantitative decision models

Supply chain risk management is a large and growing field of research. However, within this field, mathematical models for agricultural products have received relatively little attention. This is somewhat surprising as risk management is even more important for agricultural supply chains due to challenges associated with seasonality, supply spikes, long supply lead-times, and perishability. This paper carries out a thorough review of the relatively limited literature on quantitative risk management models for agricultural supply chains. Specifically, we identify robustness and resilience as two key techniques for managing risk. Since these terms are not used consistently in the literature, we propose clear definitions and metrics for these terms; we then use these definitions to classify the agricultural supply chain risk management literature. Implications are given for both practice and future research on agricultural supply chain risk management

Optimal Lot Sizing for Perishable Products under Strict Carbon Cap Policy considering Stochastic Demand and Energy Usage cost

In this paper, we have considered stochastic demand for perishable items under strict carbon cap policy and energy usage. Perishable foods like meat, poultry, fish, dairy products etc. which are likely to spoil if not kept refrigerated. So that we related to the energy usage for maintaining perishable items at certain climate conditions where the inventory is stocked. Due to the nature of perishable product starts to decay at certain time, so that vendor provide a discount for the product in demand rate. We model the system into two stage, On first stage holds fresh items as non-discount period and second stage as older items as discount period nearer to expiration. A mathematical model is developed to determine the optimal order quantity, reorder point and number of shipments in a two-echelon supply chain considering partial backorders. The objective is to minimize the total expected supply chain cost while satisfying the carbon emission constraint. A numerical example is given to illustrate the solution procedure

Beyond LIFO and FIFO: Exploring an Allocation-In-Fraction-Out (AIFO) policy in a two-warehouse inventory model

The classical formulation of a two-warehouse inventory model is often based on the Last-In-First-Out (LIFO) or First-In-First-Out (FIFO) dispatching policy. The LIFO policy relies upon inventory stored in a rented warehouse (RW), with an ample capacity, being consumed first, before depleting inventory of an owned warehouse (OW) that has a limited capacity. Consumption works the other way around for the FIFO policy. In this paper, a new policy entitled “Allocation-In-Fraction-Out (AIFO)” is proposed. Unlike LIFO and FIFO, AIFO implies simultaneous consumption fractions associated with RW and OW. That said, the goods at both warehouses are depleted by the end of the same cycle. This necessitates the introduction of a key performance indicator to trade-off the costs associated with AIFO, LIFO and FIFO. Consequently, three general two-warehouse inventory models for items that are subject to inspection for imperfect quality are developed and compared – each underlying one of the dispatching policies considered. Each sub-replenishment that is delivered to OW and RW incurs a distinct transportation cost and undertakes a 100 per cent screening. The mathematical formulation reflects a diverse range of time-varying forms. The paper provides illustrative examples that analyse the behaviour of deterioration, value of information and perishability in different settings. For perishable products, we demonstrate that LIFO and FIFO may not be the right dispatching policies. Further, relaxing the inherent determinism of the maximum capacity associated with OW, not only produces better results and implies comprehensive learning, but may also suggest outsourcing the inventory holding through vendor managed inventory

LQ Optimal Sliding Mode Control of Periodic Review Perishable Inventories with Transportation Losses

In this work we apply the control-theoretic approach to design a new replenishment strategy for inventory systems with perishable stock. Such systems are supposed to effectively satisfy an unknown and permanently time-varying consumers' demand. The main obstacle of achieving this goal is the need of obtaining supplies from a distant source. During the supply process goods are inevitably lost due to various causes. Furthermore, those goods which successfully arrive at the distribution center still deteriorate while stored in its warehouse. We explicitly take into account both of these factors in designing our control strategy. We propose a sliding mode strategy and choose its parameters to minimize a quadratic quality criterion. This approach allows us to ameliorate the bullwhip effect (the amplification of the demand variations when going up in the supply chain). The control strategy proposed in this work ensures bounded orders, guarantees full consumers' demand satisfaction, and eliminates the risk of exceeding the warehouse capacity. These properties are stated in three theorems and proved in the paper

An EOQ model for time-dependent deteriorating items with alternating demand rates allowing shortages by considering time value of money

The present paper deals with an economic order quantity (EOQ) model of an inventory problem with alternating demand rate: (i) For a certain period, the demand rate is a non linear function of the instantaneous inventory level. (ii) For the rest of the cycle, the demand rate is time dependent. The time at which demand rate changes, may be deterministic or uncertain. The deterioration rate of the item is time dependent. The holding cost and shortage cost are taken as a linear function of time. The total cost function per unit time is obtained. Finally, the model is solved using a gradient based non-linear optimization technique (LINGO) and is illustrated by a numerical example