Static and dynamic inventory models under inflation, time value of money and permissible delay in payment

In this research a number of mathematical models were developed for static and dynamic deterministic single-item inventory systems. Economic factors such as inflation, time value of money and permissible delay in payment were considered in developing the models. Nonlinear optimization techniques were used to obtain the optimal policies for the systems.;First, a static single-item inventory model was considered in which shortages are allowed and a delay is permitted in payment. In this case, suppliers allow the customers to settle their accounts after a fixed delay period during which no interest is charged.;An extension of the model was then considered in which all cost components of the model are subject to inflation and discounting, with constant rates over the planning horizon. The mathematical model of the system was developed and a nonlinear optimization technique, Hooke and Jeeves search method, was used to obtain the optimal policies for the system.;A dynamic deterministic single-item inventory model was also considered in which the demand was assumed to be a linear function of time. Suppliers allow for a delay in payment and the cost components are subject to inflation and discounting with constant rates and continuous compounding. The Golden search technique was used to obtain the optimum length of replenishment cycle such that the total cost is minimized.;Computer applications using Visual Basic and Mathematics were developed and several numerical example were solved

Inventory Model with Time-Dependent Holding cost under Inflation when Seller Credits to Order Quantity

In this study an inventory model is developed under which the seller provides the retailer a permissible delay in payments, if the retailer orders a large quantity. In this paper we establish an inventory model for non deteriorating items and time dependent holding cost under inflation when seller offers permissible delay to the retailer, if the order quantity is greater than or equal to a predetermined quantity. We then obtain optimal solution for finding optimal order quantity, optimal replenishment time and optimal total relevant cost. Finally, numerical example is given to illustrate the theoretical results and made sensitive analysis of various parameters on the optimal solution

Optimal dynamic pricing and replenishment policies for deteriorating items

Marketing strategies and proper inventory replenishment policies are often incorporated by enterprises to stimulate demand and maximize profit. The aim of this paper is to represent an integrated model for dynamic pricing and inventory control of deteriorating items. To reflect the dynamic characteristic of the problem, the selling price is defined as a time-dependent function of the initial selling price and the discount rate. In this regard, the price is exponentially discounted to compensate negative impact of the deterioration. The planning horizon is assumed to be infinite and the deterioration rate is time-dependent. In addition to price, the demand rate is dependent on advertisement as a powerful marketing tool. Several theoretical results and an iterative solution algorithm are developed to provide the optimal solution. Finally, to show validity of the model and illustrate the solution procedure, numerical results are presented

An Inventory Control Model for Fixed Deterioration and Logarithmic Demand Rates

This paper proposes an inventory control model for fixed deterioration and Logarithmic demand rat for the optimal stock of commodities to meet the future demand which may either arise at a constant rate or may vary with time. The analytical development is provided to obtain the optimal solution to minimize the total cost per time unit of an inventory control system. Numerical analysis has been presented to accredit the validity of the mentioned model. Effect of change in the values of different parameters on the decision variable and objectives function has been studied. Keywords:  Inventory Control, Fixed Deterioration, Logarithmic Demand rate, Commodities

Two-warehouse Inventory Model with Multivariate Demand and K-release Rule

AbstractIn this paper, we’ve projected a two-warehouse inventory model for deteriorating things beneath the impact of inflation and continuance of cash, wherever demand follows a rare combination of the linear time variable and on-hand inventory level. In one in the entire warehouse (OW), time-varying linear deterioration was thought-about and within the different (RW) weibull distributed deterioration was studied. Here, shortages were allowed and part backlogged. The stock is transferred from the RW to the OW following a bulk unharness rule. The target here is to seek out the optimum amount to that ought to be ordered and also the optimum variety of cycles during which the number from RW should be transferred to OW to maximize world wide web profit per unit time. The model has additionally been exemplified with the many numerical examples. The results have additionally been understood diagrammatically

Inventory models for production systems with constant/linear demand, time value of money, and perishable/non-perishable items

This research considers inventory systems for economic production models where the objective is to find the optimal cycle time, which minimizes the total cost, and optimal amount of shortage if it is allowed. Several aspects such as time value of money, inflation, constant and linear demand rates, shortages, and deterioration are considered in developing different models. Closed formulas are obtained for the optimal policy in one model. For others, more complex models where closed formulas cannot be obtained, search techniques are used to find the optimal solution.;First, a deterministic inventory control problem is considered for determination of optimal production quantities for an item with constant demand rate, while considering the effect of time value of money. Closed formulas are obtained to calculate the optimal cycle time and corresponding production quantity for the model without shortage. However, search procedures are used to find the optimal cycle time and maximum amount of shortage allowed for the models where shortage is allowed.;In the next inventory control problem, a deterministic model for items with linear demand rate over time, for a finite planning horizon, while considering the effect of time value of money, is considered. Search techniques are developed to find the optimal cycle time for the models without shortage, and the optimal cycle time and maximum amount of shortage for the models where shortage is allowed. A proof of the existence of a unique optimal point for the cost function is presented for the model without shortage.;A deterministic inventory control problem is also considered for items with constant rate of demand and exponentially decaying inventory over an infinite planning horizon, while considering the effect of time value of money. Two different search techniques are developed to find the optimal cycle time for the models without shortage, and the optimal cycle time and maximum amount of shortage allowed for the models where shortage is allowed. A proof of the existence of a unique optimal point for the cost function is presented for the model without shortage

Particle swarm optimization for bi-level pricing problems in supply chains

With rapid technological innovation and strong competition in hi-tech industries such as computer and communication organizations, the upstream component price and the downstream product cost usually decline significantly with time. As a result, an effective pricing supply chain model is very important. This paper first establishes two bi-level pricing models for pricing problems with the buyer and the vendor in a supply chain designated as the leader and the follower, respectively. A particle swarm optimization (PSO) based algorithm is developed to solve problems defined by these bi-level pricing models. Experiments illustrate that this PSO based algorithm can achieve a profit increase for buyers or vendors if they are treated as the leaders under some situations, compared with the existing methods. © 2010 Springer Science+Business Media, LLC

SUPPLY CHAINS FACING ATYPICAL DEMAND: OPTIMAL OPERATIONAL POLICIES AND BENEFITS UNDER INFORMATION SHARING

Demand patterns for products with seasonality and or short life-cycles do not follow a clear discernible pattern (to allow predictive time-series modeling of demand) for individual sales events or seasons due to such factors as considerable demand volatility, product promotions, and unforeseen marketplace events. Suppliers supporting such atypical demand patterns typically incur higher holding costs, lower capacity utilization, and lower order fill-rates, particularly under long lead-times and uncertainty in effective capacity. Retailers on the other hand struggle with product overages and supply shortages. On the other hand, atypical demand settings bring huge financial opportunity to supply chain players, and are pervasive. It is suggested in the literature that an effective means to reap these benefits is through increased information sharing between retailers and suppliers, superior forecasting with forecast update techniques, proper replenishment, and custom designed inventory/manufacturing policies. We also believe that sharing of order forecasts, also known as soft-orders, in advance by the buyer could be beneficial to both parties involved. This dissertation in particular studies a two-player supply chain, facing atypical demand. Among the two-players is a buyer (retailer/distributor/vendor) that makes ordering decision(s) in the presence of upstream supply uncertainty and demand forecast revision(s). We propose a stochastic dynamic programming model to optimally deicide on soft-order(s) and a final firm-order under a deposit scheme for initial soft-order(s). While sharing of upstream soft-order inventory position information by the supplier before receiving a final order is not a common industrial practice, nor is it discussed in the literature, our analysis shows that such information sharing is beneficial under certain conditions. Second player of the supply chain is a supplier (manufacturer) that makes production release decision(s) in the presence of limited and random effective capacity, and final order uncertainty. Our stochastic dynamic programming model for optimal production release decision making reveals that substantial savings in order fulfillment cost (that includes holding, overage, and underage costs) can be realized in the presence of advance soft-order(s). Soft-orders can also be shown to improve order fill-rate for the buyer. This research explores complex interactions of factors that affect the operational decision making process, such as costs, demand uncertainty, supply uncertainty, effective capacity severity, information accuracy, information volatility, intentional manipulation of information etc. Through extensive analysis of the operational policies, we provide managerial insights, many of which are intuitively appealing, such as, additional information never increases cost of an optimal decision; many are also counterintuitive, for example, dynamic programming models cannot fully compensate for intentional soft-order inflation by the buyer, even under conditions of a stable and linear order inflation pattern, in the absence of deposits.Supply Chain Economics, Information Sharing, Atypical Demand, Optimal Cost Model, Dynamic Program, Multi-player model

An Inventory Model for Perishable Products with Stock-Dependent Demand and Trade Credit under Inflation

We consider an inventory model for perishable products with stock-dependent demand under inflation. It is assumed that the supplier offers a credit period to the retailer, and the length of credit period is dependent on the order quantity. The retailer does not need to pay the purchasing cost until the end of credit period. If the revenue earned by the end of credit period is enough to pay the purchasing cost or there is budget, the balance is settled and the supplier does not charge any interest. Otherwise, the supplier charges interest for unpaid balance after credit period, and the interest and the remaining payments are made at the end of the replenishment cycle. The objective is to minimize the retailer’s (net) present value of cost. We show that there is an optimal cycle length to minimize the present value of cost; furthermore, a solution procedure is given to find the optimal solution. Numerical experiments are provided to illustrate the proposed model