Discrete-time Inventory Model Research Articles

Development of new hybrid discrete-time perishable inventory model based on Weibull distribution with time-varying demand using system dynamics approach

In the 20th century, there has been a significant development in logistics systems owing to market globalisation. From this perspective, our study focuses on designing novel models of inventory systems to reflect these real-time systems with improved accuracy and eventually design optimal control systems. Many mathematical inventory models lack details. Most of the existing models in the literature neglect the inclusion of closing days despite the shortening of the shelf-lifes of perishable items daily. In this study, a hybrid dynamic discrete-time inventory model with random lifetime perishable products, first in–first out (FIFO) and last in-first out (LIFO) issuing policies, positive lead time, and time-varying demand, including closing days, is developed. It is assumed that the demand is an external input to the model, and thus, it is easy to implement or test various market scenarios. The developed model is fitted to real data obtained from the research on the formation of botulinum toxin on packaged cubed melons and microbial spoilage at various incubation temperatures. Our study shows that the implementation of the Weibull distribution in modelling perishability can improve the accuracy of reflecting the performance of real physical inventory systems. We compare the developed model to an existing one in the literature, considering different issuing policies: FIFO, LIFO, and their combination. The study also includes a comparative analysis of the fixed and random lifetimes of products in terms of closing days.

Managing Inventory with Limited History of Intermittent Demand

We consider a single-product discrete-time inventory model with intermittent demand. In every period, either zero demand or a positive demand is observed with an unknown probability. The distribution of the positive demand is assumed to be from the location-scale family with unknown mean and variance. The functional form of the optimal inventory target is available but it is a function of the unknown intermittent demand parameters that must be estimated from a limited amount of historical demand data. We first quantify the expected cost associated with implementing the optimal inventory policy using the point estimates of the unknown parameters by ignoring the uncertainty around them. We then minimize this expected cost with respect to a threshold variable that factors the statistical estimation errors of the unknown parameters into the inventory decision. We find that the use of an optimized threshold leads to a significant reduction in the a priori expected cost of the decision maker.

Global Dual Sourcing and Order Smoothing: The Impact of Capacity and Lead Times

After decades of offshoring production across the world, companies are rethinking their global networks. Local sourcing is receiving more attention, but it remains challenging to balance the offshore sourcing cost advantage against the increased inventories, because of its longer lead time, and against the cost and (volume) flexibility of each source’s capacity. To guide strategic allocation in this global network decision, this paper establishes reasonably simple prescriptions that capture the key drivers. We adopt a conventional discrete-time inventory model with a linear control rule that smoothes orders and allows an exact and analytically tractable analysis of single- and dual-sourcing policies under normal demand. Distinguishing features of our model are that it captures each source’s lead time, capacity cost, and flexibility to work overtime. We use Lagrange’s inversion theorem to provide exact and simple square-root bound formulae for the strategic sourcing allocations and the value of dual sourcing. The formulae provide structural insight on the impact of financial, operational, and demand parameters, and a starting point for quantitative decision making. We investigate the robustness of our results by comparing the smoothing policy with existing single- and dual-sourcing models in a simulation study that relaxes model assumptions. This paper was accepted by Yossi Aviv, operations management.

A Stochastic Inventory System with Postponed Demands and Infinite Pool in Discrete-Time Setup

In this article, we consider a discrete-time inventory model in which demands arrive according to a discrete Markovian arrival process. The inventory is replenished according to an $$(s,S)$$ policy, and the lead time is assumed to follow a discrete phase-type distribution. The demands that occur during stock-out periods either enter a pool which has an infinite capacity or leave the system with a predefined probability. The demands in the pool are selected one by one, if the on-hand inventory level is above $$s+1,$$ and the interval time between any two successive selections is assumed to have a discrete phase-type distribution. The joint probability distribution of the number of customers in the pool and the inventory level is obtained in the steady-state case. We derive the system performance measures under steady state and using these measures, the total expected cost rate of the system is calculated. The impacts of arrival rate on the performance measures are graphically illustrated. Finally, we study the impact of cost on the optimal values of the total expected cost rate, inventory level and the reorder point.

An Algorithm for Infinite Horizon Lot Sizing with Deterministic Demand

We analyze an infinite horizon discrete time inventory model with deterministic but non-stationary demand for a single product at a single stage. There is a finite cycle of vectors of characteristics of the environment (demand, fixed ordering cost, variable procurement cost, holding cost) which is repeated after a finite number of periods. Future cost is discounted. In general, minimization of the sum of discounted total cost over the cycle does not give the minimum of the sum of discounted total cost over the infinite horizon. We construct an algorithm for computing of an optimal strategy over the infinite horizon. It is based on a forward in time dynamic programming recursion.

A discrete time inventory system with postponed demands

In this article, we consider a discrete-time inventory model in which demands arrive according to a discrete Markovian arrival process. The inventory is replenished according to an (s,S) policy and the lead time is assumed to follow a discrete phase-type distribution. The demands that occur during stock-out periods either enter a pool which has a finite capacity N(<∞) or leave the system with a predefined probability. Any demand that arrives when the pool is full and the inventory level is zero, is assumed to be lost. The demands in the pool are selected one by one, if the on-hand inventory level is above s+1, and the interval time between any two successive selections is assumed to have discrete phase-type distribution. The joint probability distribution of the number of customers in the pool and the inventory level is obtained in the steady state case. The measures of system performance in the steady state are derived and the total expected cost rate is also calculated. The results are illustrated numerically.

Global Dual Sourcing and Order Smoothing: The Impact of Capacity and Leadtime

After decades of offshoring production across the world, companies are rethinking their global networks. Local sourcing is receiving more attention, but it remains challenging to balance the offshore sourcing cost advantage against the increased inventories due to its longer leadtime, and against the cost and (volume-)flexibility of each source's capacity. To guide strategic allocation in this global network decision, this paper establishes reasonably simple prescriptions that capture the key drivers. We adopt a conventional discrete-time inventory model with a linear control rule that smoothes orders and allows an exact and analytically-tractable analysis of single and dual sourcing policies under normal demand. Distinguishing features of our model are that it captures each source's leadtime, capacity cost and flexibility to work overtime. We use Lagrange's inversion theorem to provide exact and simple square-root bound formulae for the strategic sourcing allocations and the value of dual sourcing. The formulae provide structural insight on the impact of financial, operational and demand parameters, and a starting point for quantitative decision making. We investigate the robustness of our results by comparing the smoothing policy with existing single and dual sourcing models in a simulation study that relaxes model assumptions.

Old and New Methods for Lost-Sales Inventory Systems

We consider the notoriously difficult discrete-time inventory model with stochastic demands, a constant lead time, and lost sales. We show that the effective state space is a relatively manageable compact set. Then, we test various plausible heuristics. We find that several perform reasonably well, although none is perfect. However, the standard base-stock policy (a direct analogue of the optimal policy for a backlog system) performs badly. We also show that the optimal cost is increasing in the lead time.

An inventory system with periodic regular review and flexible emergency review

We analyze a discrete time inventory model with two supply modes. Regular orders are placed periodically and arrive after a deterministic lead time. Emergency orders, characterized by a shorter deterministic lead time but higher purchase costs, can be placed in case of imminent stock-outs. We propose and analyze flexible order-up-to policies with emergency orders that arrive one, two, ⃛, up to some fixed number of time units before a regular order arrives. Based on an approximate cost model, we develop two sets of approximate explicit optimality conditions. The first set of conditions are rather complicated, but simulation shows that they do lead to near-optimal policies in most cases. The second set of conditions are very simple and seem more practical, but they only lead to a near-optimal policy if there are enough emergency supply opportunities in a review period to prevent most backorders.

An inventory system with periodic regular review and flexible emergency review

We analyze a discrete time inventory model with two supply modes. Regular orders are placed periodically and arrive after a deterministic lead time. Emergency orders, characterized by a shorter deterministic lead time but higher purchase costs, can be placed in case of imminent stock-outs. We propose and analyze flexible order-up-to policies with emergency orders that arrive one, two, ..., up to some fixed number of time units before a regular order arrives. Based on an approximate cost model, we develop two sets of approximate explicit optimality conditions. The first set of conditions are rather complicated, but simulation shows that they do lead to near-optimal policies in most cases. The second set of conditions are very simple and seem more practical, but they only lead to a near-optimal policy if there are enough emergency supply opportunities in a review period to prevent most backorders.

Optimality of Myopic Ordering Policies for Inventory Model with Stochastic Supply

This paper addresses a discrete time inventory model where the maximum amount of supply from which instantaneous replenishment orders can be made is a random variable. Optimal ordering policies are characterized as critical number policies with monotone increasing optimal critical values. A sufficient condition is then presented for myopic ordering policies to be optimal.

Die untersuchung der grenzverteilung des körperlichen bestandsprozesses in einem semi-Markovschen lagerhaltungsmodell

We consider the following discrete time inventory model: The sizes of demand are independent restricted to the integers random variables with common distribution {bi,i = 1,2,…}. The times between demands are positive independent random variables with common absolute-continuous distribution function F(t). The replenishment policy is of the modified (r, Q)-type and the lead times of orders are independent exponential distributed random variables. Unfilled demands are lost. We obtain the limit distribution of the stock on hand and compute this distribution for the special example .

A Discrete Time Inventory Model with Arbitrary Interval and Quantity Distributions of Demand

This paper considers a discrete time inventory model in which the times between successive demands and the sizes of those demands are respectively independent and identically distributed random variables. Costs considered are fixed ordering costs and proportional costs of purchase, holding, and shortage. Three types of replenishment policies are formulated as Markov renewal programs and compared. We give an illustrative example.