FIFO Versus LIFO Issuing Policies for Stochastic Perishable Inventory Systems

We consider an inventory system for perishable items in which the arrival times of the items to be stored and the ones of the demands for those items form independent Poisson processes. The shelf lifetime of every item is finite and deterministic. Every demand is for a single item and is satisfied by one of the items on the shelf, if available. A demand remains unsatisfied if it arrives at an empty shelf. The aim of this paper is to compare two issuing policies: under FIFO (‘first in, first out’) any demand is satisfied by the item with the currently longest shelf life, while under LIFO (‘last in, first out’) always the youngest item on the shelf is assigned first. We determine the long-run net average profit as a function of the system parameters under each of the two policies, taking into account the revenue earned from satisfied demands, the cost of shelf space, penalties for unsatisfied demands, and the purchase cost of incoming items. The analytical results are used in several numerical examples in which the optimal input rate and the maximum expected long-run average profit under FIFO and under LIFO are determined and compared. We also provide a sensitivity analysis of the optimal solution for varying parameter values.     

A one-dimensional bin packing problem with shelf divisions

Given bins of size B, non-negative values d and Δ, and a list L of items, each item e∈L with size s_e and class c_e, we define a shelf as a subset of items packed inside a bin with total item sizes at most Δ such that all items in this shelf have the same class. Two subsequent shelves must be separated by a shelf division of size d. The size of a shelf is the total size of its items plus the size of the shelf division. The class constrained shelf bin packing problem (CCSBP) is to pack the items of L into the minimum number of bins, such that the items are divided into shelves and the total size of the shelves in a bin is at most B. We present hybrid algorithms based on the First Fit (Decreasing) and Best Fit (Decreasing) algorithms, and an APTAS for the problem CCSBP when the number of different classes is bounded by a constant C.     

The multi-item single period problem with an initial stock of convertible units

This paper deals with the situation of a number of end items, each facing uncertain demand in a single period of interest. Besides being able to purchase units of the end items there is also available a stock of units that can be converted into end items but at unit costs that depend on the specific end item. Efficient solution procedures are presented for two situations: (i) where the end item demand distributions are assumed known (illustrated for the case of normally distributed demand) and (ii) a distribution free approach where only the first two moments of the distributions are assumed known. Computational results for a set of problems are presented.     

An uncooperative order model for items with trade credit,inventory-dependent demand and limited displayed-shelf space

This paper considers a two-echelon supply chain where a supplier sells a single product through a retailer, who faces an inventory-dependent demand. The supplier hopes to incentive the retailer to order more items by offering trade credit. The retailer places the ordered items on the display shelf (DS) with limited space and stocks the remaining items (if any) that exceed the shelf capacity in his/her backroom/warehouse (BW). From the supplier’s perspective, we focus mainly on under which conditions the supplier should offer trade credit and how he/she should design such trade credit policy and corresponding ordering policy to obtain much more benefits. From the retailer’s perspective, we discuss whether the retailer needs BW and exactly how many items need to be stocked in BW when the supplier offers trade credit. We formulate a “supplier-Stackelberg” game model, from which we obtain the conditions under which the presented simple trade credit policy not only increases the overall chain profit but also each member’s profit. We also show that the trade credit policy is always more beneficial to the retailer than to the supplier if it is offered.     

Optimal replenishment policies for deteriorating items with stock sensitive demand under two-level trade credit and limited capacity

Recently, Min et al. [18] established an inventory model for deteriorating items under stock-dependent demand and two-level trade credit and obtained the optimal replenishment policy. Their analysis imposed a terminal condition of zero ending-inventory. However, with a stock-dependent demand, it may be desirable to order large quantities, resulting in stock remaining at the end of the cycle, due to the potential profits resulting from the increased demand. As a result, to make the theory more applicable in practice, we extend their model to allow for: (1) an ending-inventory to be nonzero, (2) a maximum inventory ceiling to reflect the facts that too much stock leaves a negative impression on the buyer and the amount of shelf/display space is limited.     

Joint demand fulfillment probability in a multi-item inventory system with independent order-up-to policies

We consider a multi-item inventory system with dependent item demands represented by a multivariate normal distribution and filled under a First-Come-First-Served rule. Each item is managed independently through a periodic review order-up-to policy while all items have the same review cycle. We obtain the joint demand fulfillment probability within a pre-specified time window. We also study the problem of maximizing the joint demand fulfillment probability and discuss a heuristic approach in which equal safety factors (equal fractiles) are specified for all items. Finally we present numerical results and an application with actual data.     

Two-echelon inventory model for deteriorating items with credit period dependent demand including shortages under trade credit

In real life situation, it is observed that demand of an item depends on the length of the credit period offered by the retailer to his customers which has a positive impact on demand of an item. But the impact of credit period on demand has received a very little attention by researchers. Furthermore, by allowing shortages as backlogging, the impact on the cost from the decay of the products can be balanced out. A profitable decision policy between a supplier and the retailers can be characterized by an agreement on the permissible delay in payments. Recently, Jaggi et al. (Eur J Oper Res 190:130–135, 2008) have investigated the impact of credit linked demand on the retailer’s optimal replenishment policy. The objective of this study is to extend Jaggi et al. (Eur J Oper Res 190:130–135, 2008) model by incorporating deterioration and backlogging. That is, we formulate a two-echelon inventory model for deteriorating items with credit period dependent demand including shortages under two-level trade credit financing and determine the retailer’s optimal replenishment policy when both the supplier as well as the retailer offers the credit period to stimulate customer demand. Furthermore, we establish some useful theorems to characterize the optimal solution and provide an easy and useful computational algorithm with the help of computer code using the software Matlab 7.0 to determine the optimal shortage point, cycle length, ordering quantity and credit period. A numerical example is included to illustrate the solution procedure for the mathematical model developed. Finally, we implement sensitivity analysis of the optimal solution with respect to the major parameters of the system and obtain some important managerial insights.     

A Lot-sizing Model for Just-in-time Manufacturing

We consider the problem of determining lot sizes of multiple items that are manufactured by a single capacitated facility. The manufacturing facility may represent a bottleneck processing activity on the shop floor or a storeroom that provides components to the shop floor. Items flow from the facility to a downstream facility, where they are assembled according to a specified mix. Just-in-time (JIT) manufacturing requires a balanced flow of items, in the proper mix, between successive facilities. Our model determines lot sizes of the various items based on available capacity and four attributes of each item: demand rate, holding cost, set-up time and processing time. Holding costs for each item accrue until the appropriate mix of items is available for shipment downstream. We develop a lot-sizing heuristic that minimizes total holding cost per time unit over all items, subject to capacity availability and the required mix of items.     

An impulse control problem of a production model with interruptions to follow stochastic demand

The paper deals with the stochastic optimal intervention problem which arises in a production & storage system involving identical items. The requests for items arrive at random and the production of an item can be interrupted during production to meet the corresponding demand. The operational costs considered are due to the stock/backlog, running costs and set up costs associated to interruptions and re-initializations. The process presents distinct behaviour on each of two disjoint identical subsets of the state space, and the state process can only be transferred from one subset to the other by interventions associated to interruptions/re-initializations. A characterization is given in terms of piecewise deterministic Markov process, which explores the aforementioned structure, and a method of solution with assured convergence, that does not require any special initialization, is provided.Additionally, we demonstrate that under conditions on the data, the optimal policy is to produce the item completely in a certain region of the state space of low stock level.     

A joint optimisation model for inventory replenishment,product assortment,shelf space and display area allocation decisions

In this paper, we propose an optimisation model to determine the product assortment, inventory replenishment, display area and shelf space allocation decisions that jointly maximize the retailer’s profit under shelf space and backroom storage constraints. The variety of products to be displayed in the retail store, their display locations within the store, their ordering quantities, and the allocated shelf space in each display area are considered as decision variables to be determined by the proposed integrated model. In the model formulation, we include the inventory investment costs, which are proportional to the average inventory, and storage and display costs as components of the inventory costs and make a clear distinction between showroom and backroom inventories. We also consider the effect of the display area location on the item demand. The developed model is a mixed integer non-linear program that we solved using LINGO software. Numerical examples are used to illustrate the developed model.     

A pricing problem under Monge property

We study a pricing problem where buyers with non-uniform demand purchase one of many items. Each buyer has a known benefit for each item and purchases the item that gives the largest utility, which is defined to be the difference between the benefit and the price of the item. The optimization problem is to decide on the prices that maximize total revenue of the seller. This problem is also called the optimal product line design problem in the absence of competition.

Even though the general problem is known to be NP-hard, it can be solved efficiently under some natural assumptions on customer benefits. In this paper we study properties of optimal solutions and present a dynamic programming algorithm when customer benefits satisfy the Monge property. The same algorithm can also be used to solve the problem under the additional requirement that all buyers should be served.     

Heuristics with guaranteed performance bounds for a manufacturing system with product recovery

We consider a manufacturing system with product recovery. The system manufactures a new product as well as remanufactures the product from old, returned items. The items remanufactured with the returned products are as good as new and satisfy the same demand as the new item. The demand rate for the new item and the return rate for the old item are deterministic and constant. The relevant costs are the holding costs for the new item and the returned item, and the fixed setup costs for both manufacturing and remanufacturing. The objective is to determine the lot sizes and production schedule for manufacturing and remanufacturing so as to minimize the long-run average cost per unit time. We first develop a lower bound among all classes of policies for the problem. We then show that the optimal integer ratio policy for the problem obtains a solution whose cost is at most 1.5% more than the lower bound.     

Unbounded knapsack problem with controllable rates: the case of a random demand for items

This paper focuses on a dynamic, continuous-time control generalization of the unbounded knapsack problem. This generalization implies that putting items in a knapsack takes time and has a due date. Specifically, the problem is characterized by a limited production horizon and a number of item types. Given an unbounded number of copies of each type of item, the items can be put into a knapsack at a controllable production rate subject to the available capacity. The demand for items is not known until the end of the production horizon. The objective is to collect items of each type in order to minimize shortage and surplus costs with respect to the demand. We prove that this continuous-time problem can be reduced to a number of discrete-time problems. As a result, solvable cases are found and a polynomial-time algorithm is suggested to approximate the optimal solution with any desired precision.     

带有可变库存费的变质性物品的部分延期供给的库存控制模型

传统的库存控制模型都视需求率为常数,在这篇文章中,放松了这个假定,研究了库存费的两种可能的变化:(i)库存费的变化率为存储时间的函数;(ii)库存费的变化率为库存量的函数.在模型中允许短缺发生且假定短缺部分延期供给,且在需求率线性依赖于库存水平的情形下,发展了两个变库存费的库存控制模型.     

Inventory model for deteriorating items with freshness and price dependent demand: Optimal discounting and ordering policies

A major part of retail industry deals with items whose freshness declines with time, resulting in lower demand at the same price. The item may later begin to deteriorate, when it is customary to offer discount in order to boost sales. A discounting policy may bring many benefits for the retailer, if correctly chosen. Motivated by this we have developed and analyzed an inventory model when demand for a deteriorating item depends initially only upon its selling price and later also on the freshness condition. We consider general demand function and general deterioration distribution for an inventory model with lost sales shortage. It is shown that net profit is a concave function of the period with positive inventory and conditionally concave function of discount. Important managerial insights obtained from sensitivity analysis suggest some policies counter to those commonly practiced by the retailers while others are in concurrence with the strategies in vogue.     

Multi-item inventory control with full truckloads: A comparison of aggregate and individual order triggering

In this paper, we consider the stochastic joint replenishment problem in an environment where transportation costs are dominant and full truckloads or full container loads are required. One replenishment policy, taking into account capacity restrictions of the total order volume, is the so-called QS policy, where replenishment orders are placed to raise the individual inventory positions of all items to their order-up-to levels, whenever the aggregate inventory position drops below the reorder level. We first provide a method to compute the policy parameters of a QS policy such that item target service levels can be met, under the assumption that demand can be modeled as a compound renewal process. The approximation formulas are based on renewal theory and are tested in a simulation study which reveals good performance. Second, we compare the QS policy with a simple allocation policy where replenishment orders are triggered by the individual inventory positions of the items. At the moment when an individual inventory position drops below its item reorder level, a replenishment order is triggered and the total vehicle capacity is allocated to all items such that the expected elapsed time before the next replenishment order is maximized. In an extensive simulation study it is illustrated that the QS policy outperforms this allocation policy since it results in lower inventory levels for the same service level. Although both policies lead to similar performance if items are identical, it can differ substantially if the item characteristics vary.     

An extension of partial backordering EOQ with correlated demand caused by cross-selling considering multiple minor items

Zhang et al. (2011) proposed the partial backordering EOQ with correlated demand caused by cross-selling, where a portion of the sales of a minor item is associated with those of a major item. In this paper, we extend their model to make it more applicable to dealing with the inventory replenishment problem for multiple associated items. We formulate the model as a mixed integer nonlinear programming (MINLP) problem and develop a global optimum search procedure with the fill rate given. We further employ a one-dimensional search on the fill rate to obtain the minimum total inventory cost within a predetermined precision, which enjoys polynomial computational complexity.