Moncer Hariga

Some stochastic inventory models with deterministic variable lead time

In this paper we determine optimal reduction in the procurement lead time duration for some stochastic inventory models, jointly with the optimal ordering decisions. The models are developed with complete and partial information about the lead time demand distribution. The stochastic models analyzed in this paper are the classical continuous and periodic review models with a mixture of backorders and lost sales and the base stock model. For each of these models, we provide sufficient conditions for the uniqueness of the optimal operating policy. We also develop algorithms for solving these models and provide illustrative numerical examples.

Optimal and heuristic inventory replenishment models for deteriorating items with exponential time-varying demand

Abstract In this paper we present optimal and heuristic procedures for the inventory replenishment problem in which items are deteriorating at a constant rate. The demand rates are changing exponentially with time over a known and finite planning horizon. We have developed an iterative numerical procedure to find the optimal replenishment schedule. The first two heuristics are based on the economic order interval approximation. The third heuristic restricts all the replenishment cycles over the planning horizon to be equal over the planning horizon. The last three heuristics are extended versions of the Silver-Meal heuristic, the least cost approach, and the least-unit cost heuristic which were used in the inventory literature for the case of discrete time-varying demand without deterioration. We further assess the cost and computation time effectiveness of the six heuristics. The results of a sample of 1440 problems show that the extended least cost approach is the most cost effective.

Note : The economic manufacturing lot-sizing problem with imperfect production processes : Bounds and optimal solutions

In this paper, we consider the economic production quantity problem in the presence of imperfect processes. In the literature, the time to shift from the in-control state to the out-of-control state is assumed to be exponentially distributed. In this study, we consider general time to shift distributions and provide distribution-based and distribution-free bounds on the optimal cost. For the exponential case, we compare the optimal solutions to approximate solutions proposed in the literature. A numerical example is used to illustrate the analysis presented and to conduct a sensitivity analysis in order to see the effect of the input parameters on the various solutions to the problem.

Economic lot scheduling problem with imperfect production processes

In this paper, we model the effects of imperfect production processes on the economic lot scheduling problem (ELSP). It is assumed that the production facility starts in the in-control state producing items of high or perfect quality. However the facility may deteriorate with time and shifts at a random time to an out of control state and begins to produce nonconforming items. A mathematical model is developed for ELSP taking into account the effect of imperfect quality and process restoration. Numerical examples are presented to illustrate important issues related to the developed model.

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

Abstract 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.

Optimal time varying lot-sizing models under inflationary conditions

Abstract This paper deals with the inventory replenishment problem over a fixed planning horizon for items with linearly time-varying demand and under inflationary conditions. We develop models and optimal solution procedures with and without shortages. We do not put any restriction on the length of the replenishment cycles making the proposed methods the first optimal solution procedure for this problem. Using four examples, we illustrate the proposed solution procedures and study the effect of changing the inflation and discount rates on the optimal replenishment schedules.

Effects of inflation and time-value of money on an inventory model with time-dependent demand rate and shortages

Abstract In a recent paper, Datta and Pal investigated the effects of inflation and time-value of money on an inventory model with linearly increasing demand and finite shortage cost. However, their models are formulated under the assumption of equal inventory carrying time during each replenishment cycle. In this paper, we redevelop the models of Datta and Pal by relaxing this assumption and modifying their mathematical formulations. Our models can be applicable to both growing and declining markets with general continuous time-dependent demand rates. Numerical examples are provided to illustrate the developed models.

A chance-constrained multi-period model for a special multi-reservoir system

We develop a model for optimal multi-period operation of a multi-reservoir system for a basin operating under a conjunctive use of ground and surface Water. The inflows to the main reservoir as well as the irrigation demands are stochastic. The ground stock suffers from severe overdrafts increasing the risk of the total depletion of the aquifer in addition to the quality degradation and the threat of seawater intrusion. We treat the uncertainties in the inflows through chance constraints and penalties of failure to release the planned amounts of surface water from the main reservoir. However, we reflect uncertainties in irrigation demands by opting for deficit irrigation and using adequate production functions to estimate the expected crop yields. We attempt in the model to avoid large deficits except perhaps for periods where crop yields are relatively insensitive to water shortage. The objective is to maximize the total expected profit of the entire region. We illustrate the model through an example partially based on some hypothetical data.

Consignment and vendor managed inventory in single-vendor multiple buyers supply chains

In this paper we model a consignment (CS) and vendor-managed inventory (VMI) policy for a single vendor and multiple buyers supply chain with known demand. We study three vendor–buyers partnerships: (i) the vendor and the buyers act independently, (ii) the vendor enters in a vendor-managed inventory consignment (VMI&CS) partnership with the buyers and (iii) the vendor and the buyer belong to a vertically integrated firm where a single decision maker decides about the ordering policies. We use relationships (i) and (ii) to study the benefits of the VMI&CS agreement. We provide analytical and numerical results. We find that such an agreement is more beneficial when the vendor has a flexible capacity. It is also more attractive to buyers when they have significant order costs and the vendors setup cost is not large. Finally we find that under VMI&CS the vendor will tend to make more frequent shipments with smaller lots.

Economic analysis of dynamic inventory models with non-stationary costs and demand

Abstract With todays high rate of inflation observed in most world economies, the accuracy of standard lot-sizing models and their applicability to real inventory situations under inflationary conditions become questionable. In this paper, we have studied the effects of inflation and time value of money on the replenishment policies of items with time continuous non-stationary demand over a finite planning horizon. We have developed dynamic programming models for three commonly used replenishment policies in the inventory lot-sizing literature with time varying demand and shortages. In the case of linear time-dependent demand, we have performed a sensitivity analysis to investigate the impact of changing the system parameters on the present worth of the total cost of each of the three replenishment policies. The results showed that the initial cycle length is virtually insensitive to the type of replenishment policy. We have also extended the developed models to more practical inventory situations with exponentially deteriorating items and perishable products having fixed life time.