Central versus local multiple stage inventory planning: An analysis of solutions

Supply chain management refers to the integration of all activities associated with moving goods from raw material stages through to end users. Yet this system-wide vision of inventory planning often requires the coordination of several commercially independent entities, such as suppliers, manufacturers and distributors. This study explores the issue of friction between replenishment policies, defined as the disparity between centrally and locally planned solutions to 98,820 deterministic, multiple stage inventory planning problems modeling systems of varying levels of complexity. Friction is found to be strongly related to certain cost factors, suggesting that certain supply chains could be more vulnerable to tension and inefficiencies when replenishment policies are derived without cooperation between commercially independent yet logistically interdependent stages. These results can also be applied to identify relationships between the findings of otherwise seemingly disparate previous studies of coordination schemes for supply chain partners.     

Optimal dynamic pricing and inventory control with stock deterioration and partial backordering

This paper studies the optimal dynamic pricing and inventory control policies in a periodic-review inventory system with fixed ordering cost and additive demand. The inventory may deteriorate over time and the unmet demand may be partially backlogged. We identify two sufficient conditions under which (s,S,p) policies are optimal.     

Coordination of production planning and distribution

This is a summary of the main results presented in the author’s Ph.D thesis, supervised by C. Prins and defended at the Université de Technologie de Troyes in October 2006. The thesis, written in French, is available from the author upon request. It deals with the integrated optimization of production planning and distribution in supply chains. A single product case and a multiproduct case are investigated. Integer linear programming models are proposed and different approaches based on heuristics, metaheuristics and cooperative methods are developed. Significant savings are obtained, compared to classical decoupled methods. These results confirm both the interest of integrating production and distribution decisions and of using metaheuristics for the largest instances.      

A (Q, R) inventory replenishment model with two delivery modes

Although splitting shipments across multiple delivery modes typically increases total shipping costs as a result of diseconomies of scale, it may offer certain benefits that can more than offset these costs. These benefits include a reduction in the probability of stockout and in the average inventory costs. We consider a single-stage inventory replenishment model that includes two delivery modes: a cheaper, less reliable mode, and another, more expensive but perfectly reliable mode. The high-reliability mode is only utilized in replenishment intervals in which the lead time of the less-reliable mode exceeds a certain value. This permits substituting the high-reliability mode for safety stock, to some degree. We characterize optimal replenishment decisions with these two modes, as well as the potential benefits of simultaneously using two delivery modes.     

Pooling of repairable spare parts: A study on inventory policies

This is a summary of the most important results presented in the author's PhD thesis (Wong 2004). This thesis, written in English, was defended on 14 June 2004 at the Katholieke Universiteit Leuven (Belgium) and supervised by Dirk Cattrysse and Dirk Van Oudheusden. A copy is available from the author upon request. It presents a number of modeling and solution approaches for investigating how the use of pooling contributes to the goal of increased service performance and reduced cost in the context of repairable spare parts inventory management. MSC classification: 47N10, 90B05, 91A80     

Optimal production and rationing policies of a make-to-stock production system with batch demand and backordering

In this paper, we consider the stock rationing problem of a single-item make-to-stock production/inventory system with multiple demand classes. Demand arrives as a Poisson process with a randomly distributed batch size. It is assumed that the batch demand can be partially satisfied. The facility can produce a batch up to a certain capacity at the same time. Production time follows an exponential distribution. We show that the optimal policy is characterized by multiple rationing levels.     

Manufacturing planning and control: The evolution of MRP and JIT integration

Material Requirements Planning (MRP) and Just-in-Time (JIT) system are directed toward planning and controlling the important characteristics of material flow: how much of what materials flow and when. Since the material flow is at the heart of the manufacturing firm, MRP and JHT are the powerful management tools that could determine the success or failure of an entire manufacturing system. One of the strongest debates in manufacturing has been centered on the performance comparison and compatibility of JIT production system to the existing MRP. The primary intent of this research is to provide an overview of the manufacturing planning and control environment associated with MRP and JIT. Classifying the existing MRP/JIT comparison and integration literature, two different perspectives on MRP/JIT are discussed, and future research area is proposed based on the taxonomy.     

Raw materials and production control with random supply and demand,an outside market and production capacity

We study a capacitated periodic inventory review problem in which the optimal control of both raw materials and finished product inventories simultaneously involves optimal decisions on materials purchasing from suppliers, buying or selling of materials in spot market, and production quantity in each period. We found that the dynamic program model of the problem is decomposable, and there is an independent relationship between the decisions on materials purchasing/selling and finished product production. Optimal policies are characterized and extensions are discussed.     

An algorithm for single-item economic lot-sizing problem with general inventory cost, non-decreasing capacity, and non-increasing setup and production cost

This paper considers an economic lot-sizing model with non-decreasing capacity constraint, non-increasing setup cost and production cost, and a general inventory cost. We prove that when periodic starting inventory is not less than a certain critical value, it is optimal to produce nothing; this critical value can be computed easily which results in a new effective algorithm.     

Production planning and pricing policy in a make-to-stock system with uncertain demand subject to machine breakdowns

We consider a make-to-stock system served by an unreliable machine that produces one type of product, which is sold to customers at one of two possible prices depending on the inventory level at the time when a customer arrives (i.e., the decision point). The system manager must determine the production level and selling price at each decision point. We first show that the optimal production and pricing policy is a threshold control, which is characterized by three threshold parameters under both the long-run discounted profit and long-run average profit criteria. We then establish the structural relationships among the three threshold parameters that production is off when inventory is above the threshold, and that the optimal selling price should be low when inventory is above the threshold under the scenario where the machine is down or up. Finally we provide some numerical examples to illustrate the analytical results and gain additional insights.     

Joint determination of optimal safety stocks and production policy for an imperfect production system

In this article, we develop an imperfect economic manufacturing quantity (EMQ) model for an unreliable production system subject to process deterioration, machine breakdown and repair and buffer stock. The basic model is developed under general process shift, machine breakdown and repair time distributions. We suggest a computational algorithm for determination of the optimal safety stock and production run time which minimize the expected cost per unit time in the steady state. For a numerical example, we illustrate the outcome of the proposed model and perform a sensitivity analysis with respect to the model-parameters which have direct influence on the optimal decisions.     

Predictive control of periodic-review production inventory systems with deteriorating items

In this paper a predictive control strategy is applied to a periodic-review dynamic inventory system with deteriorating items. Given the current inventory level, we determine the optimal production rates to be implemented at the beginning of each of the following periods over the control horizon. The effectiveness of this approach is the use of future information of the inventory target level and the desired production rate, which are available, along the fixed horizon. The deterioration coefficient may be known or unknown and both cases are considered. In the case where it is unknown, the self-tuning predictive control is applied. The proposed control algorithms are illustrated by simulations.     

An integrated production and inventory model to dampen upstream demand variability in the supply chain

We consider a two-echelon supply chain: a single retailer holds a finished goods inventory to meet an i.i.d. customer demand, and a single manufacturer produces the retailer’s replenishment orders on a make-to-order basis. In this setting the retailer’s order decision has a direct impact on the manufacturer’s production. It is a well known phenomenon that inventory control policies at the retailer level often propagate customer demand variability towards the manufacturer, sometimes even in an amplified form (known as the bullwhip effect). The manufacturer, however, prefers to smooth production, and thus he prefers a smooth order pattern from the retailer. At first sight a decrease in order variability comes at the cost of an increased variance of the retailer’s inventory levels, inflating the retailer’s safety stock requirements. However, integrating the impact of the retailer’s order decision on the manufacturer’s production leads to new insights. A smooth order pattern generates shorter and less variable (production/replenishment) lead times, introducing a compensating effect on the retailer’s safety stock. We show that by including the impact of the order decision on lead times, the order pattern can be smoothed to a considerable extent without increasing stock levels. This leads to a situation where both parties are better off.     

Agricultural planning of annual plants under demand,maturation, harvest,and yield risk

In this study we present a planning methodology for a firm whose objective is to match the random supply of annual premium fruits and vegetables from a number of contracted farms and the random demand from the retailers during the planning period. The supply uncertainty is due to the uncertainty of the maturation time, harvest time, and yield. The demand uncertainty is the uncertainty of weekly demand from the retailers. We provide a planning methodology to determine the farm areas and the seeding times for annual plants that survive for only one growing season in such a way that the expected total profit is maximized. Both the single period and the multi period cases are analyzed depending on the type of the plant. The performance of the solution methodology is evaluated by using numerical experiments. These experiments show that the proposed methodology matches random supply and random demand in a very effective way and improves the expected profit substantially compared to the planning approaches where the uncertainties are not taken into consideration.     

Concepts for safety stock determination under stochastic demand and different types of random production yield

We consider a manufacturer’s stochastic production/inventory problem under periodic review and present methods for safety stock determination to cope with uncertainties that are caused by stochastic demand and different types of yield randomness. Following well-proven inventory control concepts for this problem type, we focus on a critical stock policy with a linear order release rule. A central parameter of this type of policy is given by the safety stock value. When non-zero manufacturing lead times are taken into account in the random yield context, it turns out that safety stocks have to be determined that vary from period to period. We present a simple approach for calculating these dynamic safety stocks for different yield models. Additionally, we suggest approaches for determining appropriate static safety stocks that are easier to apply in practice. In a simulation study we investigate the performance of the proposed safety stock variants.     

Modelling imperfect advance demand information and analysis of optimal inventory policies

We consider an inventory control problem where it is possible to collect some imperfect information on future demand. We refer to such information as imperfect Advance Demand Information (ADI), which may occur in different forms of applications. A simple example is a company that uses sales representatives to market its products, in which case the collection of sales representatives’ information as to the number of customers interested in a product can generate an indication about the future sales of that product, hence it constitutes imperfect ADI. Other applications include internet retailing, Vendor Managed Inventory (VMI) applications and Collaborative Planning, Forecasting, and Replenishment (CPFR) environments. We develop a model that incorporates imperfect ADI with ordering decisions. Under our system settings, we show that the optimal policy is of order-up-to type, where the order level is a function of imperfect ADI. We also provide some characterizations of the optimal solution. We develop an expression for the expected cost benefits of imperfect ADI for the myopic problem. Our analytical and empirical findings reveal the conditions under which imperfect ADI is more valuable.     

Integrating deterioration and lifetime constraints in production and supply chain planning: A survey

Items with short lifetimes that are subject to deterioration are important in the business world. Research has a long tradition in integrating deterioration and value loss effects into mathematical models for inventory planning and control where such effects are understood as a general loss or shrinkage of inventory. However, there has been little work in the modeling of lifetime restrictions of items to prevent wastage and disposals, especially in a dynamic planning context. Globalization and other trends extend the consideration of single companies to whole supply chains, implying increased coordination and information needs. This is important as planning decisions impact lead times and thus the quality of items in the whole supply chain. Products that exceed their useful lifetime can impose high costs due to inventory loss or the need to rework them. This implies increased utilization of (scarce) resources, e.g., machine time, metals, and/or energy, thereby increasing CO₂${\text{CO}}_2$-levels. We survey the state-of-the-art regarding depreciation effects and the modeling of lifetime constraints as well as a classification of models following business planning functions of the value chain. A critical evaluation of approaches and their limitations is provided, highlighting directions for future research.     

Group technology in production management: The short horizon planning level

We consider a set of parts divided into subsets called part types, determined in such a way that the parts belonging to the same part type are manufactured using the same sequence of tasks (i.e. the same working process). We are looking for a partition of the set of part types into subsets called part families, and for a partition of the set of tasks into subsets called production subsystems defined as follows: (1) the number of part families and the number of production subsystems are equal, (2) one (one only one) production subsystem corresponds to each part family, (3) one (and only one) part family corresponds to each production subsystem, (4) the previous partitions minimize the number of tasks performed in a production subsystem different from that which corresponds to the part family containing the part involved. We give a fast algorithm which leads to a good solution depending on the initial set of part families. We also propose an algorithm to find a ‘good’ initial set of part families.     

The impact of consumer returns policies on consignment contracts with inventory control

We consider a consignment contract with consumer non-defective returns behavior. In our model, an upstream vendor contracts with a downstream retailer. The vendor decides his consignment price charged to the retailer for each unit sold and his refund price for each returned item, and then the retailer sets her retail price for selling the product. The vendor gets paid based on net sold units and salvages unsold units as well as returned items in a secondary market. Under the framework, we study and compare two different consignment arrangements: the retailer/vendor manages consignment inventory (RMCI/VMCI) programs. To study the impact of return policy, we discuss a consignment contract without return policy as a benchmark. We show that whether or not the vendor offers a return policy, it is always beneficial for the channel to delegate the inventory decision to the vendor. We find that the vendor’s return policy depends crucially on the salvage value of returns. If the product has no salvage value, the vendor’s optimal decision is not to offer a return policy; otherwise, the vendor can gain more profit by offering a return policy when the salvage value turns out to be positive.