Note: A note on the production and inventory systems taking account of time value

This paper deals with the optimal inventory decisions taking account of time value by applying the concept of the present value method, and modifies the bounds for the optimal cycle time described in Chung et al. (Production Planning & Control, 1998, 9, 580–584). A modified algorithm to compute the optimal cycle time is developed to improve the paper of Chung et al. Finally, a numerical example is given to illustrate the algorithm discussed in this paper.     

Note on: An integrated vendor–buyer cooperative inventory model for items with imperfect quality

Huang [Huang, C., 2002. An integrated vendor–buyer cooperative inventory model for items with imperfect quality. Production Planning and Control, 13 (4), 355–361] proposes an integrated inventory model which allows a vendor and a buyer to minimise their expected integrated total cost function when the vendor's production process is not perfect. This note identifies two errors in the paper and provides a reformulation of the model.     

A simple approach to an integrated single-vendor single-buyer inventory system with shortage

In this article, a simple approach with two basic inequalities (Cauchy–Schwarz inequality and arithmetic–geometric mean inequality) is used to solve the integrated single-vendor single-buyer inventory problem developed by Wu and Ouyang (Wu, K.-S. and Ouyang, L.-Y., 2003. An integrated single-vendor single-buyer inventory system with shortage derived algebraically. Production Planning & Control, 14 (6), 555–561). Without the method of completing perfect square, the proposed approach yields the global minimum of the integrated total cost per year more easily than the algebraic approach used by Wu and Ouyang (2003 Wu, K-S and Ouyang, L-Y. 2003. An integrated single-vendor single-buyer inventory system with shortage derived algebraically. Production Planning & Control, 14(6): 555–561. [Taylor & Francis Online], [Web of Science ®] , [Google Scholar]). In addition, for people without the background of calculus, it is more useful to determine the buyer's economic order quantity and the vendor's optimal number of deliveries.     

Note on inventory models with Weibull distribution deterioration

This article explores the inventory model with a general demand rate function in which both the Weibull distributed deterioration and partial backlogging are considered. The inventory model discussed here is based on the important finding by Wu [Wu, K.S., 2001. An EOQ inventory model for items with Weibull distribution deterioration, ramp type demand rate and partial backlogging. Production Planning and Control, 12, 787–793]. There are four parts in our research. First, we derive the analytical framework of the inventory model for a general demand rate function1 1.?Based on detailed suggestions of Professor Wafik H. Iskander, Email: whiskander@mail.wvu.edu . Second, for the ramp type demand, we improve Wu's model to find the criterion to guarantee the existence and uniqueness of the optimal solution. Third, we develop a new model to compensate for the missing case in Wu's article. Fourth, we combine our results to show that our findings are applicable to the ramp type demand inventory model, so that the optimal solution is independent of the demand function. Finally, some numerical examples and graphs are provided to illustrate our discovery and demonstrate the application of our analytical framework.     

An online algorithm for continuous slab caster scheduling

Lee et al. (Lee, K., Chang, S.Y., and Hong, Y., 2004. Continuous slab caster scheduling and interval graphs. Production Planning & Control, 13 (5), 495–501) have introduced a slab caster scheduling problem and developed an optimal algorithm. Their algorithm is efficient but an offline algorithm that we need the information on all the customer orders a priori to implement. In this article, we propose an online algorithm that we can implement without knowledge of the orders yet to arrive. We show that the offline version of our new algorithm also provides an optimal solution and the online version has the worst case performance ratio of 3. We also give a short proof on the correctness of Lee et al.'s algorithm.     

The effect of the drum-buffer-rope (DBR) approach on the performance of a synchronous manufacturing system (SMS)

The main objective of any manufacturing system is to organize the resources in a shop floor for effective transformation of raw materials into finished products. Synchronous manufacturing (SM) is a manufacturing management philosophy that has a set of principles, procedures and techniques where every action is evaluated in terms of a common global goal of the organization (Seetharama et al., 1997, Production Planning and Inventory Control). A manufacturing system that adopts the above principle is called as synchronous manufacturing system (SMS). In order for a manufacturing plant to achieve the benefits of a synchronous operation, a logistical manufacturing (SM) is a manufacturing management philosophy that has a set of principles, procedures and techniques where every action is evaluated in terms of a common global control system that is manageable and results in predictable performance is required. The drum-buffer-rope (DBR) approach, which is a generalized system, satisfies the above requirements through computer simulation. This paper focuses on the effect of DBR principles on the performance of a synchronous manufacturing system. A case study has been taken up in a small-scale industry and analysis has been carried out on the effect of the DBR approach on the performance of the system. This work has been performed on an IBM/PC compatible system using the promodel software and C language.     

Postponement implementation in integrated production and inventory plan under deterioration effects: a case study of a juice producer with limited storage capacity

Abstract

The aim of this study is to develop a production and inventory plan for a fresh apple juice producer. During harvest season, the producer extracts premium juice from freshly picked apples and keeps an inventory of these premium apples in his temperature-controlled storage facility. The producer extracts also regular juice from regular apples purchased from third-party storages. To satisfy future demand, the producer carries inventories of juice and apple. The levels of apple inventories are constrained by the producer’s limited storage space, but he can replenish regular apples. To assist the producer in facing demand uncertainty and deterioration of apples, we develop a production and inventory plan that incorporates postponement to mitigate demand uncertainty. As postponement decisions are shaped by the cost structure of inventories, we integrate in one model the postponement decisions and the deterioration mitigation decisions that can alter the inventory costs. We build multi-period stochastic programming with recourse model to determine juice batch sizes and apple inventories that maximize the producer’s expected profit. The optimal solution illustrates the use of time and form postponements. We discuss the interactions between postponement implementation and decisions to mitigate apples deterioration. We compare the production and inventory plans with and without postponement and with and without apple deterioration. We also present sensitivity analyses for the plan under varying inventory cost and storage space.     

Production and inventory control at ABB Motors and Volvo Wheel Loaders,two examples of MRP in practical use

The paper presents the main routines of production and inventory control at ABB Motors, Västerås and Volvo Wheel Loaders, Eskilstuna. The primary interest is to present how Material Requirements Planning (MRP) is used in these two companies. If the number of end items is large, the company assembles-to-order or makes-to-order then additions to pure MRP seem to be necessary. ABB Motors and Volvo Wheel Loader use: planning bills, a normal bill of materials with 'adding bills of materials', a master production schedule planning system with an available-to-promise function and a home-made 'system' for modules available-to-promise. One important measure for the both companies is the accumulative lead-time. An increase of the Master Production Schedule in a shorter time than the accumulative lead-time is avoided, because it will lead to suggestions of purchase in past time periods and therefore most probably to future material shortages.     

THE EFFECT AND COST OF FORECAST ERROR BIAS FOR MULTIPLE-STAGE PRODUCTION-INVENTORY SYSTEMS

This paper examines forecast error with an intention not to minimize forecast error so much as to bias the resultant error in order to achieve better managerial results. Much work has been accomplished by other researchers toward the goal of minimizing forecast error—sometimes by the use of sophisticated forecasting techniques. The results of this paper indicate that manipulating forecast error bias may be the better managerial strategy as opposed to going to great lengths to minimize forecast error. Subject Areas: Forecasting, Aggregate Planning, Capacity Planning, and Production/Operations Management.     

短生命周期产品的三种库存模型的比较

讨论短生命周期产品库存模型,考虑无形变质因素,并假定无形变质率与需求率成反比关系.在线性需求和常数生产率的条件下,假设,若需求率为1,则视作产品的市场生命周期结束.并且,在产品生命周期的前期不存在缺货的情况下,给出了短生命周期产品分别在理想状态、允许缺货以及价格折扣导致需求率变化等3种状态下的库存模型,最后在相同参数条件下对这3种模型进行比较,找出了单位时间内平均总成本最小的最优库存模型,厂商可以根据自身的情况选择合适的库存策略.     

The impact of JIT on capacity management: A case study and analysis

This article describes the production planning and control techniques used at Verbatim Computer Disk Company in Charlotte, NC. The factory operates by management policy on a 24 hours-per-day, 7 days-per-week, 363 days-peryear, basis as if it were a process industry. Production of discrete units, computer disks, follows repetitive manufacturing methods including the implementation of just-in-time JIT methods into an existing material requirements planning MRP system. Production is based on the actual customer orders received from Marketing for disks from both US customers and international markets. Marketing uses price adjustments in coordination with Production Planning to ensure the factories operate at 100 capacity and within predefined inventory levels. This article discusses the relationship between Marketing and Manufacturing which allows for the attainment of a process industry-like economies of scale for a line of discrete products. Key characteristics of the production planning and control system are identified as are the current operating problems.     

Integrality in Stochastic Inventory Models

We study several finite‐horizon, discrete‐time, dynamic, stochastic inventory control models with integer demands: the newsvendor model, its multi‐period extension, and a single‐product, multi‐echelon assembly model. Equivalent linear programs are formulated for the corresponding stochastic dynamic programs, and integrality results are derived based on the total unimodularity of the constraint matrices. Specifically, for all these models, starting with integer inventory levels, we show that there exist optimal policies that are integral. For the most general single‐product, multi‐echelon assembly system model, integrality results are also derived for a practical alternative to stochastic dynamic programming, namely, rolling‐horizon optimization by a similar argument. We also present a different approach to prove integrality results for stochastic inventory models. This new approach is based on a generalization we propose for the one‐dimensional notion of piecewise linearity with integer breakpoints to higher dimensions. The usefulness of this new approach is illustrated by establishing the integrality of both the dynamic programming and rolling‐horizon optimization models of a two‐product capacitated stochastic inventory control system.     

Multi-item inventory model with quantity-dependent inventory costs and demand-dependent unit cost under imprecise objective and restrictions: A geometric programming approach

A multi-item inventory model with constant demand and infinite replenishment is developed under the restrictions on storage area, total average shortage cost and total average inventory investment cost. These restrictions may be precise or imprecise. Here, it is assumed that inventory costs are directly proportional to the respective quantities, and unit purchase/production cost is inversely related to the demand. Restricted shortages are allowed but fully backlogged. First, the problem is formulated in crisp environment taking the deterministic and precise inventory parameters. It is solved by both geometric programming (GP) and gradient-based non-linear programming (NLP) methods. Later, the problem is formulated with fuzzy goals on constraints and objectives where impreciseness is introduced through linear membership functions. It is solved using the fuzzy geometric programming (FGP) method. The inventory models are illustrated with numerical values and compared with the crisp results. A sensitivity analysis on the optimum order quantity and average cost is also presented due to the variation in the tolerance of total average inventory investment cost and total average shortage cost following Dutta et al., 1993, Fuzzy Sets and Systems, 55, 133-142.     

The Backroom Effect in Retail Operations

Traditional inventory models fail to take into account the dynamics between the retail sales floor and the backroom, commonly used by retailers for extra storage. When a replenishment order for a given item arrives at a retail store, it may not fit on the allocated shelf space, making backroom storage necessary. In this article, we introduce the backroom effect (BRE) as a consequence of misalignment of case pack size, shelf space, and reorder point. This misalignment results from the fragmented nature of inventory policy decision making in the retail industry and affects basic trade‐offs in inventory models. We specify conditions under which the BRE exists, quantify the expected amount of backroom inventory, derive an optimal short‐term inventory policy, and assess the impact of the BRE on the optimal inventory policy and total costs. Our results indicate that ignoring the BRE leads to artificially high reorder points and higher total costs. The paper concludes with a discussion of theoretical and managerial implications.     

Education: MRP/GT: A FRAMEWORK FOR PRODUCTION PLANNING AND CONTROL OF CELLULAR MANUFACTURING

American industry typically uses material requirements planning (MRP) for manufacturing control. This paper presents production planning and control procedures based on group technology (GT), which is used in British manufacturing. A translation between these ideas and the American approach is made, and it is suggested that a combination of MRP and GT is viable. The problems that arise, especially in the areas of lot-sizing and sequencing/scheduling, and their possible solutions are discussed. Since increased adoption of GT is expected within the next decade, an intensified research effort is warranted in these and other areas so that existing MRP systems can be modified or extended to handle cellular manufacturing control problems. Subject Areas: Material Requirements Planning and Production/Operations Management.     

A note on an economic production quantity model and just-in-time production

In this paper an economic production quantity (EPQ) model in which the production rate is variable is studied. An analysis is presented of the impact of a variable production rate on the optimal production quantity and the total relevant cost. It is observed that this EPQ production and inventory system, in which the production rate is close to the demand rate, possesses many characteristics that are similar to a just-in-time (JIT) production system. It is shown that the normal prerequisites and benefits of JIT production can be identified from an analysis of such an EPQ system.     

Mitigating Inventory Overstocking: Optimal Order‐up‐to Level to Achieve a Target Fill Rate over a Finite Horizon

Service level agreements (SLAs) are widely adopted performance‐based contracts in operations management practice, and fill rate is the most common performance metric among all the measurements in SLAs. Traditional procedures characterizing the order‐up‐to level satisfying a specified fill rate implicitly assume an infinite performance review horizon. However, in practice, inventory managers are liable to maintain and report fill rates over a finite performance review horizon. This horizon discrepancy leads to deviation between the target fill rate and actual achieved fill rate. In this study, we first examine the behavior of the fill rate distribution over a finite horizon with positive lead time. We analytically prove that the expected fill rate assuming an infinite performance review horizon exceeds the expected fill rate assuming a finite performance review horizon, implying that there exists some inventory “waste” (i.e., overstocking) when the traditional procedure is used. Based on this observation and the complexity of the problem, we propose a simulation‐based algorithm to reduce excess inventory while maintaining the contractual target fill rate. When the lead time is significant relative to the length of the contract horizon, we show that the improvement in the inventory system can be over 5%. Further, we extend our basic setting to incorporate the penalty for failing to meet a target, and show how one can solve large‐scale problems via stochastic approximation. The primary managerial implication of our study is that ignoring the performance review horizon in an SLA will cause overstocking, especially when the lead time is large.     

Replenishment Policies for Multi‐Product Stochastic Inventory Systems with Correlated Demand and Joint‐Replenishment Costs

This study analyzes optimal replenishment policies that minimize expected discounted cost of multi‐product stochastic inventory systems. The distinguishing feature of the multi‐product inventory system that we analyze is the existence of correlated demand and joint‐replenishment costs across multiple products. Our objective is to understand the structure of the optimal policy and use this structure to construct a heuristic method that can solve problems set in real‐world sizes/dimensions. Using an MDP formulation we first compute the optimal policy. The optimal policy can only be computed for problems with a small number of product types due to the curse of dimensionality. Hence, using the insight gained from the optimal policy, we propose a class of policies that captures the impact of demand correlation on the structure of the optimal policy. We call this class (s, c, d, S)‐policies, and also develop an algorithm to compute good policies in this class, for large multi‐product problems. Finally using an exhaustive set of computational examples we show that policies in this class very closely approximate the optimal policy and can outperform policies analyzed in prior literature which assume independent demand. We have also included examples that illustrate performance under the average cost objective.     

A NOTE ON INTEGRATING INVENTORY AND PRODUCT SALES-MIX MODELS

In a recent issue of Decision Sciences, Raiborn and Harris [2] discussed the integration of inventory and product sales-mix models. While they formulated a model which reflected some of the interactions between product sales-mix and inventory decisions, the purpose of this note is to point out deficiencies in their decision rule analysis for solving such integrated models.