Robert W. Grubbström

The EOQ with backlogging derived without derivatives

Abstract In previous work the EOQ formula without consideration to backlogging has been given a derivation without reference to the use of derivatives, neither for necessary conditions nor for second-order sufficient conditions. Furthermore, this algebraic derivation immediately provided the value of the average cost function in optimum. This paper extends the previous result to the EOQ formula taking the backlogging case into consideration. It is shown that a similar derivation immediately provides the corresponding results for this case.

A principle for determining the correct capital costs of work-in-progress and inventory

In all production-inventory planning situations one of the major cost items to be considered is the capital cost for products in inventory and in the chain of process. In practical life as well as in theoretical models such costs are usually determined as a product value multiplied by an interest rate, where this value is computed on a cost-added basis: materials, labour, share of overheads, etc. In this paper we formulate models in which the physical production processes and their associated cash flow are analysed. By computing the present value of the cash flow as a function of characteristics of the production process, this value will also reflect a correct overall capital cost. Adjusting parameters of the physical process will then disclose what values to ascribe to products at different stages of production and assembly. It is shown that usual accounting principles often yield too conservative product values at early stages of production and that if percentage factors for covering overheads, etc., ar...

A note on an industrial strategy for stock management in supply chains: modelling and performance evaluation

An analytic formulation of consignment stock (CS) policy has been proposed in Braglia and Zavanella (2003, International Journal of Production Research, 41, 3793) where an implicit analytical solution is given. In this note it is shown that this solution has properties that enable it to be developed into a completely explicit form, allowing for a joint optimization of all decision variables governing the delivery management.

Planning and replanning the master production schedule under demand uncertainty

The Master Production Schedule (MPS) is essential in maintaining customer service levels and stabilising production planning in a Material Requirements Planning (MRP) environment. Traditionally, an ...

An Overview of Input-Output Analysis Applied to Production-Inventory Systems

Input-Output Analysis, together with the Laplace transform, have been applied to multi-level, multi-period production-inventory systems in a number of papers. This article gives a historical overview of the areas involved in these studies. It is shown that the input and output matrices as well as the Leontief inverse can be generalised to include timing properties for the inputs by means of the Laplace transform. The consequent advantages are exemplified in different production models, treating, for instance, capacity requirements and safety stock problems. The main literature in this field concerns assembly systems, but the approach is easily applicable to process industries with a divergent material flow or when feedback is essential.

Economic consequences of a production and inventory control policy

The economic performance of a generalized Order-Up-To policy is investigated in response to an Auto Regressive stochastic demand process. Focus is on the case where the physical production/distribution lead time is one period and where demand is forecasted with simple exponential smoothing. Two sets of convex piece-wise linear costs are considered. The first set is the traditional inventory holding and backlog costs. The second set of costs is piece-wise linear and increasing convex costs associated with the production order rate within and above a capacity constraint. Numerical investigations reveal that the classical Order-Up-To policy is no longer optimal when a broader range of costs is considered in the objective function.

A net present value approach to safety stocks in planned production

Abstract In a number of recent papers, the Laplace transform together with input-output analysis has been applied for the sake of formulating a basic theoretical description of material requirements planning (MRP). The transform approach has had a threefold use; on the one hand, it has been useful for describing time developments of the relevant production, demand and inventory properties in a compact way including effects of order flows and lead times. Second, the transform also captures stochastic properties by functioning as a generating function, and, third, the transform is easily applied for assessing the resulting cash flows when adopting the net present value (NPV) principle (or the annuity stream principle which is a variation of NPV). Input-output analysis, in particular the input matrix, is applied for describing multi-level product structures, which has made the analysis concise and distinct. In this paper we extend the analysis of determining optimal safety stock levels for a sequence of planned production decisions (a one-level MRP system) by applying the annuity stream as a criterion to a simple model instead of the average cost approach previously used.

Inventory trigger control policies developed in terms of control theory

In this article we model standard inventory ordering rules in terms of control systems theory. A differential equation is designed describing the development of a system in which an input signal reaching a predefined level triggers an output. The reorder point of inventory control systems may be interpreted as such a level triggering a replenishment. Systems using this kind of control are frequent in a variety of applications. Apart from inventory, domestic heat and pressure control are but two examples.

The detailed coordination problem in a two-level assembly system with stochastic lead times

In this paper, we study the detailed coordination problem in a two-level assembly system with stochastic lead times for lower-level items and constant and deterministic demand for the finished item ...

A stochastic model of multi-level/multi-stage capacity-constrained production-inventory systems

A great deal of research has been done on capacity-constrained production–inventory systems, most of which concerns deterministic demand situations and single-product systems. In this paper we pres ...