Orders with different priorities

Until now, we have assumed that all orders were of equal importance. In a practical situation, this is not always the case. Some clients may find a shorter lead time more 

In Chapter 2, we have listed a number of different elements of the penalty costs. Part of these costs can be considered to be real costs, but another, often much larger part, consists of speculative elements or simply represent management policies. Therefore it will be no problem to choose the penalty costs for orders with different priorities as an integer number multiplied by p. For example, in a certain situation for some of the orders the penalty costs will be p, for some other orders 2p and for another category of orders 3p or 4/ . In the production mles which we have considered until now, we base the decisions upon the state vector r= ri.rn. If we distinguish orders with for instance three different priorities, a possible state description is given by denoting the number of orders of priority j with a residual lead time of i periods by rij. This would imply that the state vector contains iN components and diis will soon lead to an immense state space. 

Due to the increased state space, the use of the Wagner-Whitin approach and the use of the optimal policy will become much more complex, because in these production rules we have to consider the order state during a number of periods. In the Silver-Meal approach and in the (x,7 -nile we only consider the action for the first period. In order to determine the penalty costs, if we do not produce during this first period, we have to know the sum of the ri values for the different priorities weighted with the 

The weighting of the orders that contribute to the first component of the aggregated order state vector can be done in the following way. We define the penalty points of an order as the penalty costs for that order divided by p, so the penalty points may be 1,2,3 etc. Now we define r as the sum of the penalty points of those orders that have to be produced by the end of the period or in previous periods. The other elements of the order state vector, r2.rn, are defined as the sum of the number of orders with a particular residual lead time. For instance, r z is the sum over all priorities of the number of orders with a residual lead time of 2 periods. The description of the transition probabilities for this order state vector r will be slightly more complex, but on the other hand, there is a large state space reduction. 

The new state vector r does not provide the necessary information for a good use of the optimal policy and for the Wagner-Whitin approach. For these rules it is indeed necessary to know the order state vector for each of the different priorities separately. The (x,T)-rule and the Silver-Meal approach can be used straightforwardly in this situation. Of course the fixed cycle production rule n (cf. (4.2.10)) can also be used without any complications. The use of these rules is now exactly the same as described in 4.2.4.2. and 4.2.4.4. 

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The insight into the different problem aspects will be combined in Chapter 7. In this chapter we shall consider the most complex situations, with orders with different priorities and for different types. Firm-initiated lead times are proposed for the orders, based on a preliminary production plan. There is a given probability that the customer withdraws an order if the proposed lead time is too long. The orders will be produced on several machines. Some types of products can be produced on one machine, other types on two machines. This complicates the production planning, but even in this situation we can use a simple production rule, based on the (x,7)-rule, in combination with some special extensions. Finally, we will give the conclusions of our study in Chapter 8. 

The analysis of this production rale will be done in much the same way as the analysis of the uncapacitated (x,T)-rule. For every type of product we consider a Markov chain in which the state is given by the number of penalty points. The interaction between the different states is found in the transition probabilities. We will consider the situation in which there are orders with different priorities. Every order has a fixed... 

The purpose of analysing situations in this way is to get an impression of the average delivery times that are possible for the various types of products and also an impression of the number of set-ups per time unit The average delivery times may be important for the profit like in the examples above and they can influence the demand and the profit From Examples 6.4 we can learn that it would be better not to have the orders for type 4, because they only lead to a decreasing profit. Starting from the analysis of the simplified situation we can add other elements, such as orders with different priority, a realistic distribution for the arrival of orders and for the service times and we may consider decision rules for lead times. Some of these extensions can be treated with an analysis similar to the one that we have described or by using a so-called Mean Value technique. For other extensions the performance can only be measured by a simulation study. 

In Chapter 4 we have introduced the (x,r)-rule for an uncapacitated situation. In Chapter 5 we have extended the rule for a multi-type capacitated situation with fixed lead times. In this chapter we want to study the necessary extensions for the use of the (x,7>-nile in more complex situations with firm-initiated lead times. The situations in this chapter are combinations of the more simple situations that we have considered in the previous sections several product types with different demand rates, set-ups between types, orders with different priorities, backlogging, capacity constraints and overtime possibilities. 

In the third model (finite chain with different terminal groups) no reflection symmetry element exists in the Fischer projection. The individual macromolecules are, therefore, chiral and all the tertiary atoms are asymmetric and different. The stereochemical notation for a single chain, depending on the priority order of the end groups, can be R, R2, R. . . R -2, R -i, Rn or R, R2, R3... 

The plant/controller simulation should be exercised many times, with many different combinations of active constraints. Eor each constraint combination, it is important to make sure that when constraint violations are unavoidable (more active constraints than MVs), the CV violations occur in the correct order, with the highest priority given to variables related to safety. 

It is clear that the cost associated with inventory depends on the variance of demand during lead time. In such a case, the larger the demand variance, the greater the effect of lead time on safety stock. Now suppose orders to a fadlity came from two sources that differ in their demand variability. Suppose we provide priority to the higher demand variance orders and low priority to the low demand variance order what is the impact Note that, as shown analytically and illustrated with a numerical example in Chapter 4 on capacity management, if one set of orders receives a priority, the lead time for those orders will decrease. But, since the capacity level is unchanged, the lead time for the lower priority orders will increase. Thus, priorities are one mechanism to offer differentiated lead times across order streams and thus improve supply chain performance for spare parts. 

Using these probability and severity categories, a risk analysis matrix can be developed for any type of event and used to identify imacceptable risks for the operation. It can also be used to prioritize which risks wiU be addressed—where action is taken to eliminate or reduce them—and in which order. An example risk-analysis matrix is given in Figure 18.1, with high priority cells identified. The highest priority cells are located in the upper left part of the matrix, while the lowest priority cells are in the lower right corner. The approach could be used to compare the impact of many different events, such as roof faU accidents, rock burst events, and mine fires. It can also be used to combine both quantitative and quahtative risks. 

Preemptive GP ranks the objective fimctions with respect to the ordered preferences of the DMs and minimizes the deviations from the target values associated with each objective in the ranked order. Several different techniques can be used to derive preemptive priorities. One convenient way is to use discrete alternative multi-criteria decision-making methods such as rating, Borda count, pairwise comparison, or the analytic hierarchy process (AHP) method (see Ravindran et al. [2010] for an application). These methods also provide a numerical strength-of-preference value that can be used in non-preemptive GP models. The preemptive GP model formulation, assuming that the preference ordering of the objectives is Zy Zy Zy Zy as follows ... 

In both examples we will assume a geometrical distribution for the demand. To simplify the analysis, we will set a maximum for the number of orders per period for a certain type and priority, but neither this maximum nor the distribution will be an essential element in the analysis. We will assume that a set-up takes one unit of time. In the examples we will measure the performance of the rule with a given set of penalty points in three situations with different costs ... 

The different priorities of the orders imply that the reaction upon the proposed lead times will be different and that the penalty costs and the revenues will be different. The decisions about the lead times and about the production are made periodically, but different from the periodic review models in Chapter 4 and Chapter 5, the production of a type can be continued in the next period without an extra set-up at the beginning of a period. This assumption allows us to treat non-stop production processes in the same way as production processes with only one or two working shifts per day. It will be required that the average amount of capacity that is used for working overtime will be less than a few percent of the fixed capacity that is available... 

The capacity will be allocated to one or more types of products in several steps. Hrst we detmnine which of the types is the most important type, of course with a sufficient number of penalty points. If the number of orders for this most important type is less than or equal to the available capacity, then all the orders for this type will be produced. If not, then we will start with the orders with the earliest due date and if orders have the same due date we will start with the orders with the highest priority. The allocation of the capacity stops if all the normal available capacity has been allocated and if the number of periods until the due dates of the remaining orders is larger than some priority-dependent constant. If there are remaining orders for which the number of periods until the due date is not larger than this priority-dependent constant, then extra capacity will be used to produce these orders. In Example 7.1. we will consider orders with two different priorities normal and urgent orders. For the normal orders we will use extra capacity for all orders with a residual lead time that is less than or equal to one period. For the urgent orders we will use extra capacity for all orders with a residual lead time that is less than or equal to two periods. 

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