
Lesson 22: material requirements planning: lot sizing lotSizing In Lesson 21

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LESSON 22: MATERIAL REQUIREMENTS PLANNING: LOT SIZING
LotSizing In Lesson 21  We employ lot for lot ordering policy and order production as much as it is needed.
 Exception are only the cases in which there are constraints on the order quantity.
 For example, in one case we assume that at least 50 units must be ordered. In another case we assume that the order quantity must be a multiple of 50.
The motivation behind using lot for lot policy is minimizing inventory. If we order as much as it is needed, there will be no ending inventory at all!
LotSizing However, lot for lot policy requires that an order be placed each period. So, the number of orders and ordering cost are maximum. So, if the ordering cost is significant, one may naturally try to combine some lots into one in order to reduce the ordering cost. But then, inventory holding cost increases. Therefore, a question is what is the optimal size of the lot? How many periods will be covered by the first order, the second order, and so on until all the periods in the planning horizon are covered. This is the question of lot sizing. The next slide contains the statement of the lot sizing problem.
LotSizing The lot sizing problem is as follows: Given net requirements of an item over the next T periods, T >0, find order quantities that minimize the total holding and ordering costs over T periods. Note that this is a case of deterministic demand. However, the methods learnt in Lessons 1115 are not appropriate because  the demand is not necessarily the same over all periods and
 the inventory holding cost is only charged on ending inventory of each period
LotSizing Although we consider a deterministic model, keep in mind that in reality the demand is uncertain and subject to change. It has been observed that an optimal solution to the deterministic model may actually yield higher cost because of the changes in the demand. Some heuristic methods give lower cost in the long run. If the demand and/or costs change, the optimal solution may change significantly causing some managerial problems. The heuristic methods may not require such changes in the production plan. The heuristic methods require fewer computation steps and are easier to understand. In this lesson we shall discuss some heuristic methods. The optimization method is discussed in the text, Appendix 7A, pp 406410 (not included in the course).
LotSizing Some heuristic methods:  LotforLot (L4L):
 Order as much as it is needed.
 L4Lminimizes inventory holding cost, but maximizes ordering cost.
 EOQ:
 Every time it is required to place an order, lot size equals EOQ.
 EOQ method may choose an order size that covers partial demand of a period. For example, suppose that EOQ is 15 units. If the demand is 12 units in period 1 and 10 units in period 2, then a lot size of 15 units covers all of period 1 and only (1512)=3 units of period 2. So, one does not save the ordering cost of period 2, but carries some 3 units in
LotSizing Some heuristic methods:  the inventory when that 3 units are required in period 2. This is not a good idea because if an order size of 12 units is chosen, one saves on the holding cost without increasing the ordering cost!
 So, what’s the mistake? Generally, if the order quantity covers a period partially, one can save on the holding cost without increasing the ordering cost. The next three methods, SilverMeal heuristic, least unit cost and part period balancing avoid order quantities that cover a period partially. These methods always choose an order quantity that covers some K periods, K >0.
 Be careful when you compute EOQ. Express both holding cost and demand over the same period. If the holding cost is annual, use annual demand. If the holding cost is weekly, use weekly demand.
LotSizing Some heuristic methods:  SilverMeal Heuristic
 As it is discussed in the previous slide, SilverMeal heuristic chooses a lot size that equals the demand of some K periods in future, where K>0.
 If K =1, the lot size equals the demand of the next period.
 If K =2, the lot size equals the demand of the next 2 periods.
 If K =3, the lot size equals the demand of the next 3 periods, and so on.
 The average holding and ordering cost per period is computed for each K=1, 2, 3, etc. starting from K=1 and increasing K by 1 until the average cost per period starts increasing. The best K is the last one up to which the average cost per period decreases.
LotSizing Some heuristic methods:  Least Unit Cost (LUC)
 As it is discussed before, least unit cost heuristic chooses a lot size that equals the demand of some K periods in future, where K>0.
 The average holding and ordering cost per unit is computed for each K=1, 2, 3, etc. starting from K=1 and increasing K by 1 until the average cost per unit starts increasing. The best K is the last one up to which the average cost per unit decreases.
 Observe how similar is SilverMeal heuristic and least unit cost heuristic. The only difference is that SilverMeal heuristic chooses K on the basis of average cost per period and least unit cost on average cost per unit.
LotSizing Some heuristic methods:  Part Period Balancing
 As it is discussed before, part period balancing heuristic chooses a lot size that equals the demand of some K periods in future, where K>0.
 Holding and ordering costs are computed for each K=1, 2, 3, etc. starting from K=1 and increasing K by 1 until the holding cost exceeds the ordering cost. The best K is the one that minimizes the (absolute) difference between the holding and ordering costs.
 Note the similarity of this method with the SilverMeal heuristic and least unit cost heuristic. Part period balancing heuristic chooses K on the basis of the (absolute) difference between the holding and ordering costs.
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