# Lesson 22: material requirements planning: lot sizing lot-Sizing In Lesson 21

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• ## 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.

• ## Note that this is a case of deterministic demand. However, the methods learnt in Lessons 11-15 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

• ## Some heuristic methods:

• Lot-for-Lot (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 (15-12)=3 units of period 2. So, one does not save the ordering cost of period 2, but carries some 3 units in

• ## 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, Silver-Meal 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.

• ## Some heuristic methods:

• Silver-Meal Heuristic
• As it is discussed in the previous slide, Silver-Meal 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.

• ## 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 Silver-Meal heuristic and least unit cost heuristic. The only difference is that Silver-Meal heuristic chooses K on the basis of average cost per period and least unit cost on average cost per unit.

• ## 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 Silver-Meal 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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