# economic lot scheduling problem

• Instead the machine needs to be set up to produce one product, incurring a setup cost and/or setup time, after which it will produce this product at a known rate .

• Beyond the selection of (expected) cycle times, with some amount of slack designed in (“safety time”), one has to also consider the amount of safety stock (buffer stock) that
is needed to meet desired service level.

• The term was first used in 1958 by professor Jack D. Rogers of Berkeley,[1] who extended the economic order quantity model to the case where there are several products to
be produced on the same machine, so that one must decide both the lot size for each product and when each lot should be produced.

• 7.Enter items in schedule and check it’s feasibility Stochastic ELSP Of great importance in practice is to design, plan and operate shared capacity across multiple products
with changeover times and costs in an uncertain demand environment.

• Total quantity of an item required = UT Total production time for an item = UT/P Check that productive capacity is satisfied: 3.Compute: as a whole number If for a certain
item, θ0 is not an even number, calculate: And change L0 to L in the direction which incurs the least cost increase between +Δ and -Δ 4.Compute for each item and list items in order of increasing 5.For each pair of items ij check: To forms
pairs take the ith with the i+1th, i+2th, etc.

• When it is desired to produce a different product, the machine is stopped and another costly setup is required to begin producing the next product.

• The model is known as a NP-hard problem since it is not currently possible to find the optimal solution without checking nearly every possibility.

• Model formulation The classic ELSP is concerned with scheduling the production of several products on a single machine in order to minimize the total costs incurred (which
include setup costs and inventory holding costs).

• This product switching must not be done too often or the setup costs will be large, but equally too long a production run of apple juice would be undesirable because it would
lead to a large inventory investment and carrying cost for unsold cases of apple juice and perhaps stock-outs in orange juice and milk.

• N is the number of runs made, U the use rate, L the lot size and T the planning period.

• If any of these inequalities is violated, calculate +Δ and -Δ for lot size increments of 2U and in order of size of cost change make step-by-step lot size changes.

• Let be the setup cost when switching from product i to product j and inventory cost is charged based on average inventory level of each item.

Works Cited

[‘1. Jack D. Rogers: A Computational Approach to the Economic Lot Scheduling Problem, Management Science, Vol. 4, No. 3, April 1958, pp. 264–291
2. ^ Welch, W. Evert, A Case of Simple Linear Programming, Management Methods 1956 in Jack D. Rogers:
A Computational Approach to the Economic Lot Scheduling Problem, Management Science, Vol. 4, No. 3, April 1958, pp. 264–291
3. ^ Tayur, S. (2000). “Improving Operations and Quoting Accurate Lead Times in a Laminate Plant”. Interfaces. 30 (5): 1–15.
doi:10.1287/inte.30.5.1.11637.
4. ^ Zipkin Paul H., Foundations of Inventory Management, Boston: McGraw Hill, 2000, ISBN 0-256-11379-3
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