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MULTI-PERIOD PRODUCTION-SMOOTHINGG MODEL Example 2.4.4 on page 65 of Taha's book A company will manufacture a product for the next four months: March, April, May, and June The demands for each month are 520, 720, 520, and 620 units, respectively. • The company has a steady work force of 10 employees but can meet fluctuating production needs by hiring and firing temporary workers at the beginning of each month, if necessary The extra costs of hiring and firing in any month are $200 and $400 per worker, respectively. A permanent worker can produce 12 units per month, and a temporary worker, lacking comparable experience, only produce 10 units per month. • The company can produce more than needed in any month and carry the surplus over to a succeeding month at a holding cost of $50 per unit per month. 27

Answer 1

Column (A) x $200 Extraunits Extra Entra carring hiving diting Cost Cost $200 $ 400 Cost required (d) 120 Answer first considered the all given information in one table Table) Month Demand, permenent units difference No. of units worker produced Entra produced Carrind wakers Ito next (6) =(a-b) month (A) e=CC-d) 18000 16000 March 5ao 10 400 40 400 (12410) (hox 200 (40x400) Jone water (hoxig 720 10 120 600 60 600 12000 240000 (box 200) (60XH00) lao too 8000 16000 o lo 40 Sao (*oxaoo) (hox voo) 10,000 200000 500 10 120 500 50. June 620 (50x200) (50x400) 38000 76000 480 1900 nothers) April 400 o May Totals 2380 Expl D Eid 4) Explanation - A B Explanation nou Units is per

ie - 10x12 = 120 As per the above data, Explanation A units produced by fermament wellner in Each month is lo (no. of workers, noe of units froduce by Each worker Explanation- Consider the march month, the demand of is 500 units. but produced units 120 Brits i. Balance demand 400 (520-120] writs to be satisfied by Entra Explanation - c manpower so, Extra man power required to Satisfy the demand in the month (520-120)/0 = 40 so to temporary workers required demand to satisfy the sy Extra Crnits are produced in the Carried on next monlts, the holding Cost will be $50 per unit per month Here & Explanation- of march of march month menth is (294) Cost of hoing to workers = $200 ie. (Cost of living for worker) x 40

ie. $200X40 = $800 Explanation-E Cost of firing = $400 Perwather $400x to $16 of holding inventory = do (because no Entra unit produced more thom needed in March ) 16000 Cost any morth le. In march month no Extra unit produced So. The holding Cost = 0 Same Explanation is applies April & may menth and une (3/4) to

1 Based on table or The total Entra kiving cost of all months "ic. March April, May & June 8000 +12000 + 8000 + 10000 - $ 38000 The tatal Extra Fiving Cost of all. months 16ooo tauoro + 16 ouro + 20000 $76000 8 The total Extra Cost $38000 + $ 76000 - $114000 of any change in increase of numbe of Entra workers in any of the month and adjusting the Extra worker in next Conseguentive months, will result in total increase in Extra Cost of all the Jour months. So lowest posible Extra Cost is $114000 > 0