Question

Case Problem WORKFORCE SCHEDULING Davis Instruments has two manufacturing plants located in Atlanta, Georgia. Product de mand varies considerably from month to month, causing Davis extreme difficulty in work force scheduling. Recently Davis started hiring temporary workers supplied by WorkForce Unlimited, a company that specializes in providing temporary employees for firms in the greater Atlanta area. WorkForce Unlimited has offered to provide temporary employees under three contract options that differ in terms of the length of employment and the cost. The three options are summarized: Option Length of Employment One month Two months Three months ہم نوا Cost $2000 $4800 $7500

This is a Construction Management class, so will you please be able to provide a step wise solution of how you were able to calculate the answer.

Answer 1

Refer the below images for the above asked questions in a detailed way of solution with explanation.

Answer: Requirement : Let tij = no. of temporary comployees hired under option ilin 1,2,3) in mouth iic i for Jan , j = 2 for Feb. Jo on) The following tables depicts the decision variables used in this case problem. costs contract cost plos training cost. 2000 options Contract cast Training cast Toral cost $875 $2875 $4800 $ 845 15675 $7500 1975 $8375 Min. 2675 (tutkia +tiattigt tis+to) + 5675 (tait tar+t23+t24 +225) +8375 (+31+t32+ 133t t34). One Constraint is required for each of the six months & Constraint : need to additional employees in January. employees hired under option i Cone-month contract) tu = number of temporary in January. temporary ta= nomber of in January employees hired under option al two-month contract) + 3 = employees hired under option 3 (three month number of Contract) in temporary January tutto + t = 10.

& constraint 2 : Need 23 additional employees in February employees hived temporary under t 12, too, ki2 are options 42 43 in the no of rebrary But, temporary employees hired under options a cor) oprons 3 in January will also be available to satisfy February needs. in this constraint tait t3, + tiatt azt t 32= 23. The following tables shows the decision variables used options Jan Feb Mar Apr May June uption i option a dar tar Option 3 31 32 x 12 & constraint 3: Need 19 additional employees in March. options Jan Feb Mar Apr May Jone - +13 و با t22 23 tzi +32 +33 tzottas +232 + + 3+ t23 +t33=19 * constraint 4: options Need 26 odditional comployees in May. Jan Feb Mar Apr May Jone +4 tag tay tza tzz t34 - D W t32 + tattzz & ty + tay tt 3 = 26.

& constraint s = Need 20 additional employees in May. options Jan Feb Mar Apr May June tis t24 tas +33 34 .t33+ tay & t34 + tog & tas = 20. & constraint 6 : Need 14 additional employees in Jone. options Jan Feb Mar Apr May June - t16 & tas +34 w t34 + tast ti6 - 14 optimal solotion : Goral cost - $313525 options Jan Feb Mar Apr May June د 7 12 0 لما 14

Requirement : options Number tired Contract cast 10191 cost Training cast у 612 $2625 $28875 بار $ 14000 $14400 $247500 3 $20125 I 17025 $276375 $313525 اليمية Toral : $275900 $37625 Reajuirement : wiring to full time employees at the beginning of January will reduce the no. of temporary employees needed each morth by to using the same tinear programing model with the right hand sides of o, 13, 9, 16, 10 44 provides the following Schedule for temporary employees options Jan 0 Feb 4 Mar 0 Apr 0 May 3 Jone 0 0904 w Contract 101 al cost cost Nomber fired Training cost option S 20125 $ 14000 $ 14400 397.500 I 6125 1 2625 $ 11375 I 17025 $ 108875 $ 146.25

Full time employees cost : Training Cost: 10 (1875) = $ 8750 salary 10 (6) (168) ($16.50) - 1 166320 Total cost : & 146025 + $8750 + $ 166320 = 9321095. a time employees is & 321095 $313525 - 17570 more expensive than oling temporary employees. Do not hir Davis Should continue to employees. Contract with work force to obtain temporary employees. Requirement per with the employee lower for each training option costs, are as the costs follows: (ost Total cost option Training cost 1900 $ 2000 2900 م $ 4800 fb° مهدکو به لي $ 7500 1700 $ 8200 Resolving the original linear programming model with the above cost indicates that Davis Should live all temporary employees on a one-month contract specifically to meet each month's employee needs. Thus, the monthly hire Schedule would be as follows a January 10 February 27 March 19 April 26 May 201 June 14. the total cost of this Strategy is $302.400. at vaining costs were any lower, this would still be the optimal Living Strafts for Davis.