Inventory Management and Control Israa Mohamed October 2019 [email protected] EOQ Models for Production Planning • This model is an extension of the finite production planning. • The problem here is to find an optimal procedure for producing n products on a single machine to guarantee that: – Holding and setup cost are minimized. – No stock outs are occurred. • We need to assume that feasibility. to ensure system EOQ Models for Production Planning • It is further assumed that we follow a rotation cycle policy. • We need to find the optimal producgion quantity for each item. • If we used for each item, we might be faced by stock-out in some items. • Sooooo.............................. Cycle Time T EOQ Models for Production Planning • • • • To avoid stock out we know that The average annual cost for this Qj = This cost for all items = Substituting for T giving, • Optimizing the above function (first derivative = 0) will give optimal EOQ Models for Production Planning • We still need to check that T* is above the minimum T. • If setup times are considered, then minimum T must be greater than setup and production times for all items. • Qs for all items are then computed based on the optimal T EOQ Models for Production Planning - Example Bali produces several styles of men’s and women’s shoes at a single facility. The leather for both the uppers and the soles of the shoes is cut on a single machine. This plant is responsible for seven styles and several colors in each style. (The colors are not considered different products for our purposes, because no setup is required when switching colors.) Bali would like to schedule cutting for the shoes using a rotation policy that meets all demand and minimizes setup and holding costs. Setup costs are proportional to setup times. Setup costs are averaged to $110 per hour, holding costs are based on a 22 percent annual interest charge. EOQ Models for Production Planning - Example Setup cost = 3.2 * 110 = 352 h' = 0.22 * 40 * (1- (4520 / 3580) = 7.69 ( 4520 / 35800) + ( 6600 / 62600) + ( 2340 / 41000) + ( 2600 / 71000) +........ = 0.693 EOQ Models for Production Planning - Example 34758.8 33792 25248.6 9906 59752 34844 32188 2 * 2695 0.15 year 38days 230458.4 EOQ Models for Production Planning - Example • We must check if T* is larger than Tmin . • Tmin = 24.5 /(8 * 250) 0.03999 0.04 year 10days = 1 0.69355 • It should be noted that we assumed a 250 working days per year and a day of 8 working hours. • Then T* is the optimal cycle time. • Next step is to find optimal production size for each item and the associated average cost. EOQ Models for Production Planning - Example • We use the following equation for estimating optimal Qs EOQ Models for Production Planning Interesting notes • This policy guarantees minimum cost BUT doesn't guarantee optimal time management. n Q j ( ) • Uptime for the previous example j 1 Pj will be 70% of the time, i.e. the machine will be idel 30% of the time. • Another interesting point is that if the setup costs were sequence dependent, we would change the solution dramatically. • Also, we assumed a rotation cycle which mightnot be suitable in all cases, for example when demand rates and setup costs differ widely, it might be advantageous to do two or more production runs of a product in a cycle.